ABSTRACT
Title of dissertation: VEHICLE ROUTING PROBLEMS
THAT MINIMIZE THE COMPLETION TIME:
HEURISTICS, WORST-CASE ANALYSES,
AND COMPUTATIONAL RESULTS
Xingyin Wang
Doctor of Philosophy, 2016
Dissertation directed by: Professor Bruce Golden
Applied Mathematics & Statistics,
and Scientific Computation
Robert H. Smith School of Business
In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles
to deliver the demands of all customers such that the total distance traveled by the
fleet is minimized. In this dissertation, we study variants of the VRP that minimize
the completion time, i.e., we minimize the distance of the longest route. We call it
the min-max objective function. In applications such as disaster relief efforts and
military operations, the objective is often to finish the delivery or the task as soon as
possible, not to plan routes with the minimum total distance. Even in commercial
package delivery nowadays, companies are investing in new technologies to speed up
delivery instead of focusing merely on the min-sum objective.
In this dissertation, we compare the min-max and the standard (min-sum)
objective functions in a worst-case analysis to show that the optimal solution with
respect to one objective function can be very poor with respect to the other. The
results motivate the design of algorithms specifically for the min-max objective. We
study variants of min-max VRPs including one problem from the literature (the
min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery
Multi-Depot VRP with Minimum Service Requirement and the min-max Close-
Enough VRP). We develop heuristics to solve these three problems. We compare
the results produced by our heuristics to the best-known solutions in the literature
and find that our algorithms are effective. In the case where benchmark instances are
not available, we generate instances whose near optimal solutions can be estimated
based on geometry.
We formulate the Vehicle Routing Problem with Drones and carry out a theo-
retical analysis to show the maximum benefit from using drones in addition to trucks
to reduce delivery time. The speed-up ratio depends on the number of drones loaded
onto one truck and the speed of the drone relative to the speed of the truck.
VEHICLE ROUTING PROBLEMS THAT MINIMIZE THE
COMPLETION TIME : HEURISTICS, WORST-CASE
ANALYSES, AND COMPUTATIONAL RESULTS
by
Xingyin Wang
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2016
Advisory Committee:
Professor Bruce Golden, Chair/Advisor
Professor Edward Wasil
Professor Radu Balan
Professor Ilya Ryzhov
Professor Paul Schonfeld
c© Copyright by
Xingyin Wang
2016
Dedication
This dissertation is dedicated to my wife, Yuejia, and my first born son, Jonah.
ii
Acknowledgments
I am indebted to so many people who have helped me with the dissertation. I
do not think these two pages are enough to thank them.
I thank my adviser, Dr. Bruce Golden. He puts the right amount of pressure on
me, not too much so that I will not feel discouraged, and not little so that I will not
waste my time. He has taught me an important principle from the beginning: Make
progress every week. I still remember he told me that even small progress every week
will make a huge difference in two years. He is also a caring adviser. I remember the
first time I received a rejection from a journal. He comforted me, assuring me that
the paper was well-written. He encouraged me to improve the paper by addressing
the reviewers’ comments. We had the paper published in another journal later.
I thank Dr. Edward Wasil, especially for the infinite number of hours he spent
to edit my writings. I am not a native speaker, so he has to improve almost every
sentence I write. I was shocked the first time I saw the paper full of red comments
returned to me. But I really appreciate his help. I leaned from him how to write
with clarity and with style.
I want to thank Dr. Radu Balan, Dr. Ilya Ryzhov, and Dr. Paul Schonfeld
who served on my committee with Dr. Golden and Dr. Wasil. Thanks for the
questions and comments on my dissertation and presentation.
I want to thank my coauthors. Chapter 2 is joint work with Dr. Luca Bertazzi.
He initiated this collaboration and proved the worst-case results for the versions of
infinite vehicle capacity and the multiple TSP. Even though we were communicating
iii
via email, the work was completed in less than three months. I want to thank Rui
Zhang. In Chapter 4, he used his expertise in Integer Linear Programming to prove
that our estimated solutions to a set of tested instances are optimal or near-optimal.
I thank Stefan Poikonen. We have been working together on the drone project. Part
of the project is now in Chapter 5 and we will continue to publish more results. I
want to thank Dr. Carmine Cerrone and Oliver Lum. They are my coauthors for
work not included in the dissertation. I want to thank them here because I learned
lots of coding techniques from these two expert programmers.
I want to thank the senior Ph.D. students in our group Dr. David Anderson
and Dr. Stuart Price. Thanks for giving me a ride to the group meeting when
I did not know how to drive. Thanks for all the advice on the way. I thank the
program coordinators Alverda McCoy and Janet Cavanagh for being so helpful with
the administrative work whenever I needed help.
I do not think I have included all the people who have helped me along the
way. I thank God for his amazing grace to give me the opportunity to study at the
University of Maryland and to meet so many great people.
iv
Table of Contents
List of Tables viii
List of Figures xiii
List of Abbreviations xv
1 Introduction 1
2 Min-Max vs. Min-Sum Vehicle Routing: A Worst-Case Analysis 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Description of problems . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Capacitated VRP with an infinite number of vehicles . . . . . . . . . 12
2.4 Capacitated VRP with a finite number of vehicles . . . . . . . . . . . 16
2.4.1 Worst-case ratios of the min-max and min-sum solutions . . . 17
2.4.2 Relation between min-max, min-sum, and route-optimal rout-
ing plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Multiple TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Service time VRP with a finite number of vehicles . . . . . . . . . . . 30
2.6.1 Impact of service time on min-max and min-sum solutions . . 31
2.6.1.1 Invariant min-sum solution . . . . . . . . . . . . . . 31
2.6.1.2 Impact on min-max solution . . . . . . . . . . . . . . 31
2.6.2 Worst-case ratios with service times . . . . . . . . . . . . . . . 35
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 The Min-Max Multi-Depot Vehicle Routing without service time 41
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 LP-based load balancing . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 MD algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1.1 Step 1: Assignment . . . . . . . . . . . . . . . . . . . 47
3.3.1.2 Step 2: Solving the TSP . . . . . . . . . . . . . . . . 48
3.3.2 Local search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.3 Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
v
3.4 Alternative methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.1 VNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4.1.1 Local Search . . . . . . . . . . . . . . . . . . . . . . 52
3.4.1.2 Neighborhood structure . . . . . . . . . . . . . . . . 53
3.4.1.3 VNS algorithm . . . . . . . . . . . . . . . . . . . . . 55
3.4.2 VRPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.1 Comparing LB, MD, VNS, and VRPH . . . . . . . . . . . . . 57
3.5.2 Detailed comparison of MD and VNS . . . . . . . . . . . . . . 62
3.5.2.1 New data sets . . . . . . . . . . . . . . . . . . . . . . 62
3.5.2.2 Practical data . . . . . . . . . . . . . . . . . . . . . . 65
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4 The Min-Max Multi-Depot Vehicle Routing with service 68
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Structural properties of optimal solutions . . . . . . . . . . . . . . . . 72
4.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.1 Improving MD . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.2 Cluster balance subroutine . . . . . . . . . . . . . . . . . . . . 88
4.4.2.1 Alternative objective functions in the cluster balance
subroutine . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4.3 Local search . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.4 Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4.5 Satisfying the minimum delivery requirement . . . . . . . . . . 101
4.5 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.5.1 Test Set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.5.2 Test Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.5.2.1 Data generation . . . . . . . . . . . . . . . . . . . . 106
4.5.2.2 Estimated solution . . . . . . . . . . . . . . . . . . . 107
4.5.2.3 Mathematical model and exact solutions for Test Set 2109
4.5.2.4 MDS solution . . . . . . . . . . . . . . . . . . . . . . 120
4.5.3 Test Set 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5 The Vehicle Routing Problem with Drones 128
5.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . . 128
5.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.4 Extending our model . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.5 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . 166
vi
6 The Min-Max Close-Enough Vehicle Routing Problem 168
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.2 MMCEVRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.2.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . 171
6.2.2 Steiner zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
6.3.1 Construction procedures . . . . . . . . . . . . . . . . . . . . . 175
6.3.1.1 Customer pruning . . . . . . . . . . . . . . . . . . . 175
6.3.1.2 Steiner zone construction . . . . . . . . . . . . . . . 178
6.3.1.3 Set covering . . . . . . . . . . . . . . . . . . . . . . . 181
6.3.1.4 MMVRP solver . . . . . . . . . . . . . . . . . . . . . 183
6.3.2 Improvement procedures . . . . . . . . . . . . . . . . . . . . . 183
6.3.2.1 Intra-route improvement . . . . . . . . . . . . . . . . 184
6.3.2.2 Inter-route improvement . . . . . . . . . . . . . . . . 185
6.4 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.4.1 CETSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.4.2 MMCEVRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.5 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . 191
7 Conclusions and future work 193
A The MD algorithm illustration 196
A.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
A.2 Local search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
A.2.1 Improvement by perturbation . . . . . . . . . . . . . . . . . . 201
B Min-Max Multi-Depot Vehicle Routing Problem test instances 209
C Min-Max Single-Depot Vehicle Routing Problem test instances 544
D Close-Enough Traveling Salesman Problem test instances 599
Bibliography 759
vii
List of Tables
1.1 Recent Survey Articles in Vehicle Routing . . . . . . . . . . . . . . . 3
2.1 Distance matrix for Example 5 . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Travel time matrix for Example 8 . . . . . . . . . . . . . . . . . . . . 32
2.3 Travel time matrix for Example 9 . . . . . . . . . . . . . . . . . . . . 33
2.4 Travel time matrix for Example 10 . . . . . . . . . . . . . . . . . . . 34
3.1 VNS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Computational results for LB, MD, VNS, and VRPH . . . . . . . . . 58
3.3 Contributions of local search and perturbation in MD . . . . . . . . . 61
3.4 MD vs VNS on uniform customer locations and small customer-to-
vehicle ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5 MD vs VNS on uniform customer locations and large customer-to-
vehicle ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.6 MD vs VNS on non-uniform customer locations and small customer-
to-vehicle ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.7 MD vs VNS on non-uniform customer locations and large customer-
to-vehicle ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.1 Estimated arc cost of the auxiliary graph for cyclic transfer [87] . . . 82
4.2 Algorithm to generate the auxiliary graph for cyclic transfer in the
min-max problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3 One-point move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Two-point move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5 Route destruction and reconstruction . . . . . . . . . . . . . . . . . . 87
4.6 Modified MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.7 Results of MD and MMD on Test Set 1 . . . . . . . . . . . . . . . . . 105
4.8 Average improvement of MMD over MD . . . . . . . . . . . . . . . . 106
4.9 Algorithm to estimate the optimal solution . . . . . . . . . . . . . . . 108
4.10 Estimated solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.11 Two Symmetric Solutions . . . . . . . . . . . . . . . . . . . . . . . . 113
4.12 Results for Test Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.13 MDS solutions vs the estimated solutions . . . . . . . . . . . . . . . . 121
viii
4.14 Savings (in %) from the non-split solutions . . . . . . . . . . . . . . . 123
4.15 Average savings (in %) from splitting with four minimum delivery
fractions and three service times . . . . . . . . . . . . . . . . . . . . . 124
4.16 Average savings (%) from splitting with four minimum delivery frac-
tions and three rctv values . . . . . . . . . . . . . . . . . . . . . . . . 124
4.17 Split distribution (in %) by the number of times a customer receives
service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.18 Split distribution (in %) by the smallest portion a customer receives . 126
5.1 Positions of the depot and the customers in Figure 5.11(a) . . . . . . 162
6.1 Status of the sweep line . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.2 Overview of MMSZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.3 Results produced by MMSZ and seven heuristics on 14 CETSP in-
stances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6.4 Results produced by MMSZ on 14 MMCEVRP instances . . . . . . . 192
A.1 Savings if a customer is removed from route 3 . . . . . . . . . . . . . 198
A.2 Cost of inserting customer 10 onto routes 1 and 2 . . . . . . . . . . . 199
A.3 Savings if a customer is removed from route 2 . . . . . . . . . . . . . 200
A.4 Cost of inserting customer 10 onto route 3 . . . . . . . . . . . . . . . 200
A.5 Cost of inserting customer 7 onto routes 1 and 3 . . . . . . . . . . . . 204
A.6 Depot perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.7 Angles of each perturbation . . . . . . . . . . . . . . . . . . . . . . . 208
B.1 Depot locations and number of vehicles for MS1 . . . . . . . . . . . . 210
B.2 Customer locations and service time for MS1 . . . . . . . . . . . . . . 210
B.3 Depot locations and number of vehicles for MS2 . . . . . . . . . . . . 211
B.4 Customer locations and service time for MS2 . . . . . . . . . . . . . . 211
B.5 Depot locations and number of vehicles for MS3 . . . . . . . . . . . . 217
B.6 Customer locations and service time for MS3 . . . . . . . . . . . . . . 217
B.7 Depot locations and number of vehicles for MS4 . . . . . . . . . . . . 223
B.8 Customer locations and service time for MS4 . . . . . . . . . . . . . . 223
B.9 Depot locations and number of vehicles for MS5 . . . . . . . . . . . . 233
B.10 Customer locations and service time for MS5 . . . . . . . . . . . . . . 233
B.11 Depot locations and number of vehicles for MS6 . . . . . . . . . . . . 243
B.12 Customer locations and service time for MS6 . . . . . . . . . . . . . . 243
B.13 Depot locations and number of vehicles for MS7 . . . . . . . . . . . . 253
B.14 Customer locations and service time for MS7 . . . . . . . . . . . . . . 253
B.15 Depot locations and number of vehicles for MS8 . . . . . . . . . . . . 254
B.16 Customer locations and service time for MS8 . . . . . . . . . . . . . . 254
B.17 Depot locations and number of vehicles for MS9 . . . . . . . . . . . . 260
B.18 Customer locations and service time for MS9 . . . . . . . . . . . . . . 260
B.19 Depot locations and number of vehicles for MS10 . . . . . . . . . . . 270
B.20 Customer locations and service time for MS10 . . . . . . . . . . . . . 270
B.21 Depot locations and number of vehicles for MS11 . . . . . . . . . . . 272
ix
B.22 Customer locations and service time for MS11 . . . . . . . . . . . . . 272
B.23 Depot locations and number of vehicles for MS12 . . . . . . . . . . . 275
B.24 Customer locations and service time for MS12 . . . . . . . . . . . . . 275
B.25 Depot locations and number of vehicles for MS13 . . . . . . . . . . . 278
B.26 Customer locations and service time for MS13 . . . . . . . . . . . . . 278
B.27 Depot locations and number of vehicles for MS14 . . . . . . . . . . . 283
B.28 Customer locations and service time for MS14 . . . . . . . . . . . . . 283
B.29 Depot locations and number of vehicles for MS15 . . . . . . . . . . . 289
B.30 Customer locations and service time for MS15 . . . . . . . . . . . . . 289
B.31 Depot locations and number of vehicles for MS16 . . . . . . . . . . . 295
B.32 Customer locations and service time for MS16 . . . . . . . . . . . . . 295
B.33 Depot locations and number of vehicles for MS17 . . . . . . . . . . . 308
B.34 Customer locations and service time for MS17 . . . . . . . . . . . . . 308
B.35 Depot locations and number of vehicles for MS18 . . . . . . . . . . . 317
B.36 Customer locations and service time for MS18 . . . . . . . . . . . . . 317
B.37 Depot locations and number of vehicles for MS19 . . . . . . . . . . . 327
B.38 Customer locations and service time for MS19 . . . . . . . . . . . . . 327
B.39 Depot locations and number of vehicles for MS20 . . . . . . . . . . . 337
B.40 Customer locations and service time for MS20 . . . . . . . . . . . . . 337
B.41 Depot locations and number of vehicles for MS21 . . . . . . . . . . . 350
B.42 Customer locations and service time for MS21 . . . . . . . . . . . . . 350
B.43 Depot locations and number of vehicles for MS22 . . . . . . . . . . . 357
B.44 Customer locations and service time for MS22 . . . . . . . . . . . . . 357
B.45 Depot locations and number of vehicles for MS23 . . . . . . . . . . . 364
B.46 Customer locations and service time for MS23 . . . . . . . . . . . . . 364
B.47 Depot locations and number of vehicles for MS24 . . . . . . . . . . . 370
B.48 Customer locations and service time for MS24 . . . . . . . . . . . . . 370
B.49 Depot locations and number of vehicles for MS25 . . . . . . . . . . . 381
B.50 Customer locations and service time for MS25 . . . . . . . . . . . . . 381
B.51 Depot locations and number of vehicles for MS26 . . . . . . . . . . . 392
B.52 Customer locations and service time for MS26 . . . . . . . . . . . . . 392
B.53 Depot locations and number of vehicles for MS27 . . . . . . . . . . . 400
B.54 Customer locations and service time for MS27 . . . . . . . . . . . . . 400
B.55 Depot locations and number of vehicles for MS28 . . . . . . . . . . . 407
B.56 Customer locations and service time for MS28 . . . . . . . . . . . . . 407
B.57 Depot locations and number of vehicles for MS29 . . . . . . . . . . . 420
B.58 Customer locations and service time for MS29 . . . . . . . . . . . . . 420
B.59 Depot locations and number of vehicles for MS30 . . . . . . . . . . . 429
B.60 Customer locations and service time for MS30 . . . . . . . . . . . . . 429
B.61 Depot locations and number of vehicles for MS31 . . . . . . . . . . . 440
B.62 Customer locations and service time for MS31 . . . . . . . . . . . . . 440
B.63 Depot locations and number of vehicles for MS32 . . . . . . . . . . . 446
B.64 Customer locations and service time for MS32 . . . . . . . . . . . . . 446
B.65 Depot locations and number of vehicles for MS33 . . . . . . . . . . . 448
B.66 Customer locations and service time for MS33 . . . . . . . . . . . . . 448
x
B.67 Depot locations and number of vehicles for MS34 . . . . . . . . . . . 454
B.68 Customer locations and service time for MS34 . . . . . . . . . . . . . 454
B.69 Depot locations and number of vehicles for MS35 . . . . . . . . . . . 467
B.70 Customer locations and service time for MS35 . . . . . . . . . . . . . 467
B.71 Depot locations and number of vehicles for MS36 . . . . . . . . . . . 471
B.72 Customer locations and service time for MS36 . . . . . . . . . . . . . 471
B.73 Depot locations and number of vehicles for MS37 . . . . . . . . . . . 482
B.74 Customer locations and service time for MS37 . . . . . . . . . . . . . 482
B.75 Depot locations and number of vehicles for MS38 . . . . . . . . . . . 491
B.76 Customer locations and service time for MS38 . . . . . . . . . . . . . 491
B.77 Depot locations and number of vehicles for MS39 . . . . . . . . . . . 497
B.78 Customer locations and service time for MS39 . . . . . . . . . . . . . 497
B.79 Depot locations and number of vehicles for MS40 . . . . . . . . . . . 504
B.80 Customer locations and service time for MS40 . . . . . . . . . . . . . 504
B.81 Depot locations and number of vehicles for MS41 . . . . . . . . . . . 510
B.82 Customer locations and service time for MS41 . . . . . . . . . . . . . 510
B.83 Depot locations and number of vehicles for MS42 . . . . . . . . . . . 523
B.84 Customer locations and service time for MS42 . . . . . . . . . . . . . 523
B.85 Depot locations and number of vehicles for MS43 . . . . . . . . . . . 535
B.86 Customer locations and service time for MS43 . . . . . . . . . . . . . 535
C.2 Min-Max Single-Depot Split-Delivery VRP instance SD1 . . . . . . . 544
C.1 SD instance specifications . . . . . . . . . . . . . . . . . . . . . . . . 545
C.3 Min-Max Single-Depot Split-Delivery VRP instance SD2 . . . . . . . 545
C.4 Min-Max Single-Depot Split-Delivery VRP instance SD3 . . . . . . . 545
C.5 Min-Max Single-Depot Split-Delivery VRP instance SD4 . . . . . . . 546
C.6 Min-Max Single-Depot Split-Delivery VRP instance SD5 . . . . . . . 547
C.7 Min-Max Single-Depot Split-Delivery VRP instance SD6 . . . . . . . 548
C.8 Min-Max Single-Depot Split-Delivery VRP instance SD7 . . . . . . . 549
C.9 Min-Max Single-Depot Split-Delivery VRP instance SD8 . . . . . . . 550
C.10 Min-Max Single-Depot Split-Delivery VRP instance SD9 . . . . . . . 551
C.11 Min-Max Single-Depot Split-Delivery VRP instance SD10 . . . . . . 553
C.12 Min-Max Single-Depot Split-Delivery VRP instance SD11 . . . . . . 554
C.13 Min-Max Single-Depot Split-Delivery VRP instance SD12 . . . . . . 556
C.14 Min-Max Single-Depot Split-Delivery VRP instance SD13 . . . . . . 559
C.15 Min-Max Single-Depot Split-Delivery VRP instance SD14 . . . . . . 561
C.16 Min-Max Single-Depot Split-Delivery VRP instance SD15 . . . . . . 564
C.17 Min-Max Single-Depot Split-Delivery VRP instance SD16 . . . . . . 568
C.18 Min-Max Single-Depot Split-Delivery VRP instance SD17 . . . . . . 572
C.19 Min-Max Single-Depot Split-Delivery VRP instance SD18 . . . . . . 576
C.20 Min-Max Single-Depot Split-Delivery VRP instance SD19 . . . . . . 580
C.21 Min-Max Single-Depot Split-Delivery VRP instance SD20 . . . . . . 584
C.22 Min-Max Single-Depot Split-Delivery VRP instance SD21 . . . . . . 591
D.1 CETSP instance kroD100rdmRad . . . . . . . . . . . . . . . . . . . . 600
xi
D.2 CETSP instance rat195rdmRad . . . . . . . . . . . . . . . . . . . . . 603
D.3 CETSP instance lin318rdmRad . . . . . . . . . . . . . . . . . . . . . 608
D.4 CETSP instance rd400rdmRad . . . . . . . . . . . . . . . . . . . . . 616
D.5 CETSP instance pcb442rdmRad . . . . . . . . . . . . . . . . . . . . . 626
D.6 CETSP instance d493rdmRad . . . . . . . . . . . . . . . . . . . . . . 637
D.7 CETSP instance dsj1000rdmRad . . . . . . . . . . . . . . . . . . . . 650
D.8 CETSP instance team1 100rdmRad . . . . . . . . . . . . . . . . . . . 675
D.9 CETSP instance team 200rdmRad . . . . . . . . . . . . . . . . . . . 678
D.10 CETSP instance team3 300rdmRad . . . . . . . . . . . . . . . . . . . 683
D.11 CETSP instance team4 400rdmRad . . . . . . . . . . . . . . . . . . . 691
D.12 CETSP instance team5 499rdmRad . . . . . . . . . . . . . . . . . . . 701
D.13 CETSP instance team6 500rdmRad . . . . . . . . . . . . . . . . . . . 714
D.14 CETSP instance bonus1000rdmRad . . . . . . . . . . . . . . . . . . . 727
xii
List of Figures
1.1 Number of articles published in JORS, Networks, C&OR, and EJOR
from 1970 to 2013 [93] . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Min-sum vs. min-max optimal solutions in Example 1 . . . . . . . . . 13
2.2 Min-max vs. min-sum optimal solutions in Example 2 . . . . . . . . . 15
2.3 Min-sum vs. min-max optimal solutions in Example 3 . . . . . . . . . 20
2.4 Min-max vs. min-sum optimal solutions in Example 4 . . . . . . . . . 22
2.5 Illustrating the sequence of travel . . . . . . . . . . . . . . . . . . . . 24
2.6 Solutions to Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Min-sum vs. min-max optimal solutions in Example 6 . . . . . . . . . 27
2.8 Min-max vs. min-sum optimal solutions in Example 7 . . . . . . . . . 29
2.9 The impact of service times (Example 8) . . . . . . . . . . . . . . . . 33
2.10 The impact of service times (Example 9) . . . . . . . . . . . . . . . . 34
2.11 The impact of service times (Example 10) . . . . . . . . . . . . . . . 34
2.12 Min-sum vs. min-max optimal solutions in Example 11 . . . . . . . . 36
2.13 Min-max vs. min-sum optimal solutions in Example 12 . . . . . . . . 39
3.1 Comparison of MD, VNS, and VRPH to LB . . . . . . . . . . . . . . 59
3.2 MD running time against average number of customers per route . . 62
4.1 Illustrating Property 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Examples of clusters of routes . . . . . . . . . . . . . . . . . . . . . . 76
4.3 Cyclic transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Auxiliary graphs of the clustomers in Figure 4.2 . . . . . . . . . . . . 91
4.5 Example 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6 Example 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 Intersections of contours of objective functions (4.17), (4.18), and
(4.19) with Π . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.8 Illustration of cluster merge . . . . . . . . . . . . . . . . . . . . . . . 100
4.9 Large minimum delivery fraction causing infeasibility . . . . . . . . . 102
4.10 Example of instances . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.11 Sub-problem of SD10 and its estimated solution . . . . . . . . . . . . 107
xiii
5.1 A VRPD1,1 solution with k = 2 . . . . . . . . . . . . . . . . . . . . . 134
5.2 Decomposition of a VRPD1,1 solution . . . . . . . . . . . . . . . . . . 134
5.3 A feasible TSP solution from the optimal VRPD solution . . . . . . . 135
5.4 A worst-case VRPD1,1 example with k = 2 . . . . . . . . . . . . . . . 136
5.5 A worst-case VRPD1,α example with k = 2 . . . . . . . . . . . . . . . 139
5.6 A worst-case VRP* example with m = 3 . . . . . . . . . . . . . . . . 142
5.7 Adding drone customers to truck route . . . . . . . . . . . . . . . . . 146
5.8 Comparison of the intermidate routes in TSP route construction . . . 147
5.9 Comparison of the TSP solutions constructed in the proofs . . . . . . 148
5.10 A worst-case VRPDm,α example with k = 2 . . . . . . . . . . . . . . 151
5.11 Truck and drone follow different distance metrics . . . . . . . . . . . 162
6.1 An MMCEVRP example with 11 customers and routes for two vehicles172
6.2 Steiner zones of various degrees . . . . . . . . . . . . . . . . . . . . . 174
6.3 Customer pruning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.4 Sweep line algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.5 One pass of the selection process . . . . . . . . . . . . . . . . . . . . 185
A.1 Locations of customers and depots . . . . . . . . . . . . . . . . . . . 198
A.2 Initial solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
A.3 Iteration 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
A.4 A feasible solution to the perturbed problem . . . . . . . . . . . . . . 202
A.5 Solution to the perturbed problem after local search . . . . . . . . . . 205
A.6 A feasible solution to the original problem . . . . . . . . . . . . . . . 206
A.7 The feasible solution generated after one perturbation . . . . . . . . . 207
D.1 Solution to kroD100rdmRad produced by MMSZ . . . . . . . . . . . 752
D.2 Solution to rat195rdmRad produced by MMSZ . . . . . . . . . . . . . 752
D.3 Solution to lin318rdmRad produced by MMSZ . . . . . . . . . . . . . 753
D.4 Solution to rd400rdmRad produced by MMSZ . . . . . . . . . . . . . 753
D.5 Solution to pcb442rdmRad produced by MMSZ . . . . . . . . . . . . 754
D.6 Solution to d493rdmRad produced by MMSZ . . . . . . . . . . . . . 754
D.7 Solution to dsj1000rdmRad produced by MMSZ . . . . . . . . . . . . 755
D.8 Solution to team1 100rdmRad produced by MMSZ . . . . . . . . . . 755
D.9 Solution to team2 200rdmRad produced by MMSZ . . . . . . . . . . 756
D.10 Solution to team3 300rdmRad produced by MMSZ . . . . . . . . . . 756
D.11 Solution to team4 400rdmRad produced by MMSZ . . . . . . . . . . 757
D.12 Solution to team5 499rdmRad produced by MMSZ . . . . . . . . . . 757
D.13 Solution to team6 500rdmRad produced by MMSZ . . . . . . . . . . 758
D.14 Solution to bonus1000rdmRad produced by MMSZ . . . . . . . . . . 758
xiv
List of Abbreviations
BIP Binary Integer Program
BPP Bin Packing Problem
CEVRP Close–Enough Vehicle Routing Problem
CETSP Close–Enough Traveling Salesman Problem
LKH Lin Kernighan Helsgaun
LP Linear Program
MMCEVRP min–max Close–Enough Vehicle Routing Problem
MMMDVRP min–max Multi–Depot Vehicle Routing Problem
MMSDMDVRP–MSR min-max Split-Delivery Multi-Depot Vehicle Routing
Problem with Minimum Service Requirement
RFID Radio Frequency Identification
VRP Vehicle Routing Problem
VRPD Vehicle Routing Problem with Drones
TSP Traveling Salesman Problem
xv
Chapter 1: Introduction
In the standard version of the Vehicle Routing Problem (VRP), a homogeneous
fleet of vehicles makes deliveries to customers. All routes start and end at the depot.
The total demands delivered on one route cannot exceed a vehicle’s capacity. Each
customer must have its demand delivered by one vehicle in one visit. The objective
is to minimize the total distance traveled by the fleet. The VRP is related to two
well-known combinatorial optimization problems: the Traveling Salesman Problem
(TSP) and the Bin Packing Problem (BPP). In the TSP, a salesman is required
to visit a set of cities and return to the starting city, such that each city is visited
exactly once (except the starting city). The total distance traveled is minimized. In
the BPP, we want to pack a set of items of known weights into identical bins, such
that the total weight of items packed into one bin cannot exceed the bin capacity.
The number of bins used is minimized. In the VRP, if the vehicle capacity is at least
the total demand of all customers, the problem reduces to the TSP. If all customers
are at the same location, the VRP reduces to the BPP. Therefore, the VRP has
both a TSP dimension and a BPP dimension.
The VRP was introduced by Dantzig and Ramser [34] as the truck dispatching
problem. The authors modeled the distribution of gasoline from a central depot.
1
Figure 1.1: Number of articles published in JORS, Networks, C&OR, and EJOR
from 1970 to 2013 [93]
Since the publication of the Dantzig and Ramser paper in 1959, many papers have
been published on the VRP and its variants. In Figure 1.1, we show the number
of articles published on the VRP in four journals: Journal of the Operational Re-
search Society (JORS), Networks, Computers & Operations Research (C&OR), and
European Journal of Operational Research (EJOR) from 1970 to 2013 (Figure 1.1
is taken from [93]). These four journals are the primary outlets for publishing work
on the VRP. For recent books on the VRP and its variants, we refer the reader
to Golden et al. [46] and Toth and Vigo [89]. In Table 1.1, we present a list of
references of recent survey articles on VRP. Table 1.1 is taken from [93] with a few
recent articles added.
In this dissertation, we focus on variants of the VRP with the min-max objec-
tive. Instead of minimizing the total distance traveled by all vehicles, we minimize
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3
the duration (distance plus service time, if there is any) of the longest route. The
min-max objective function is more applicable than the classic (min-sum) objective
function when we want to finish delivering all demands as soon as possible or when
the timing of the last delivery is crucial. For example, in disaster relief efforts, it is
vital that all victims receive supplies as soon as possible. In military operations, it
is crucial that we finish surveying targets as soon as we can. In newspaper delivery,
it is important that we deliver papers to all the subscribers early in the morning.
Some problems that do not appear to have a routing component can also be modeled
by the min-max VRP. For example, in computer networks, a server and its clients
can be modeled by the depot and customers. When the connection cost between
a server and a client is high while the connection cost between clients is low, it is
important to minimize the maximum latency between a server and a client [23]. It
can be achieved using the min-max objective function. Furthermore, the min-max
solution tends to have balanced routes. If the longest route is minimized, the vari-
ability in route lengths tends to be small. Therefore, the min-max objective can
also be used to balance the workload among drivers.
Each of the five chapters in this dissertation describes work on variants of the
min-max VRP. We use both theoretical and computational approaches. Compu-
tational approaches use local-search-based heuristics organized in multi-phase al-
gorithms. Every algorithm constructs an initial feasible solution and iteratively
improves on it. Sometimes an exact solver is employed to solve a small subproblem.
Theoretical approaches focus on worst-case analyses. We compare new variants to
standard problems to show how their solutions differ in the worst (or best) cases.
4
In Chapter 2, we compare the optimal solutions of several variants of the min-
sum and min-max VRP from a worst-case point of view. The aim is two-fold. First,
we motivate the design of algorithms for the min-max VRP, because the optimal
solution to the min-sum VRP can be very poor when used to solve the min-max
VRP. Second, we show that the min-max approach should be adopted only when
it is well justified, because the corresponding total distance can be very large with
respect to the one obtained by optimally solving the classical min-sum VRP.
In Chapter 3, we study the min-max VRP with multiple depots proposed by
Carlsson [23]. This problem is called the min-max Multi-Depot Vehicle Routing
Problem (MMMDVRP) and does not have customer service times. We develop a
heuristic (denoted by MD) that has three stages: (1) assign customers to routes
and optimize the routes; (2) improve the solution using local search strategies; (3)
improve the solution by perturbation and local search strategies.
In Chapter 4, we extend the MMMDVRP by incorporating customer service
times. We also consider the possibility of service splits and minimum service re-
quirement. We call this problem the min-max Split-Delivery Multi-Depot Vehicle
Routing Problem with Minimum Service Requirement (MMSDMDVRP-MSTR).
We develop a heuristic (denoted by MDS) that solves the MMSDMDVRP-MSTR in
three stages: (1) initialize a feasible solution without splits; (2) improve the longest
routes by splitting service times; (3) ensure all minimum service time requirements
are satisfied.
In Chapter 5, we introduce the Vehicle Routing Problem with Drones (VRPD).
A fleet of trucks loaded with drones delivers packages to customers. The objective
5
minimizes the maximum duration of the routes (i.e., the completion time). The
VRPD is motivated by package delivery companies including Amazon, DHL, and
Federal Express actively exploring the use of commercial drones. After stating our
simplifying assumptions, we pose several questions in order to study the maximum
savings that can be obtained from using drones. Then we derive some worst-case
results. The worst-case results depend on the number of drones per truck and the
speed of the drone relative to the speed of the truck. We consider several extensions
to the basic model.
In Chapter 6, we introduce the min-max Close-Enough Vehicle Routing Prob-
lem (MMCEVRP), where a vehicle only needs to get close enough to service a
customer. The objective minimizes the distance of the longest route. The problem
is motivated by the development of radio frequency identification (RFID) technol-
ogy. A utility company employee does not have to visit a house to read its meter.
Instead, the employee uses a wireless receiver and drives close to a house to read
its meter. The MMCEVRP has other applications such as surveying ground targets
with a drone. We develop a heuristic that has a four-step construction phase, an
intra-route improvement phase, and an inter-route improvement phase.
In Chapter 7, we provide our concluding remarks and mention directions for
future research.
6
Chapter 2: Min-Max vs. Min-Sum Vehicle Routing: A Worst-Case
Analysis
2.1 Introduction
The Vehicle Routing Problem (VRP) is the problem of determining a set of
routes that visit a set of customers at minimum distance, where each route satisfies
a capacity constraint. This problem is interesting both from the theoretical and the
practical points of view. In fact, finding an optimal solution is really challenging and
this problem is solved daily by companies worldwide. In the last 50 years, numerous
variants have been studied, including the case with one vehicle (Traveling Salesman
Problem - TSP), the case with multiple uncapacitated vehicles (Multiple TSP -
MTSP), and the more traditional case with several capacitated vehicles (Capacitated
VRP - CVRP). The latter case, which was introduced in Dantzig and Ramser in 1959
[34], plays a central role in distribution management. The first exact algorithms for
the CVRP were proposed by Christofides et al. ([26, 27]). The best known exact
algorithms are the ones proposed by Fukasawa et al. ([41]) and Baldacci et al.
([8, 9]). For a recent survey on exact algorithms for the CVRP, we refer the reader
to Baldacci et al. ([10]). Although it is possible to optimally solve instances of
7
the TSP with several thousands of customers, the CVRP remains very difficult to
solve optimally, even if a few hundred customers are considered. Therefore, both
heuristic and metaheuristic algorithms have been proposed for its solution. The
most famous heuristic is the Saving algorithm by Clarke and Wright [28]. The best
known metaheuristics are the Adaptive large neighborhood search by Pisinger and
Ropke [76] and the Hybrid genetic algorithm recently proposed by Vidal et al. [92].
We refer to Toth and Vigo [88, 89] and Golden et al. [46] for two comprehensive
books on the VRP and to Laporte et al. [67] for a recent overview of exact, heuristic,
and metaheuristic approaches.
The classical objective function of the VRP is the minimization of the total
distance traveled by all vehicles (min-sum). In this paper, we also focus on the case
in which the aim is to minimize the longest route (min-max). This new objective
function is important in several situations. For example, in disaster relief efforts
the aim is to serve all victims as soon as possible, in computer networks the aim
is to minimize the maximum latency between a server and a client, in workload
balance the aim is to balance the amount of work among drivers on a given day
or across a time horizon. A limited number of papers is devoted to the min-max
VRP. A tabu search algorithm is proposed in Franc¸a et al. [40] for the Multiple TSP.
Averbakh and Berman [7] study the problem in which two salesmen must visit nodes
on a tree. Applegate et al. [3] develop specialized cutting planes and a distributed
search algorithm to solve the so-called Newspaper routing problem. Carlsson et
al. [23] study the multi-depot case and propose an LP-based balancing approach
and a region partition heuristic. Wang et al. [94, 96] develop two heuristics that
8
are able to significantly improve upon the LP-based balancing approach. Ren [80]
proposes a hybrid genetic algorithm. Campbell et al. [21] propose for the first time
a comparison of the solutions obtained with alternative objective functions. They
define min-max and min-sum in a different way: Min-max aims at minimizing the
arrival time to the latest customer and min-avg (or min-sum) aims at minimizing the
average arrival time or, equivalently, the sum of the arrival times to the customers.
The paper by Huang et al. [58] extends this work by studying how alternative
objectives, based on equity, efficiency, and efficacy metrics, influence the structure
of the routes. The solutions obtained on the basis of the definitions of min-max and
min-sum used in Campbell et al. [21] can be very different from the ones obtained
on the basis of our definition of min-max and min-sum. Consider for example the
simpler TSP case. Our min-sum and min-max objectives are equivalent, while if
the aim is to minimize the latest arrival, the routing can significantly differ. In fact,
Campbell et al. [21] show that the worst-case ratio between the total length of the
route obtained by minimizing the latest arrival and the total length of the route
obtained by minimizing the total length is 3/2.
The length of the longest route in the min-sum VRP is not lower than the
length of the longest route in the min-max VRP, while the total distance in the
min-max VRP is not lower than the total distance in the min-sum VRP. Our aim is
to consider several variants of the VRP. For each of these variants, we aim to answer
the following questions:
1. What is the ratio of the length of the longest route in the min-sum VRP to
9
the length of the longest route in the min-max VRP, in the worst case?
2. What is the ratio of the total distance of the min-max VRP to the total
distance of the min-sum VRP, in the worst case?
The answer to the first question tells us if minimizing the total distance can imply
a significant increase in the length of the longest route. In that case, the design of
heuristic, metaheuristic, and matheuristic algorithms for the min-max VRP is well-
motivated. The answer to the second question tells us if minimizing the longest route
can imply a significant increase in the total distance. In that case, this objective
should be really well-justified to be adopted.
The remainder of the chapter is organized as follows. In Section 2.2, the
variants of the VRP studied in the paper are formally described. In Section 2.3,
the worst-case analysis concerning the Capacitated VRP with an infinite number
of vehicles is shown. Section 2.4 focuses on the Capacitated VRP with a finite
number of vehicles. Section 2.5 concerns the Multiple TSP. Section 2.6 focuses
on the Service time VRP with a finite number of vehicles. Some conclusions are
presented in Section 2.7.
2.2 Description of problems
Let G(V,E) be a complete graph, where V = {0, 1, . . . , n} is the set of vertices
and E is the corresponding set of edges. Vertex 0 corresponds to the depot, while
vertices 1, 2, . . . , n correspond to the customers. Each customer has to be served in
full by one route (i.e., splitting of the demand is not allowed). Let cij be the distance
10
corresponding to the edge (i, j) ∈ E. We consider the following four variants of the
VRP:
1. Capacitated VRP with an infinite number of vehicles: Each customer i =
1, 2, . . . , n has a demand di > 0 not greater than the vehicle capacity C. An
infinite fleet of vehicles is available.
2. Capacitated VRP with a finite number of vehicles: Each customer i = 1, 2, . . . , n
has a demand di > 0 not greater than the vehicle capacity C. At most k ve-
hicles are available.
3. Multiple TSP: The customers just have to be visited (i.e., no demand has to
be satisfied). Each vehicle has infinite capacity. Exactly k routes have to be
determined.
4. Service time VRP with a finite number of vehicles: Distances are replaced by
travel times. Customer demands are given in terms of service times. The du-
ration of any route is the sum of travel time and service times of the customers
visited by the route. At most k vehicles are available and there is no limit on
the total load or duration of a route.
In the min-sum VRP, the problem is to determine a set of routes that minimizes
the total distance (or total time). Instead, in the min-max VRP, the problem is to
determine a set of routes that minimizes the length (or duration) of the longest
route.
11
2.3 Capacitated VRP with an infinite number of vehicles
In the Capacitated VRP with an infinite number of vehicles, each customer
i = 1, 2, . . . , n has a demand di > 0 not greater than the vehicle capacity C. An
infinite fleet of vehicles is available.
Let us denote by r∞MM the length of the longest route in the optimal solution
of the min-max Capacitated VRP with an infinite number of vehicles and by r∞MS
the length of the longest route in the optimal solution of the min-sum Capacitated
VRP with an infinite number of vehicles.
Theorem 1. There exists an instance class with parameter  such that
r∞MS
r∞MM
→ ∞
for → 0.
Proof. Let 0 ≤  < 1 be a real number such that 1

is an integer. Consider the
following instance class with parameter :
Example 1.
• Single depot called node 0.
• Number of customers: n = 1 + 1

(nodes 1, 2, . . . , 1 + 1

).
• Vehicle capacity: C = 1

.
• Demand of customer 1: d1 = 1 .
• Demand of customers i = 2, 3, . . . , n: di = .
• Depot to customer distances: c0i = 1, for i = 1, 2, . . . , n.
12
1
2
3
n− 1
n
0
1 1 1
1− 
1− 
1− 
1− 
1
1
 



(a) Min-sum solution: two routes
1
2
3
n− 1
n
0
1 1 1
11
1
1
11 1
1
 



(b) Min-max solution: n routes
Figure 2.1: Min-sum vs. min-max optimal solutions in Example 1
• Customer to customer distances: cij = 1−  for i, j = 1, 2, . . . , n, i 6= j.
The corresponding optimal solutions are shown in Figures 2.1(a) and 2.1(b).
An optimal solution of the min-sum Capacitated VRP with an infinite num-
ber of vehicles is the following: Serve customer 1 directly and all the remaining
customers 2, 3, . . . , n in the same route. In fact, since d1 = C and splitting of the
demand is not allowed, customer 1 has to be served directly. Moreover, the length
of the route serving customers 2, 3, . . . , n is 1 + (1 − )(1

− 1) + 1 = 1

+ . This
length cannot be reduced by using more routes to serve these customers. In fact,
let 2 ≤ R ≤ 1

(R integer) be the number of routes to serve these customers. The
corresponding length is 2R+ (1− )(1

−R), which is greater than 1

+  for R ≥ 2.
Therefore, the length of the longest route is r∞MS =
1

+ .
An optimal solution of the min-max Capacitated VRP with an infinite number
13
of vehicles is the following: Serve each customer 1, 2, . . . , n directly. In fact, since
customer 1 has to be served directly, a lower bound on the optimal length of the min-
max VRP is given by the length of the route serving customer 1, that is 2. Since the
solution in which each customer 1, 2, . . . , n is served directly has length equal to 2,
this solution is optimal for the min-max Capacitated VRP with an infinite number
of vehicles. Therefore, the length of the longest route is r∞MM = 2.
Hence, in this instance class
r∞MS
r∞MM
=
1

+ 
2
→∞ for → 0.
Let us now denote by z∞MS the total distance in an optimal solution of the min-
sum Capacitated VRP with an infinite number of vehicles and by z∞MM the total
distance in an optimal solution of the min-max Capacitated VRP with an infinite
number of vehicles.
Theorem 2. There exists an instance class with parameter  such that
z∞MM
z∞MS
→ ∞
for → 0.
Proof. Let 0 ≤  < 1 be a real number such that 1

is an integer. Consider the
following instance class with parameter :
Example 2.
• Single depot called node 0.
• Number of customers: n = 1 + 1

(nodes 1, 2, . . . , 1 + 1

).
14
1
2
3
n− 1
n
0
1 1 1
11
1
1
11 1
1
 



(a) Min-max solution: n routes
1
2
3
n− 1
n
0
1 1 1




1
1
 



(b) min-sum solution: two routes
Figure 2.2: Min-max vs. min-sum optimal solutions in Example 2
• Vehicle capacity: C = 1

.
• Demand of customer 1: d1 = 1 .
• Demand of customers i = 2, 3, . . . , n: di = .
• Depot to customer distances: c0i = 1, for i = 1, 2, . . . , n.
• Customer to customer distances: cij = , for i, j = 1, 2, . . . , n, i 6= j.
The corresponding optimal solutions are shown in Figures 2.2(a) and 2.2(b).
An optimal solution of the min-max Capacitated VRP with an infinite number
of vehicles is the following: Serve each customer 1, 2, . . . , n directly. In fact, since
d1 = C and splitting of the demand is not allowed, customer 1 has to be served
directly. Therefore, a lower bound on the optimal length of the min-max Capacitated
VRP with an infinite number of vehicles is given by the length of the route serving
15
customer 1, that is 2. Since the solution in which each customer 1, 2, . . . , n is served
directly has length equal to 2, this solution is optimal for the min-max Capacitated
VRP with an infinite number of vehicles. Therefore, the optimal total distance is
z∞MM = 2n = 2(1 +
1

).
An optimal solution of the min-sum Capacitated VRP with an infinite number
of vehicles is the following: Serve customer 1 directly and all the remaining cus-
tomers 2, 3, . . . , n in the same route. In fact, customer 1 has to be served directly.
Moreover, the length of the route serving customers 2, 3, . . . , n is 1 + (1

− 1) + 1 =
3− . This length cannot be reduced by using more routes to serve these customers.
In fact, even the length of any solution having just two routes to serve these cus-
tomers is at least 4. Therefore, the optimal total distance is z∞MS = 5− .
Hence, in this instance class
z∞MM
z∞MS
=
2(1 + 1

)
5−  →∞ for → 0.
2.4 Capacitated VRP with a finite number of vehicles
In subsection 2.4.1, we develop Theorems 3 and 4 relating to the worst-case
ratios of the min-sum and min-max solutions. In subsection 2.4.2, we define route-
optimal routing plans and extend Theorems 3 and 4. (We point out that route-
optimal routing plans are used in proving Theorem 11.) We discover that the bounds
apply not only to the ratios between the min-max and the min-sum solutions, but
16
also to ratios between any route-optimal solution and the min-max or the min-sum
solutions.
2.4.1 Worst-case ratios of the min-max and min-sum solutions
In the Capacitated VRP with a finite number of vehicles, each customer i =
1, 2, . . . , n has a demand di > 0 not greater than the vehicle capacity C. At most k
vehicles are available.
Let us denote by rkMM the length of the longest route in the min-max VRP
solution, rkMS the length of the longest route in the min-sum VRP solution, z
k
MM
the total distance of the min-max VRP solution, and zkMS the total distance of the
min-sum VRP solution.
In this section, we want to extend what we know about r∞MM vs. r
∞
MS and
z∞MM vs. z
∞
MS beyond Theorems 1 and 2, when we add the constraint that there are
at most k vehicles available.
Theorem 3.
rkMS
rkMM
≤ k and the bound is tight.
Proof. rkMS ≤ zkMS ≤ zkMM ≤ krkMM . A worst-case example is displayed in Example
3. Note that Theorem 3 reduces to Theorem 1 as k → ∞. Consider the following
instance class with parameter :
Example 3.
• Single depot called node 0.
• 2k customers:
17
– k inner loop customers (nodes 1 to k)
– k outer loop customers (nodes k + 1 to 2k).
• Vehicle capacity: C.
• Customer demand: di = C2k (i = 1, . . . , 2k).
• Depot to customer distances:
– inner loop: c0i =  1 (i = 1, . . . , k)
– outer loop: c0,k+i = 1 +  (i = 1, . . . , k).
• Customer to customer distances:
– between inner customers: cij =  (i, j = 1, . . . , k, i 6= j)
– between outer customers: ck+i,k+j = 2 +  (i, j = 1, . . . , k, i 6= j)
– between inner and outer customers:
ci,k+j =

1 if i = j
1 +  if i 6= j.
The optimal solutions of the min-sum and the min-max VRP are shown in
Figures 2.3(a) and 2.3(b). The min-sum solution has a single route, serving the
inner and outer customers alternatingly in a sequence {1, k + 1, 2, k + 2, . . . , k, 2k}.
The min-sum solution has objective rkMS = 2k + (k + 1). The solution cannot be
improved by using more routes. In fact, all the outer customers must be served on
the same route. Suppose the customers are served on R routes with 2 ≤ R ≤ k
18
(R integer). The length of these R routes is at least 2R(1 + ) + (2 + )(k − R) =
2k+(k+R) > 2k+(k+1). If all the outer customers are served on a single route,
this route has length at least 2k + (k + 1). Hence, a lower bound on the min-sum
solution is 2k+ (k+ 1) and the solution in Figure 2.3(a) is optimal with respect to
the min-sum objective.
The min-max solution has k routes. The ith route (i ∈ {1, 2, . . . , k}) serves the
inner customer i and the outer customer i+ k. The min-max solution has objective
rkMM = 2 + 2. In fact, in any feasible solution, the route serving at least one outer
customer has length no less than 2 + 2. Therefore, a lower bound on the optimal
length of the min-max solution is 2 + 2. Hence, the solution in Figure 2.3(b) is
optimal with respect to the min-max objective. Since rkMS = 2k + (k + 1) and
rkMM = 2 + 2, we have the relationship r
k
MS = kr
k
MM − (k − 1). Hence, in this
instance class
rkMS
rkMM
=
krkMM − (k − 1)
rkMM
→ k for → 0.
Theorem 4.
zkMM
zkMS
≤ k and the bound is tight.
Proof. zkMM ≤ krkMM ≤ krkMS ≤ kzkMS. A worst-case example is displayed in Ex-
ample 4. Note that Theorem 4 reduces to Theorem 2 as k → ∞. Consider the
following instance class with parameter :
Example 4.
• Single depot called node 0.
19
12
k
k + 1
k + 2
2k
0





1
1
1
(a) Min-sum solution: single route
1
2
k
k + 1
k + 2
2k
0
 

1
1
1
(b) Min-max solution: k routes
Figure 2.3: Min-sum vs. min-max optimal solutions in Example 3
20
• k customers (nodes 1 to k).
• Vehicle capacity: C.
• Customer demand: di = Ck (i = 1, . . . , k).
• Depot to customer distances: c0i = 1 (i = 1, . . . , k).
• Customer to customer distances cij =  1 (i, j = 1, . . . , k, i 6= j).
The optimal solutions of the min-max and the min-sum VRPs are shown in
Figures 2.4(a) and 2.4(b). The min-max solution has objective zkMM = 2k and the
min-sum solution has objective zkMS = 2 + (k − 1). The solution in Figure 2.4(a)
is optimal with respect to the min-max objective because any route serving at least
one customer will have length at least 2. The solution in Figure 2.4(b) is optimal
with respect to the min-sum objective because a solution with R routes, where
2 ≤ R ≤ k (R integer), has length not less than 2R + (k − R). For sufficiently
small , this value is greater than 2 + (k − 1). Therefore, we have the relationship
zkMM = kz
k
MS − k(k − 1). Hence, in this instance class
zkMM
zkMS
=
kzkMS − k(k − 1)
zkMS
→ k for → 0.
21
1
2
3
k − 1
k
0
1 1 1
11
1
1
11 1
(a) Min-max solution: k
routes
1
2
3
k − 1
k
0
1





1
(b) Min-sum solution: single
route
Figure 2.4: Min-max vs. min-sum optimal solutions in Example 4
2.4.2 Relation between min-max, min-sum, and route-optimal rout-
ing plans
A route-optimal routing plan is one in which every individual route in the
plan is optimized in terms of total distance. Therefore, what differentiates two
route-optimal routing plans is only the assignment of customers to the routes. The
min-sum solution is obviously route-optimal. A min-max solution may not be route-
optimal because, if we focus on only the maximal route, the other routes do not need
to be optimal. However, among these min-max solutions, there is at least one route-
optimal solution. We consider route-optimal min-max solutions in this paper.
Let us denote with rkMM the length of the longest route in the min-max so-
22
lution, rkMS the length of the longest route in the min-sum solution, r
k
R the length
of the longest route in any route-optimal solution, zkMM the total distance of the
min-max solution, zkMS the total distance of the min-sum solution, and z
k
R the total
distance of any route-optimal solution.
Theorem 5. Assume the triangle inequality is valid, then
rkR
rkMM
≤ k and the bound
is tight.
Proof. Given a min-max solution with at most k routes, we traverse every route in
a sequence. For example, as illustrated in Figure 2.5, the min-max solution has two
routes. Suppose route one is 0 − 1 − 2 − 0 and route two is 0 − 3 − 4 − 0. The
sequence is therefore 0 − 1 − 2 − 0 − 3 − 4 − 0. The length of travel is L = zkMM .
Then rkR ≤ L = zkMM ≤ krkMM . The first inequality is valid because the maximal
route of a route-optimal solution serves only a subset of the customers served by the
giant route. By route-optimality and the triangle inequality, rkR ≤ L. The bound is
tight (see Example 3), since a min-sum solution is a route-optimal solution.
Remark 1. If rkR is replaced by r
k
MS, Theorem 5 reduces to Theorem 3.
Theorem 6. Assume the triangle inequality is valid, then
zkR
zkMS
≤ k and the bound
is tight.
Proof. Given a min-sum solution with at most k routes, we traverse every route
in a sequence in the same manner as in the proof of Theorem 5. The length of
travel is L = zkMS. The length of each route ρ in a route-optimal solution r
(k,ρ)
R ≤
L = zkMS because every route serves only a subset of the customers served by the
23
12
3
4
0
1st
6th3rd
4th
2nd 5th
Figure 2.5: Illustrating the sequence of travel
giant route. By route-optimality and the triangle inequality, the above inequality
holds. Therefore, zkR =
∑k′
ρ=1 r
(k,ρ)
R ≤ kL = kzkMS, where k′ ≤ k indicates the actual
number of routes in a solution. The bound is tight because the min-max solution in
Example 4 is a route-optimal solution. So, we can use Example 4 as our worst-case
example.
Remark 2. If zkR is replaced by z
k
MM , Theorem 6 reduces to Theorem 4.
Remark 3. The distances must satisfy the triangle inequality, otherwise the bounds
in Theorems 5 and 6 may not hold. In fact, these ratios can be arbitrarily large, as
shown in Example 5.
Example 5. There are four customers and at most two vehicles. We assume that
the capacity of each vehicle is greater than the sum of demands of all the customers.
The distance matrix is presented in Table 2.1. Observe that the triangle inequality
is violated if M > 2. The solution displayed in Figure 2.6(a) is optimal with respect
to both the min-max and the min-sum objectives. Therefore, r2MM = 3 and z
2
MS = 6.
The solution shown in Figure 2.6(b) is route-optimal and r2R = 2 + M and z
2
R =
24
Nodes 0 1 2 3 4
0 - 1 1 1 1
1 1 - M 2 1
2 1 M - 1 2
3 1 2 1 - M
4 1 1 2 M -
Table 2.1: Distance matrix for Example 5
1 2
34
01 1
1
1
1
1
M
M
(a) Min-max and min-sum solution
1 2
34
01 1
1
1
1
1
M
M
(b) A route-optimal solution
Figure 2.6: Solutions to Example 5
4 + 2M . The ratio
r2R
r2MM
=
z2R
z2MS
= 2+M
3
can be made arbitrarily large for sufficiently
big M .
2.5 Multiple TSP
In the Multiple TSP, the customers just have to be visited (i.e., no demand
has to be satisfied), the capacity of each vehicle is infinite, and exactly k ≥ 2 routes
have to be determined.
Let us denote by rMMM the length of the longest route in the optimal solution
of the min-max Multiple TSP, rMMS the length of the longest route in the min-
sum Multiple TSP, zMMM the total distance in the optimal solution of the min-max
25
Multiple TSP, and zMMS the total distance in the optimal solution of the min-sum
Multiple TSP.
Theorem 7.
rMMS
rMMM
≤ k and the bound is tight.
Proof. rMMS ≤ zMMS ≤ zMMM ≤ krMMM . From Example 6, we see that the bound is
tight. Consider the following instance class with parameter :
Example 6.
• Number of routes: k ≥ 2.
• Single depot called node 0.
• Number of customers: 2k − 1 (nodes 1, 2, . . . , 2k − 1).
• Depot to customer distances: c0i = 1 for customers i = 1, 2, . . . , k, while
c0i = 
2 for customers i = k + 1, k + 2, . . . , 2k − 1, where  < 1
2(k−1) .
• Customer to customer distances: cij = 2−  for i, j = 1, 2, . . . , k, i 6= j, while
ci,k+i = 1 − 2 for i = 1, 2, . . . , k − 1. The remaining distances satisfy the
triangle inequality.
The corresponding optimal solutions are displayed in Figures 2.7(a) and 2.7(b).
An optimal solution of the min-sum Multiple TSP is as follows: Serve cus-
tomers i = 1, 2, . . . , k in the same route and serve customers i = k+1, k+2, . . . , 2k−1
directly. The total distance of this solution is 2 + (2− )(k − 1) + 22(k − 1). This
solution is optimal. In fact, since the triangle inequality holds, any solution in
which the customers i = 1, 2, . . . , k are not served in the same route has a length
26
12
3
k − 1
k
k + 1
k + 2
k + 3
2k − 1
0
2 2
2
2
1
1
2− 
2− 
2− 
2− 
2− 
(a) Min-sum solution: k routes
1
2
3
k − 1
k
k + 1
k + 2
k + 3
2k − 1
0
2 2
2
2
1
1− 2
1− 2
1− 2
1− 2
(b) Min-max solution: k routes
Figure 2.7: Min-sum vs. min-max optimal solutions in Example 6
27
at least equal to 2R + (2 − )(k − R), where 2 ≤ R ≤ k (R integer) is the number
of routes built to serve these customers. Since  < 1
2(k−1) , 2R + (2 − )(k − R) >
2 + (2 − )(k − 1) + 22(k − 1). Therefore, in any optimal solution, customers
i = 1, 2, . . . , k are served in the same route. Moreover, since k routes have to be
built, customers i = k + 1, k + 2, . . . , 2k − 1 have to be served directly. Therefore,
the length of the longest route is rMMS = 2 + (2− )(k − 1) = 2k − (k − 1).
An optimal solution of the min-max Multiple TSP is as follows: Serve cus-
tomers i and k + i in the same route, for i = 1, 2, . . . , k − 1, and serve customer k
directly. The length of the corresponding longest route rMMM is 2. This solution is
optimal because any route serving one of the customers i = 1, 2, . . . , k has a length
at least equal to 2.
Hence, in this instance class
rMMS
rMMM
=
2k − (k − 1)
2
→ k for → 0.
Theorem 8.
zMMM
zMMS
≤ k and the bound is tight.
Proof. zMMM ≤ krMMM ≤ krMMS ≤ kzMMS. From Example 7, we see that the bound is
tight. Consider the following instance class with parameter :
Example 7.
• Number of routes: k ≥ 2.
• Single depot called node 0.
28
12
3
k − 1
k
k + 1
k + 2
k + 3
2k − 1
0
 


1
1− 
1− 
1− 
1− 
(a) Min-max solution: k routes
1
2
3
k − 1
k
k + 1
k + 2
k + 3
2k − 1
0
 


1
1





(b) min-sum solution: k routes
Figure 2.8: Min-max vs. min-sum optimal solutions in Example 7
• Number of customers: 2k − 1 (nodes 1, 2, . . . , 2k − 1).
• Depot to customer distances: c0i = 1 for customers i = 1, 2, . . . , k, while
c0i =  for customers i = k + 1, k + 2, . . . , 2k − 1, where  < 23(k−1) .
• Customer to customer distances: cij =  for i, j = 1, 2, . . . , k, i 6= j, while
ci,k+i = 1 −  for i = 1, 2, . . . , k − 1. The remaining distances satisfy the
triangle inequality.
The corresponding optimal solutions are shown in Figures 2.8(a) and 2.8(b).
An optimal solution of the min-max Multiple TSP is as follows: Serve cus-
tomers i and k + i in the same route, for i = 1, 2, . . . , k − 1, and serve customer k
29
directly. The length of the corresponding longest route is 2. This solution is optimal
because any route serving one of the customers i = 1, 2, . . . , k has a length at least
equal to 2. Therefore, zMMM = 2k.
An optimal solution of the min-sum Multiple TSP is as follows: Serve cus-
tomers i = 1, 2, . . . , k in the same route and serve customers i = k+1, k+2, . . . , 2k−1
directly. The total distance of this solution is 2 + 3(k − 1) < 4, as  < 2
3(k−1) . This
solution is optimal. In fact, any solution in which the customers i = 1, 2, . . . , k are
not served in the same route has a total distance at least equal to 4, as at least two
routes are needed to serve these customers and the length of each of these routes is
at least equal to 2. Therefore, in any optimal solution, these customers are served
in the same route. Moreover, since k routes are needed to have a feasible solution,
customers i = k + 1, k + 2, . . . , 2k − 1 have to be served directly.
Hence, in this instance class
zMMM
zMMS
=
2k
2 + 3(k − 1) → k for → 0.
2.6 Service time VRP with a finite number of vehicles
In this section, we introduce a variant of the VRP in which the customer
demands are given in terms of service times. Therefore, the demands contribute
directly to route duration. We replace distances with travel times, so the total
duration of a route is the sum of travel time and service times of the customers
30
visited by the route. We assume there are at most k routes and no limit on the
duration of a route. Additional notation is introduced in Section 2.6.1. The goal is
to compare the quality of the min-max and the min-sum solutions.
This section is organized as follows. In subsection 2.6.1, we discuss how and
to what extent the routing of the Min-sum and min-max solutions will change with
the addition of customer service times. In subsection 2.6.2, we explore whether the
bounds for the ratios in Theorems 3 and 4 are still valid or tight when we include
service times.
2.6.1 Impact of service time on min-max and min-sum solutions
Here, we provide some additional notation. Let T be the total service time
of all the customers, zSMM be the total duration of the min-max solution including
travel and service times, and zSMS be the total duration of the min-sum solution
including travel and service times.
2.6.1.1 Invariant min-sum solution
Theorem 9. Since no maximum route-duration constraint is assumed, the routing
of the min-sum solution is unaffected by service times. Therefore, zSMS = z
k
MS + T .
2.6.1.2 Impact on min-max solution
The routing of the min-max solution may, however, be affected by customer
service times. We present three examples next. In Figure 2.9, we see that the
31
Nodes 0 1 2 3 4
0 - 1 1 1 1
1 1 - 2 2 1
2 1 2 - 1 2
3 1 2 1 - 2
4 1 1 2 2 -
Table 2.2: Travel time matrix for Example 8
min-max routing plan may change by adding different service times for customers.
In Figure 2.10, we see that even with uniform service times, the min-max solution
can change. In Figure 2.11, we see that even when the original solution is perfectly
balanced (same number of customers and same travel time on every route), the
solution may still change with the addition of uniform service times. Therefore we
have zSMM 6= zkMM + T in general.
Example 8. There are four customers and two routes. The travel time matrix is
presented in Table 2.2. Assume a service time of 1 unit for customers 1 and 4 and
service time of 3 units for customers 2 and 3. The min-max solutions without and
with service times are displayed in Figures 2.9(a) and 2.9(b). The travel times are
labeled next to edges and the service times are labeled next to nodes. If the routing
plan in Figure 2.9(a) were used in the problem with service times, the min-max value
would be 9. The min-max value of the routing plan in Figure 2.9(b) is 8.
Example 9. There are four customers and two routes. The travel time matrix
is presented in Table 2.3. Assume a uniform service time of 10 units. The min-
max solutions without and with service times are displayed in Figures 2.10(a) and
2.10(b). If the routing plan in Figure 2.10(a) were used in the problem with service
32
1 2
34
01 1
1
1
1
1
2
2
0 0
0 0
(a) Min-max solution without service times
1 2
34
01 1
1
1
1
1
2
2
1 3
1 3
(b) Min-max solution with service times
Figure 2.9: The impact of service times (Example 8)
Nodes 0 1 2 3 4
0 - 2 1 1 1
1 2 - 3 3 3
2 1 3 - 1 2
3 1 3 1 - 1
4 1 3 2 1 -
Table 2.3: Travel time matrix for Example 9
times, the min-max value would be 34. The min-max value of the routing plan in
Figure 2.10(b) is 26.
Example 10. There are six customers and two routes. The travel time matrix
is presented in Table 2.4. Assume a uniform service time of 10 units. The min-
max solutions without and with service times are displayed in Figures 2.11(a) and
2.11(b). If the routing plan in Figure 2.11(a) were used in the problem with service
times, the min-max value would be 53. The min-max value of the routing plan in
Figure 2.11(b) is 45.
33
12
3
4
0
3
1
2
2
1
1
1
3
1
2
0
0
0
0
(a) Min-max solution without service times
1
2
3
4
0
3
1
2
1
1
1
3
1
2
10
10
10
10
(b) Min-max solution with service times
Figure 2.10: The impact of service times (Example 9)
Nodes 0 1 2 3 4 5 6
0 - 10 10 1 1 1 1
1 10 - 5 11 11 11 11
2 10 5 - 11 11 11 11
3 1 11 11 - 1 2 2
4 1 11 11 1 - 1 2
5 1 11 11 2 1 - 1
6 1 11 11 2 2 1 -
Table 2.4: Travel time matrix for Example 10
1
2
3
4
5
6
0
10 1
10
1
1
5
1
11
11
1
1
1
11
11
0
0
0
0
0
0
(a) Min-max solution without service times
1
2
3
4
5
6
0
10
1
10
1
1
5
1
11
11
1
1
1
11
11
10
10
10
10
10
10
(b) Min-max solution with service times
Figure 2.11: The impact of service times (Example 10)
34
2.6.2 Worst-case ratios with service times
In this subsection, we extend Theorems 3 and 4 to include nontrivial service
times. Let rSMS be the duration of the longest route in the min-sum solution, r
S
MM
be the duration of the longest route in the min-max solution, including travel and
service times.
Theorem 10. When we consider service times,
rSMS
rSMM
≤ k and the bound is tight.
Proof. The inequality can be proved in the same way as with Theorem 3. To show
that the bound is tight, we modify Example 3, which was used to prove Theorem
3, by considering a uniform service time of t units for each customer (see Example
11).
Example 11. The solution in Figure 2.12(a) is optimal with respect to the min-sum
objective by Theorem 6, so rSMS = 2k+2kt+(k+1). We now show that the solution
in Figure 2.12(b) is optimal with respect to the min-max objective. The duration of
the maximal route is the sum of three parts, the travel time and the service times of
inner and outer customers.
• Service of the outer customers:
The solution in Figure 2.12(b) is feasible which gives the objective function
value an upper bound of 2 + 2t + 2. Therefore, every route in the optimal
solution could serve at most one outer customer. If a route serves two or
more outer customers, the duration of that route is at least 4 + 2t+ 3. Since
there are k routes and k outer customers, each route serves exactly one outer
35
12
k
k + 1
k + 2
2k
0





1
1
1
t
t
t
t
t
t
(a) Min-sum solution: single route
1
2
k
k + 1
k + 2
2k
0
 

1
1
1
t
t
t
t
t
t
(b) Min-max solution: k routes
Figure 2.12: Min-sum vs. min-max optimal solutions in Example 11
36
customer. The service time contribution is exactly t for this one customer.
• Travel time:
Given that a route serves one outer customer, its travel time is at least 2 + 2.
• If any route serves two or more inner customers, its duration is at least 2 +
3t+ 3 and the solution is worse than the one in Figure 2.12(b), so all routes
serve exactly one inner customer in the optimal solution. The service time
contribution from each inner customer is t.
Summing the three parts, a lower bound on the min-max objective function value
is 2 + 2t + 2 and it is achieved by the solution in Figure 2.12(b). Hence, rSMM =
2 + 2t+ 2 and rSMS = kr
S
MM − (k − 1).
Therefore, in this instance class
rSMS
rSMM
=
krSMM − (k − 1)
rSMM
→ k for → 0.
Theorem 11. Assume the triangle inequality is valid, then zSMM ≤ kzSMS−(k−1)T ,
and the bound is tight.
37
Proof.
zSMM = z
k
R + T (2.1)
≤ kzkMS + T (2.2)
= k
(
zSMS − T
)
+ T (2.3)
= kzSMS − (k − 1)T. (2.4)
In equation (2.1), the total duration of the min-max solution is the sum of service
times and travel time. We assume that the min-max solution is route-optimal (if
not, we can apply to each individual route an exact algorithm to optimally solve
the corresponding TSP), which allows us to apply Theorem 6, which states that
zkR ≤ kzkMS, to obtain equation (2.2). From Theorem 9, we have zSMS = zkMS + T ,
which yields equation (2.3).
To show that the bound is tight, we modify Example 4, which was used to
prove Theorem 4, by considering a uniform service time of t = T
k
units for each
customer (see Example 12).
Example 12. The optimal solutions of the min-max and the min-sum VRPs are
shown in Figures 2.13(a) and 2.13(b). The min-max solution has objective zSMM =
2k + T and the min-sum solution has objective zSMS = 2 + (k − 1) + T . The
solution in Figure 2.13(a) is optimal with respect to the min-max objective because
any route serving at least one customer will have duration at least 2 + t. The min-
sum solution in Figure 2.13(b) has the same configuration as that in Figure 2.4(b)
38
1
2
3
k − 1
k
0
1 1 1
11
1
1
11 1
t
t
t
t
t
(a) Min-max solution: k routes
1
2
3
k − 1
k
0
1





1
t
t
t
t
t
(b) Min-Sum solution: single
route
Figure 2.13: Min-max vs. min-sum optimal solutions in Example 12
because the min-sum solution is independent of service time (Theorem 9). Therefore,
zSMM = 2k+T = k(2+(k−1)+T )−k(k−1)−(k−1)T = kzSMS−k(k−1)−(k−1)T .
Hence, in this instance class
zSMM → kzSMS − (k − 1)T for → 0.
Remark 4. Although the RHS of the inequality in Theorem 11 is written as a
difference, it is never negative because zSMS ≥ T . In fact the RHS is at least equal
to T .
Remark 5. When T = 0 or k = 1 and the triangle inequality is valid, Theorem 11
39
reduces to Theorem 4.
2.7 Conclusion
In this paper, the optimal solutions of several variants of min-max and min-sum
VRPs are compared from the worst-case point of view. The carried out theoretical
analysis allows us to draw the following two key conclusions. The first is that
the length of the longest route in the min-sum VRP problems is at most k times,
where k is the number of available vehicles, the length of the longest route in the
min-max VRP. Therefore, when k tends to infinity, the ratio of these two lengths
tends to infinity. This motivates the need to design heuristic, metaheuristic, and
matheuristic algorithms for the min-max VRP. The second conclusion concerns the
comparison of the total distance of the min-max VRP with the total distance of the
min-sum VRP. The worst-case analysis shows that the former total distance is at
most k times, where k is the number of available vehicles, the latter total distance.
Therefore, when k tends to infinity, the ratio of these two total distances tends to
infinity. This implies that the aim of minimizing the longest route should be really
well-justified before deciding to adopt a min-max approach. Future research can
be devoted to study variants of the problems analyzed in this paper, e.g., the case
with asymmetric distances, the case with a limit on the total length of a route, and
the case with split delivery. Moreover, the exploration of the efficient frontier of the
multi-objective VRP, with both min-sum and min-max objectives, is a promising
research avenue.
40
Chapter 3: The Min-Max Multi-Depot Vehicle Routing without ser-
vice time
3.1 Introduction
In the classic vehicle routing problem (VRP) proposed by Dantzig and Ramser
[34], a fleet of vehicles needs to be routed to meet the demands of customers. Each
vehicle starts and ends at the same depot. Each tour must not exceed a maximum
length. The total demand of customers on a route must not exceed a vehicle’s
capacity. Each customer is visited exactly once, so that all demand is satisfied at
one time by one vehicle. The objective is to minimize the total distance traveled by
the fleet.
In the multi-depot vehicle routing problem (MDVRP), there are several de-
pots. A vehicle must start and end at the same depot. The objective is to minimize
the total distance traveled by all vehicles across the depots. The MDVRP has
been studied in the literature with a variety of assumptions. For example, Chen,
Golden, and Wasil [25] solved the VRP with split deliveries by applying an inte-
ger programming-based heuristic to iteratively improve the solutions. Gulczynski,
Golden, and Wasil [50] solved the MDVRP with a similar integer programming-based
41
method but improved the solution by relocating strings of consecutive customers on
the routes.
The min-max multi-depot vehicle routing problem (Min-max MDVRP) is a
new variant that was recently proposed by Carlsson et al. [23]. Their objective
was to minimize the distance of the longest tour. According to the authors, there
are a variety of applications for the min-max MDVRP. For example, in computer
networks, the depots and customers represent servers and clients, respectively. The
objective is to minimize the maximum latency between a server and a client. This
formulation is useful when the connection cost between a server and a client is high
while the cost between clients is low. Other relevant applications include newspa-
per distribution and humanitarian logistics. In both cases, it is desirable that all
customers be served as soon as possible. Furthermore, a solution to the min-max
problem tends to be balanced, which means the route lengths are similar. From
this observation, the formulation can also be applied to balance the amount of work
among drivers. If each route represents trips on different working days, the min-max
approach balances the workload on each working day.
There are two papers that develop procedures for the min-max MDVRP. Carls-
son et al. [23] proposed four procedures and found that an LP-based heuristic with
load balancing and a region partition heuristic with local improvement performed
the best. In the LP-based heuristic, customers are assigned to vehicles by solving
a linear program. A solver for the traveling salesman problem (TSP) is applied to
generate a route from the depot where a vehicle is stationed over the customers
assigned to the vehicle. In the region partition heuristic, the entire region is di-
42
vided into equal convex polygons with exactly one vehicle in each polygon. A TSP
solver is applied to the customers in the same region. On 13 test instances with
uniform customer locations, both heuristics produced nearly the same number of
best solutions. Narasimha et al. [73] developed an ant colony optimization tech-
nique and, in limited computational experiments, tested it on three instances with
uniform customer locations. The results were better than the LP-based heuristic
with load balancing. They also demonstrated the consistency of the performance in
two simulation studies on a 5-depot, 16-vehicle, 140-customer scenario with uniform
customer locations.
We point out that two papers consider the min-max routing problem with a
single depot. Ren [80] suggested a hybrid genetic algorithm with mountain climbing
and simulated annealing in addition to crossover and mutation operators. The
algorithm was applied to an instance with 20 customers. Yakici and Karasakal [99]
studied a variant in which vehicles did not have to return to the depot. The fleet
was heterogeneous and split deliveries were allowed.
In this chapter, we develop a heuristic (denoted by MD) that has three stages:
(1) simplify the multi-depot problem into a single depot problem and solve the sim-
plified problem; (2) improve the maximal route; (3) improve all routes by exchanging
customers between routes. MD adapts the load balancing idea of Carlsson et al. [23]
to generate an initial solution and continues with local search and a scheme that
perturbs the current solution to break away from a local optimum. The local search
and improvement procedures of MD are much different from the LP-based heuristic
which concentrates on load balancing at the global level and the ant colony method
43
which uses parameters (heuristic desirability, pheromone updating rule, and proba-
bilistic transition rule) to mimic real ants searching for food.
The remainder of the chapter is organized as follows. In Section 3.2, we present
the LP-based, load balancing algorithm from Carlsson et al. [23]. In Section 3.3, we
develop our first algorithm, denoted by MD, which incorporates the load balancing
idea to initialize a solution followed by local improvements and perturbation proce-
dures. In Section 3.4, we discuss two alternative heuristic approaches. In Section
3.5, we compare the results from the four methods on a set of test problems. Finally,
we give brief concluding remarks in Section 3.6.
3.2 LP-based load balancing
Carlsson et al. [23] are the first to discuss the min-max MDVRP. The au-
thors implemented several heuristic methods to solve this problem. Their linear
programming-based load balancing method (LB) is among the best performers. LB
is based on the idea that, in an optimal plan, the loads of all vehicles must be nearly
balanced, that is, all vehicles travel about the same distance. Therefore, in a model
with uniformly distributed customer locations, the number of customers visited by
each vehicle is nearly equal. A MATLAB implementation of LB is available online
([100]).
Next, an overview of the solution procedure developed by Carlsson et al. [23]
is presented. The assumptions used by the authors are then relaxed and the new
implementation details are described. Given a set of m depots, indexed by j, each
44
with one vehicle of unlimited capacity, and a set of n customers (n divisible by m),
indexed by i, uniformly distributed on a square region, the LB-based method solves
the relaxation of the following binary integer program to produce a customer-vehicle
assignment.
(IP) min
n∑
i=1
m∑
j=1
cijxij (3.1)
s.t.
m∑
j=1
xij = 1 ∀i = 1, 2, . . . , n (3.2)
n∑
i=1
xij =
n
m
∀j = 1, 2, . . . ,m (3.3)
xij ∈ {0, 1} ∀i = 1, 2, . . . , n, j = 1, 2, . . . ,m (3.4)
Constraint (2) assigns each customer i to one and only one vehicle. Constraint
(3) specifies the number of customers that each vehicle can serve. The Euclidean
distance between customer i and depot j is denoted by cij. The binary variable xij
is equal to 1 if customer i is assigned to depot j.
After the assignment of customers to depots, an optimal TSP route is gener-
ated for each vehicle by the Concorde solver [30]. The length of route j (denoted by
Lj) is stored in descending order L1, L2, . . . , Lm. If the lengths are nearly balanced,
i.e., L1−Lm
Lm
< r for some predetermined r, the procedure terminates. Otherwise,
IP is solved with a decreased number of customers assigned to the vehicles with
longer routes and an increased number of customers assigned to the vehicles with
shorter routes. This procedure is repeated until the lengths are nearly balanced or
a maximum number of iterations is reached. The best solution is returned.
45
We now give the details of the implementation.
1. If there are multiple vehicles per depot, the locations of the vehicles are per-
turbed before solving IP.
2. For m and n, there exist integers p and q, such that n = pm + q with 0 ≤
q ≤ m − 1. The first q vehicles are assigned with p + 1 customers and the
remaining vehicles are assigned with p customers.
3. If L1−Lm
Lm
≥ r , denote L¯ as the average length of all routes, U = {k|Lk ≥ L¯}
as the set of long routes, and D = {k|Lk < L¯} as the set of short routes. If
|U | ≤ |D| , compute dj = Lj−L¯L¯ which is the relative drift defined by Carlsson et
al. [23]. For each j ∈ U , decrease the number of customers assigned to vehicle
j by bαdj
r
c, where α is set to 2 by the authors. For each j ∈ D, increase
the number of customers assigned to vehicle j by bαdj
r
c. If the number of
customers removed from U is more than those added to D, add one customer
to each element in D sequentially from the vehicle with the fewest nodes. A
similar procedure is used when |U | > |D|.
We have two observations about LB.
1. LB starts with an initial solution based on the load balancing idea and per-
forms refinement by global adjustment. It is faster than methods that include
local improvement. The running time seems to be independent of the size of
the problem.
2. Empirically, LB performs relatively well for uniformly distributed customer
46
locations, but does not do well if the customer locations are not generated
uniformly. It also does not perform well if there are multiple vehicles at a
depot.
3.3 MD algorithm
Our algorithm (MD) for the min-max MDVRP uses three stages to produce
solutions: initialization, local search, and improvement by perturbation. The first
stage produces a feasible solution. The second stage uses a procedure repeatedly
to improve an existing solution and generate a local optimum. The third stage
perturbs the solution to search for better solutions. Next, we describe the three
stages in detail. We illustrate MD by applying it to an example in Appendix A.
3.3.1 Initialization
MD applies the load balancing idea from [23] to construct an initial solution
in two steps.
3.3.1.1 Step 1: Assignment
Given a set of m depots, indexed by j, each with one vehicle of unlimited
capacity, and a set of n customers (n divisible by m), indexed by i, distributed over
a square region, we solve IP using Gurobi [52] to produce an initial assignment of
customers to vehicles.
If there is only one depot and there is more than one vehicle at the depot,
47
all possible assignments of customers to the vehicles produce the same objective
function value for IP. A similar problem exists if there are multiple depots and
some of them have more than one vehicle. To avoid this, we perturb the location
of any depot having multiple vehicles. We call this the specification of the vehicle
locations. Vehicles are placed symmetrically on a circle centered at the depot with a
small radius (0.1 is used in our implementation). The vehicles are rotated counter-
clockwise around the depot using a randomly specified angle.
3.3.1.2 Step 2: Solving the TSP
A vehicle and the customers assigned to it form a group of nodes. The Lin-
Kernighan-Helsgaun (LKH) solver [55] is used to obtain a near-optimal TSP tour
on the group of nodes. Each tour is called a route. The tour with the longest length
is called the maximal route. The objective is to minimize the length of the maximal
route. We modified an initialization procedure described by Golden, Magnanti, and
Nguyen. [47] that was used by Gulczynski, Golden, and Wasil [50]. This method
assigns customers to depots in two rounds. In the first round, if the distance from a
customer to its nearest depot is much shorter than the distance to its second nearest
depot, this customer is assigned to its nearest depot. In the second round, those
customers that are unassigned are allocated to one of their two nearest depots (the
depot with the shorter route). This method did not perform as well as the load
balancing procedure.
48
3.3.2 Local search
We perform a local search on the maximal route. The idea is to remove a
customer from the maximal route and insert it onto another route. This approach
has three steps.
First, we need to determine the customer to remove from the maximal route.
For each customer on the maximal route, the reduction of route length, or savings,
is estimated if that customer is removed. Suppose the customer located at (xi, yi)
is preceded by customer (xi−1, yi−1) and followed by customer (xi+1, yi+1). Either
the preceding customer or the succeeding customer may be a depot in the analysis.
The savings is estimated to be
dist ((xi, yi) , (xi−1, yi−1))+dist ((xi, yi) , (xi+1, yi+1))−dist ((xi+1, yi+1) , (xi−1, yi−1)) ,
(3.5)
where dist ((P1, P2)) is the Euclidean distance between points P1 and P2. The esti-
mated savings is conservative and the actual savings can be greater. We generate a
sequence of customers arranged in descending order of their savings. The customer
with the largest estimated savings on the maximal route is removed first.
Second, we identify the route on which to insert the customer. The insertion
cost is the increase in the length of the route due to the insertion of the customer.
The insertion cost is estimated in the following way. Assume customers located at
(xi−1, yi−1) and (xi+1, yi+1) are adjacent nodes on the same route. If the customer
located at (xi, yi) is inserted between them, the insertion cost is also given by (3.5).
49
The cost of inserting the customer onto a route is estimated to be the least cost
considering all adjacent pairs of nodes on the route. This is a conservative estimate
and the actual cost may be smaller. The customer is inserted onto the route with
the least insertion cost.
Third, the LKH solver is used to solve the TSP on the old maximal route
with the customer removed and on the new route with the customer inserted. If the
length of the new maximal route is less than the length of the previous maximal
route, the solution is updated. We continue to compute the savings of each customer
on the maximal route. If the objective function is not improved, we try to remove
the customer on the maximal route with the second largest savings. The local
improvement procedure ends when all the customers on the maximal route have
been considered and no improvement is found.
3.3.3 Perturbation
The solution generated so far is a local minimum. It cannot be improved any
further by assigning a customer on the maximal route to other routes. To move away
from the local minimum, we apply the idea described by Codenotti et al. [29] to
generate a new solution by perturbing the locations of the depots. For each depot,
we compute the average of its distances from the preceding customer (last customer
on the route) and the succeeding customer (first customer on the route). The depot
is then relocated to a location at this average distance away from its original position.
The angle of the first perturbation or the direction in which we move the depot is
50
random. We keep the same sequence of customer visits in the feasible solution to
the original problem to obtain a feasible solution to the perturbed problem. The
solution may not be optimal or even locally optimal, so we apply the local search
procedure to get a locally optimal solution. The depots are then set to their original
positions to recover the original problem. Our local search procedure is applied to
generate a different solution from the solution before perturbation. If it improves,
the solution is updated. This completes one perturbation. In our implementation,
the perturbation procedure is carried out until there is no improvement for five
consecutive iterations. The angle of each subsequent perturbation depends on the
previous one. The second is at an angle of 144◦ from the first one, the third is at
an angle of 144◦ to the second, and so on. The sixth direction is the same as the
first direction. When perturbation stops, we have good coverage of the perturbation
directions and consecutive directions are almost opposite each other.
3.4 Alternative methods
In this section, we present two alternative methods for generating solutions. In
Section 3.4.1, the improvement stages of MD are replaced by variable neighborhood
search (VNS). In Section 3.4.2, the initialization stage of MD is replaced by one
which makes use of a library for solving the standard VRP (minimize the total
distance traveled by the fleet).
51
3.4.1 VNS
3.4.1.1 Local Search
The local search procedure for VNS (LSVNS) is similar to the local search
procedure for MD (LSMD). Both procedures improve a solution by removing a
customer on the maximal route and inserting it onto another route. First, we
estimate the savings generated by the removal of each customer on the maximal
route. The three customers with the greatest potential savings are candidates for
removal. A random number is drawn from a uniform distribution so that each of
the three candidates is selected with equal probability.
We try to insert the removed customer onto other routes with the smallest
estimated cost. We apply the LKH solver to the newly constructed route (old
route plus the inserted customer). If the total cost of the new route is less than
the old route, an improved solution is found. We apply the LKH solver to the
old maximal route. Across all routes, we try to find the new maximal route and
we repeat removing one of the three most costly customers on that route. If the
total cost of the route after accepting the customer is greater than the old objective
function value, the move is rejected and no improved solution is found. We return
to the maximal route and try to remove another candidate customer. (The same
customer may be chosen with a probability of 0.33). If no improvement is found in
five consecutive trials, LSVNS terminates.
LSVNS differs from LSMD in three ways.
52
1. LSMD always tries to remove a customer with the greatest potential savings
among all unexplored customers on the maximal route. LSVNS randomly tries
to remove one of the three customers with the greatest potential savings.
2. LSMD explores the customers on the maximal route in a defined sequence
(decreasing estimated savings). LSVNS randomly picks one of the three cus-
tomers with the greatest potential savings.
3. LSMD terminates after exploring all the customers on the maximal route with-
out improving the solution. LSVNS terminates after five consecutive iterations
without an improvement.
3.4.1.2 Neighborhood structure
Solution B is in the first neighborhood (Nbr1) of solution A if it can be obtained
from solution A by swapping a customer on the maximal route with a customer not
on the maximal route. In the basic VNS [54], a random solution from a neighborhood
is generated and local search is then applied. In our implementation of VNS, three
promising solutions from Nbr1 are identified deterministically, and we randomly
select one of the three solutions with equal probability. For each customer on the
maximal route, we find the nearest neighbor not on the maximal route. We compute
the distance from this nearest customer and select the three customers with the
shortest distances. Each of the three candidate solutions is obtained by swapping
one of these three customers with a neighbor. We apply the LKH solver to the
affected routes immediately after the swap.
53
Solution C is in the second neighborhood (Nbr2) of solution A if it can be
obtained by moving a fragment of two or three consecutive customers from the
maximal route to some other route. Two random numbers are generated. One
number determines the length of the fragment to remove (two or three customers),
and the other number determines the position of the fragment on the maximal route.
We now need to determine where to insert the fragment. For all customers on the
fragment, we find their nearest customers not on the maximal route. If there is any
common neighbor (there can be at most one), we insert the entire fragment before
this common neighbor. If the two or three neighbors are distinct, we insert the
entire fragment before one of the neighboring customers according to a probability
distribution. If the distance between the fragment and a neighboring customer is
given by the distance from the neighbor to its nearest customer on the fragment,
then the probability of inserting the fragment in front of a neighboring customer
is proportional to the sum of the other neighbors’ distances from the fragment.
For example, suppose customers 1, 2, and 3 are the three neighbors which are
at a distance of 10, 10, and 30 away from the fragment, respectively. Then the
probabilities of inserting the fragment before customers 1, 2, and 3 have the ratio
40 : 40 : 20, which corresponds to a probability distribution of 0.4, 0.4, and 0.2. In
our implementation, we apply the LKH solver to the affected routes immediately
after the insertion.
54
3.4.1.3 VNS algorithm
In the basic VNS algorithm, neighborhoods are ordered 1 through n. If the
local search procedure does not improve a random solution from the k
th
neighbor-
hood, another random solution is generated from the (k + 1) st neighborhood. When
a solution from the nth neighborhood does not lead to an improvement, the algo-
rithm terminates. In our implementation of VNS, there are only two neighborhoods.
We do not move to the next neighborhood or terminate the algorithm immediately
when a solution does not lead to an improvement. If the first solution from the first
neighborhood does not improve the current solution, we generate a second solution
from the same neighborhood. If the second solution does not improve the current
solution, we generate a third one and so on until we have produced five solutions
from the first neighborhood. We then move to the second neighborhood. We do
not terminate the algorithm until we have generated 20 solutions from the second
neighborhood and none of them leads to an improvement. Our VNS algorithm is
shown in Table 3.1.
3.4.2 VRPH
This approach uses the local search heuristic library for the standard VRP
developed by Chris Groe¨r (see [48]) and denoted by VRPH. First, customers are
assigned to depots (not vehicles) by a procedure described in Golden, Magnanti,
and Nguyen [47]. A customer is assigned to the nearest depot unless the customer is
about the same distance from its nearest and second nearest depots. Subsequently,
55
Table 3.1: VNS algorithm
Given an initial feasible solution x.
1. x← LSVNS (x) 4. Set k = 0
2. Set k = 0 5. While k < 20
3. While k < 5 (a) x2 ← Nbr2 (x)
(a) x1 ← Nbr1 (x) (b) x2 ← LSVNS (x2)
(b) x1 ← LSVNS (x1) (c) If x2 is better than x
(c) If x1 is better than x i x← x2
i. x← x1 ii Go to step 2
ii. Go to step 2 else
else i k++
i k++ end if
end if end while
end while
those customers are assigned to one of the two nearest depots depending which
depot has a shorter route.
Second, the depot with its assigned customers is a single depot VRP. We use
VRPH to solve this problem. The customer demands are set to 1. The capacity of
the vehicle is set so that the number of routes in the VRPH solution matches the
number of vehicles in that depot in the min-max problem. We then generate an
initial feasible solution and we carry out the second and third stages of MD.
3.5 Computational results
In this section, we apply four heuristics (LB, MD, VNS, and VRPH) to a set
of test instances and compare their results. The code for LB is given in [100]. We
point out that neither the code nor the test instances for the ant colony optimization
technique are available.
56
3.5.1 Comparing LB, MD, VNS, and VRPH
Twenty sets of data were generated with varying numbers of depots, customers,
and vehicles per depot (five were supplied by Carlsson in a personal communication).
The locations of customers and depots for each data set are given in the online
appendix. The detailed computational results are given in Table 3.2. MD, VNS,
and VRPH used an Intel Pentium CPU with a 2.20GHz processor, while LB used
an Intel Core i3 CPU with a 2.40GHz processor (the MATLAB code from [100] for
LB could only be implemented on a 32-bit machine).
In Table 3.2, the first column shows the problem identifier. The second and the
third columns give the number of depots and the number of customers. The fourth
column gives the number of vehicles per depot: 1 means a single vehicle per depot, 2
means there are two vehicles per depot, and 3, 2, 2, 1 means there are three vehicles
at the first depot, two vehicles at the second and third depots, and a single vehicle
at the fourth depot. The fifth to the twelfth columns give computational results
for the four algorithms (LB, MD, VNS, VRPH). All algorithms produce the same
solution to MM6 which appears to be optimal, based on geometric considerations.
However, the resulting objective function values are not identical. This could be
due to the accumulation of rounding error from the TSP solver. Specifically, the
LKH solver produces only integer lengths.
In Figure 3.1, we show the percentage improvement of the objective function
values of MD, VNS, and VRPH compared to LB. For each test instance, the three
57
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58
Figure 3.1: Comparison of MD, VNS, and VRPH to LB
-15 
-10 
-5 
0 
5 
10 
15 
20 
25 
30 
35 
P
e
r
c
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(
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Problem 
MD 
VNS 
VRPH 
bars show results, from left to right, of MD, VNS, and VRPH. For example, for MM5,
the objective function value of the solution produced by MD is 20% less than the
objective function value produced by LB. In most of the instances, MD, VNS, and
VRPH outperform LB, and MD is the most effective in terms of objective function
value. On average, over the 20 instances, MD outperforms LB by 12.89%, VNS
outperforms LB by 11.67%, and VRPH outperforms LB by 8.1%. It is surprising that
VNS is not as effective as MD which relies on simple local search and a perturbation
technique. If we apply the second and the third stages to solutions produced by
VNS, the final result will outperform MD by only 0.7%. Over the 20 instances, MD
produces 15 best solutions, followed by VNS, which produces four best solutions.
LB produces two best solutions and VRPH produces none.
Data sets MM2, MM3, MM7, MM8, MM10 to MM16, and MM18 are generated
by a uniform distribution of customer locations. On these 12 data sets, the average
improvement by MD over LB is 12.27%. Data sets MM4, MM5, MM9, MM17,
59
MM19, and MM20 are generated by non-uniform distributions of customer locations.
The average improvement by MD over LB is 18.51%. MD outperforms LB to a
greater extent when the distribution of customers is not uniform.
In Table 3.3, we give a detailed account of the improvements contributed by
three steps in MD. Columns two, three, and four show the objective function value
of the feasible solution at the end of initialization, local search, and perturbation.
Columns five and six give the amount of improvement and the percentage of to-
tal improvement of the final solution with respect to the initial solution. Columns
seven and eight give the improvement due to local search (Step 2). Columns nine
and ten give the improvement due to perturbation (Step 3). To illustrate, for prob-
lem MM20, MD produces an initial solution value of 391.043. After local search,
the value is 346.700 which is a decrease of 11.34%. After perturbation, the value
is 339.920 which is a decrease of 1.73%. On average, over all 20 problems, the im-
provement procedures of MD decrease the value of the initial solution by 19.23%
(16.12% is from local search and 3.11% is from perturbation).
The running time for MD increases as the average number of customers per
route increases. In Figure 3.2, we plot the running time for MD against the av-
erage number of customers per route together with y = 0.1x2 and the best fit
y = 0.07511x1.6915 on a logarithmic scale. On these 20 instances, the worst-case
growth in running time is bounded quadratically. The average growth in running
time is of the order 1.7 with R2 = 0.8377. It is not straightforward to compare the
running times for LB and MD. LB is implemented in MATLAB, while MD is imple-
60
T
ab
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3:
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17
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M
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M
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78
0
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73
A
ve
ra
ge
19
.2
3
16
.1
2
3.
11
61
Figure 3.2: MD running time against average number of customers per route
100 101 102
10−2
10−1
100
101
102
103
Average number of customers per route
R
un
ni
ng
 ti
m
e 
/s
 
 
MD running time
y = 0.1 x2
y = 0.07511 x1.6915
mented in C++. The 32-bit requirement of MATLAB forced us to solve problems
with LB and MD on different machines (they are very close in processor speed).
However, we observe that MD runs faster when the average number of customers
per route is small (less than 40).
3.5.2 Detailed comparison of MD and VNS
3.5.2.1 New data sets
We now focus our attention on the two best-performing methods (MD, VNS)
and examine their performance on instances with specific distributions of customer
locations and customer-to-vehicle ratios (number of customers divided by the num-
ber of vehicles).
We generated an additional 23 test instances and combined them with 17
instances from MM1 to MM20 (we did not use the two smallest problems, MM1
62
and MM7, and a highly symmetric problem, MM6). The 40 test instances are
grouped into four categories with 10 instances each based on the distribution of
customer locations and size of the customer-to-vehicle ratios. We applied MD and
VNS to these 40 instances and report the results in Tables 3.4 to 3.7. We retain the
problem identifier for instances 1 to 20 and denote the additional test instances by
21 to 43. The locations of customers and depots for the additional test instances
are given in appendix B.
In Table 3.4, customers are uniformly located and the customer-to-vehicle ra-
tio is less than 40. A small ratio implies that the average number of customers per
route is small. The first column gives the problem identifier. The second column
gives the customer-to-vehicle ratio. All ratios are less than or equal to 40. The
third and fourth columns give the objective function values of the MD and VNS
solutions, respectively. The fifth column compares the result of MD to VNS. A neg-
ative percentage indicates that MD underperforms VNS. Overall, the two methods
perform about the same. MD is slightly better than VNS by 0.22%, on average.
On the instances where VNS outperforms MD (MM10, MM13, and MM15), the
customer-to-vehicle ratios tend to be small, 10, 15, and 13.3, respectively.
In Table 3.5, customers are uniformly distributed and the customer-to-vehicle
ratio is high (greater than or equal to 50). MD outperforms VNS on all 10 instances.
On average, MD is better than VNS by 2.47%.
In Table 3.6, the customer-to-vehicle ratios are less than or equal to 40. On
average, MD is slightly better than VNS by 0.05%. In Table 3.7, when the average
number of customers per route is large, MD produces solutions which are better
63
Table 3.4: MD vs VNS on uniform customer locations and small customer-to-vehicle
ratios
% MD
Uniform Customer-to outperforms
small -vehicle ratio MD VNS VNS
MM2 20.0 130.80 131.50 0.53
MM3 40.0 238.94 240.40 0.61
MM8 33.3 217.38 231.49 6.10
MM10 10.0 197.89 182.93 -8.18
MM11 10.0 102.35 103.66 1.27
MM12 6.7 78.90 80.83 2.38
MM13 15.0 121.87 120.69 -0.98
MM14 20.0 134.61 137.22 1.90
MM15 13.3 99.81 96.52 -3.40
MM16 25.0 101.68 103.70 1.94
# best solutions 7 3
Average 19.3 0.22
Note: Italics indicate better solutions.
Table 3.5: MD vs VNS on uniform customer locations and large customer-to-vehicle
ratios
% MD
Uniform Customer-to outperforms
small -vehicle ratio MD VNS VNS
MM5 100.0 390.16 400.27 2.53
MM21 50.0 259.14 274.10 5.46
MM22 83.3 400.60 413.27 3.07
MM23 66.7 374.97 378.71 0.99
MM24 50.0 204.00 206.22 1.08
MM25 66.7 272.61 274.84 0.81
MM26 75.0 364.56 369.10 1.23
MM27 50.0 290.37 298.46 2.71
MM28 100.0 354.31 367.72 3.65
MM29 87.5 364.01 376.18 3.24
# best solutions 10 0
Average 72.9 2.47
Note: Italics indicate better solutions.
64
Table 3.6: MD vs VNS on non-uniform customer locations and small customer-to-
vehicle ratios
% MD
Uniform Customer-to outperforms
small -vehicle ratio MD VNS VNS
MM18 39.0 315.89 333.38 5.25
MM30 40.0 140.34 149.54 6.16
MM31 20.0 124.32 112.52 -10.49
MM32 10.0 103.15 98.45 -4.78
MM33 13.3 97.56 100.93 3.34
MM34 25.0 84.64 85.58 1.09
MM35 15.0 109.30 107.86 -1.34
MM36 33.3 155.99 153.27 -1.77
MM37 23.3 156.41 151.19 -3.46
MM38 33.3 155.46 166.30 6.52
# best solutions 5 5
Average 25.22 0.05
Note: Italics indicate better solutions.
than VNS by 2.42%, on average.
Based on our computational experiments, MD outperforms VNS by about
2.4%, on average, when the customer-to-vehicle ratios are large for both uniform
and non-uniform distributions of customers. For small ratios, MD and VNS perform
nearly the same, on average, for both types of customer distributions.
3.5.2.2 Practical data
We apply MD and VNS to a real-world instance (problem real01 given in [98]).
The original problem has a single depot and 914 customers. We modify this problem
and treat the first nine customer locations as depots. We now have a multi-depot
problem with 10 depots and 905 customers. The coordinates are scaled by a factor
of 10−4. MD generates a solution with an objective function value of 9893.52 in
65
Table 3.7: MD vs VNS on non-uniform customer locations and large customer-to-
vehicle ratios
% MD
Uniform Customer-to outperforms
small -vehicle ratio MD VNS VNS
MM4 79.0 479.68 481.60 0.40
MM9 50.0 153.74 156.97 2.06
MM17 87.5 248.59 259.26 4.11
MM19 100.0 365.66 395.37 7.52
MM20 100.0 339.92 356.18 4.56
MM39 50.0 209.85 223.67 6.18
MM40 66.7 243.47 250.68 2.88
MM41 83.3 257.16 255.27 -0.74
MM42 90.0 367.44 357.17 -2.88
MM43 87.5 375.16 375.55 0.10
# best solutions 8 2
Average 79.4 2.42
Note: Italics indicate better solutions.
2005 seconds and VNS generates a solution with objective function value 10907.6 in
1892 seconds. MD outperforms VNS by 9.3% on this instance.
3.6 Conclusions
We developed three heuristic procedures (MD, VNS, VRPH) for the min-max
MDVRP. We applied these three procedures and an existing heuristic based on load
balancing (LB) to 20 test instances with 10 to 500 customers and 1 to 20 depots.
Among the four procedures, MD produced 15 best solutions. Furthermore, com-
putational experiments on instances with various distributions of customers and
different ratios of customers to vehicles showed that MD was very effective in pro-
ducing high-quality results.
In future work, we would like to extend the min-max MDVRP to handle
66
the service time at each customer and apply our heuristic to additional real-world
problems.
67
Chapter 4: The Min-Max Multi-Depot Vehicle Routing with service
4.1 Introduction
The classical Vehicle Routing Problem (VRP) models the distribution of goods
from a single depot to the customers. A customer has a demand that must be
satisfied in full by one visit of a vehicle. The sum of the demands delivered by a
vehicle cannot exceed its capacity. A vehicle must start and end its route at the
depot. There is usually no constraint on the number of vehicles used. The objective
is to minimize the total distance traveled by all vehicles. The VRP was introduced
by Dantzig and Ramser [34] in 1959 to model gasoline delivery. Many variants of
the VRP have been developed to model real-world problems. We refer interested
readers to Golden et al. [46] and Toth and Vigo [88, 89] for comprehensive surveys
of the VRP and its variants.
While most of the published research focuses on minimizing the sum of the
route costs, minimizing the maximum route cost is applicable in situations where
the last delivery is crucial or the balance of the route lengths is desired. Last delivery
applications include military operations, disaster relief routing, newspaper delivery,
and computer networks. Balancing route length applications include school bus
routing and workload balance among drivers. Campbell et al. [21] and Bertazzi
68
et al. [15] showed that, from the worst-case perspective, a solution to the min-
max objective can be very different from the solution to the traditional min-sum
objective. This finding motivates the development of exact and heuristic algorithms
specifically designed for the min-max objective. Carlsson et al. [23] first proposed
the min-max Multi-Depot VRP and solved it using a linear program-based, load
balancing approach [100] and a region partitioning approach. Wang et al. [94]
developed a three-stage heuristic (denoted by MD) that combined local search and
perturbation strategies and improved the results of Carlsson et al. [23] significantly.
Narasimha et al. [73] constructed an ant colony procedure to solve both the multi-
depot and single-depot versions of the min-max problem. Ren [80] proposed a hybrid
genetic algorithm for the single-depot min-max VRP.
Recently, Yakici and Karasakal [99] studied a min-max service VRP with split
delivery and heterogeneous demands. Customer demands are described by the ser-
vice times and the service types that are required. Customer service can be split
among vehicles if it improves the min-max objective. If there is no route duration
constraint, service times do not alter the routing plan of the classic VRP solution,
but can change the routing plan of the min-max solution [15]. Split delivery of-
ten reduces the total cost to the carrier ([4], [5],[38]), but can inconvenience the
customers because of work disruptions and paper work. Gulczynski et al. [49] intro-
duced a split delivery VRP with minimum delivery amounts. A customer’s demand
can be satisfied by multiple visits, provided each delivery is not less than a specified
fraction of total demand.
In this chapter, we study the min-max Split Delivery Multi-Depot Vehicle
69
Routing Problem with Minimum Service Time Requirement (min-max SDMDVRP-
MSTR). The objective function value has two components: (1) the travel times
of the vehicles and (2) the service times of the customers on the route. They
contribute differently to the objective. When the minimum delivery fraction is
greater than one half, i.e., no split deliveries allowed, the service time contribution is
determined entirely by individual customers. However, the travel time contribution
is determined by all customers. In particular, if a new customer is added to the
route, the increase in service time can be readily obtained, but the exact increase in
travel time cannot be computed easily. When travel times dominate, the problem is
closer to the min-max MDVRP studied by Carlsson et al. [23]. When service times
dominate, the problem is closer to the Multi-Way Number Partitioning Problem
[61]. Both problems are difficult to solve. When the travel times and service times
are comparable, the problem represents a trade-off between the two equally weighted
objectives.
We develop a heuristic algorithm (denoted by MDS) to solve the min-max
SDMDVRP-MSTR. The MD solver developed by Wang et al. [94] is modified to
generate a good initial solution without splits. Next, a network flow model is used
to improve the solution by splitting service, assuming no minimum service time
requirement. Finally, a linear program is solved to ensure that each visit by a
vehicle has at least the minimum service time.
There are numerous potential applications of the SDMDVRP-MSTR including
military operations, disaster relief, and the distribution of industrial gases and other
products where the delivery service time is relatively large.
70
The remainder of the chapter is organized as follows. In Section 4.2, the min-
max SDMDVRP-MSTR is described formally. In Section 4.3, structural properties
of the optimal solution when the minimum service time fraction is zero are provided.
In Section 4.4, a heuristic algorithm (MDS) for the general problem is developed. In
Section 4.5, the computational results are presented and discussed. Finally, Section
4.6 gives our concluding remarks.
4.2 Problem description
Let G (W ∪ V,E) be a complete graph, where W = {w1, w2, . . . , wm−1, wm}
and V = {v1, v2, . . . , vn−1, vn} are two sets of vertices, and E is the corresponding
set of edges. A vertex, wj ∈ W , where j = 1, 2, . . . ,m, corresponds to a depot where
a fixed number, lj, of vehicles are stationed. A vehicle that starts from wj must
return to wj at the end of its route. Unlike the classic min-sum VRP, which seldom
specifies a finite number of vehicles, the min-max problem requires the number of
vehicles in advance; otherwise the optimal solution will consist entirely of routes
serving only one customer. A vertex, vi ∈ V , where i = 1, 2, . . . , n, corresponds to
a customer who requires a service time of si. A customer can be visited multiple
times by different vehicles as long as the service requirement is met in full at the end
of the last visit and each visit delivers the minimum required service time. An edge
e ∈ E is associated with a cost, te, representing the travel time between the two
vertices that define the edge. We assume that the travel times satisfy the triangle
inequality. The total cost of a route, or its duration T , is the sum of the travel times
71
spent on the road and the service times spent at the customers. Unlike the classic
min-sum VRP, which often poses a constraint on the maximum length of a route,
the min-max problem does not require a maximum duration constraint, because the
objective is to minimize the duration of the longest route.
4.3 Structural properties of optimal solutions
Dror and Trudeau [38] provided a set of properties for the optimal solution
to the (min-sum) Split Delivery Capacitated Vehicle Routing Problem (SDCVRP).
In this section, we develop a similar set of properties that provide insights on the
structure of an optimal solution to the min-max SDMDVRP with no minimum
service time fraction.
Property 1. Any min-max SDMDVRP has an optimal solution in which no two
routes share more than one customer.
Proof. Suppose that, in an optimal solution, routes R1 and R2 both service cus-
tomers C1 and C2, as illustrated in Figure 4.1(a). Let s
(j)
i be the service time
delivered by route Rj at customer Ci, where i, j = 1 or 2. Without loss of general-
ity, assume further that s
(1)
2 ≥ s(2)1 . We can construct a new solution by transferring
the service time spent at C1 by route R2 (s
(2)
1 ) to route R1 and, at the same time,
transferring the same amount of service time spent at C2 by route R1 to route R2.
The new solution is shown in Figure 4.1(b). Route R1 serves C1 in full and spends
s
(1)
2 − s(2)1 at C2. Route R2 spends the remaining service time required by C2. The
duration of R1 remains unchanged and the duration of R2 may be reduced because
72
R1 R2
C1
C2
s
(1)
1 s
(2)
1
s
(1)
2 s
(2)
2
(a)
R1 R2
C1
C2
s
(1)
1 + s
(2)
1
s
(1)
2 − s(2)1 s(2)2 + s(2)1
(b)
Figure 4.1: Illustrating Property 1
it does not have to visit C1. Therefore, the objective function value of this solution
is no more than the objective function value of the previous solution, and routes R1
and R2 share only one customer.
Corollary 1. Let vi and vj be two customers. Any min-max SDMDVRP has
an optimal solution in which the edge (vi, vj) is traversed at most once (in either
direction). If the edge is traversed by one route, it will never by traversed by another
route.
Proof. Assume this is not true. Then, we can have at least two routes which share
customers vi and vj at the same time which is contrary to the Property 1.
We can generalize Property 1 to Property 2 by using the definition of the
k-split cycle given by Dror and Trudeau [38].
Definition 1. A set of k customers C1, C2, . . . , Ck−1, and Ck form a k-split cycle, if
there exists a set of k routes, R1, R2, . . . , Rk−1, and Rk such that R1 visits customers
73
C1 and C2, R2 visits customers C2 and C3, . . . , Rk−1 visits customers Ck−1 and Ck,
and Rk visits customers Ck and C1.
Property 2. Any min-max SDMDVRP has an optimal solution in which there is
no k-split cycle.
Proof. Assume that there exists a k-split cycle. Let s
(j)
i be the service time spent
at customer Ci by route Rj. Let
lmin = arg min
l∈{1,2,...,k}
{s(l)l }
and
smin = s
(lmin)
lmin
.
We construct a new solution by transferring smin amount of service time of customer
Ci from route Ri to Ri−1 for i = 2, 3, . . . , k and transferring smin amount of service
time of customer C1 from route R1 to Rk. The sum of service times on each route
remains unchanged, but the travel time of route Rlmin may be reduced because it
does not have to visit customer Clmin . Therefore, the objective function value of the
new solution is no more than the objective function value of the previous solution
and the k-split cycle is broken.
Property 3. Any min-max SDMDVRP has an optimal solution in which any two
routes that split a customer have the same duration.
Proof. Suppose that two routes, R and R′, in the optimal solution split a customer
C, but the duration of R, denoted by TR, is strictly greater than the duration of
74
R′, denoted by TR′ . Let s
(R)
C be the service time spent at customer C by route R.
If s
(R)
C ≤ TR − TR′ , we construct a new solution by transferring the entire service
time s
(R)
C from route R to route R
′, so that customer C is serviced in full by R′.
The resulting solution is no worse than the previous solution, and the two routes R
and R′ no longer both serve customer C. On the other hand, if s(R)C > TR − TR′ ,
we construct a new solution by transferring 1
2
(TR − TR′) of customer C’s service
time from route R to route R′. In the new solution, both routes have duration
1
2
(TR + TR′) < TR, and they still split customer C.
Definition 2. Consider an auxiliary graph whose vertices represent the routes in
a solution. Two vertices are connected by an edge if and only if the corresponding
two routes have a customer in common. Then a cluster of routes is a set of routes
with the corresponding vertices in a connected component.
Possible structures of clusters are shown in Figure 4.2. The larger unfilled
circles represent routes and the smaller filled circles represent split customers. Figure
4.2(a) shows a single route that serves all of its customers in full. Figure 4.2(b)
shows a cluster with two routes splitting one customer. Figure 4.2(c) has three
routes splitting two customers. Figure 4.2(d) has three routes splitting only one
customer. Figure 4.2(e) has a cluster with four routes in which two routes split one
customer and three routes split a different customer.
Using the definition of clusters of routes, we extend Property 3 to Property 4.
Property 4. Any min-max SDMDVRP has an optimal solution with all routes in
the same cluster having the same duration.
75
R1
(a) Cluster 1
R2 R3
C1
(b) Cluster 2
R4 R5 R6
C2 C3
(c) Cluster 3
R8 R7
R9
C4
(d) Cluster 4
R10
R11 R12
R13
C5 C6
(e) Cluster 5
Figure 4.2: Examples of clusters of routes
Proof. We start with an optimal solution with no k-split cycle. Each cluster is
optimized with respect to the min-max objective function. In general, if a cluster
does not contain the longest route of the solution, it need not be min-max optimal.
However, an optimal solution with all clusters min-max optimal always exists be-
cause we can think of the customers, vehicles, and depots in this cluster as a smaller
min-max problem and solve it optimally. (Although solving the sub-problem may
lead to a solution with more clusters, we can apply the same procedure and solve
the smaller problems.)
Suppose that, in this solution, a cluster has routes of different duration, and
there are n longest routes in the cluster. In this cluster, we can always identify
a longest route that splits a customer with another shorter route, because not all
routes have the same duration and the vertices representing the routes are connected.
76
We apply the same procedure in the proof of Property 3 to transfer some or all of
the service time of the shared customer from the longer route to the shorter route.
There are two possibilities. Both routes have the same duration (the number of
longest routes drops by one) or the cluster breaks up into two smaller clusters.
The cluster breaks when all of the shared customer’s service time is shifted to the
shorter route (and there is no k-split cycle within the cluster). In either case, the
min-max objective function value is no worse than the previous value. We apply
this procedure to any cluster that contains routes with unequal duration until either
all the n longest routes are shortened, which implies that the original cluster is not
optimized with respect to the min-max objective, or the cluster breaks into a set of
clusters with single routes and clusters with routes of equal duration.
4.4 Algorithm
We develop a three-stage algorithm for the min-max SDMDVRP-MSTR. First,
we modify a procedure developed by Wang et al. [94] in order to generate a good
solution with no split service and no minimum service time requirement. Second,
clusters are formed, merged, and broken through local search in order to improve
solutions through split service while ignoring the minimum service time requirement.
When our local search procedure cannot improve solutions anymore, a perturbation
procedure is applied to improve the solution from the local minimum. Finally, a
clean-up process ensures that the minimum service time requirement is satisfied.
77
4.4.1 Improving MD
Wang et al. [94] developed an effective heuristic (denoted by MD) to solve
the min-max MDVRP. MD has three operators: initialization by solving a linear
program, local search by relocating customers from the longest route to other routes,
and perturbation by repositioning the depots. The three operators are summarized
below with an emphasis on how we modify each one to solve a problem with service
time. In addition, we develop four operators that improve MD.
To initialize a feasible solution, MD solved a generalized assignment problem
using the Gurobi solver [52] to allocate an approximately equal number of customers
to each vehicle. The generalized assignment problem (AP) formulation was intro-
duced by Carlsson et al. [23] in their LP-based load balancing heuristic. The cost
of assigning a customer to a vehicle was the Euclidean distance from the customer
location to the depot where the vehicle was stationed. In the min-max SDMDVRP,
the assignment cost is the travel time from the customer to the depot. The objective
was to minimize the total assignment cost. The Lin-Kernighan-Helsgaun (LKH) [55]
78
solver was used to route the customers that were assigned to the same vehicle.
(AP) min
n∑
i=1
m∑
j=1
tijxij (4.1)
s.t.
m∑
j=1
xij = 1 ∀i = 1, 2, . . . , n (4.2)
n∑
i=1
xij =
⌊ n
m
⌋
or
⌊ n
m
⌋
+ 1 ∀j = 1, 2, . . . ,m (4.3)
xij ∈ {0, 1} ∀i = 1, 2, . . . , n, j = 1, 2, . . . ,m (4.4)
The decision variable xij takes the value 1 if and only if customer i is assigned
to route j. In the objective function (4.1), n and m are the number of customers and
the number of routes, respectively. tij is the distance between customer i and the
depot of route j. Constraints (4.2) imply that every customer is served on exactly
one route. Constraints (4.3) imply that every route serves either
⌊
n
m
⌋
or
⌊
n
m
⌋
+ 1
customers. Constraints (4.4) define a binary decision variable.
To improve a solution, a local search procedure (denoted by LS NoSplit) was
applied. MD tried to remove a customer with the greatest potential savings from
the longest route and insert it onto other routes in the least-cost way. The sequence
for which a customer was considered depended on the estimate of the savings. For
example, if a vehicle served customers at locations A, B, and C in that sequence,
and the customer at B was considered for removal, then the savings was estimated to
be (AB+BC−AC). To adapt the procedure to the service problem, we include the
service time of the customer at B, denoted by sB, in the estimation of the savings.
Furthermore, the savings estimation is modified to (sB +AB +BC − λAC), where
79
λ is a parameter whose value is determined based on computational experiments
(more about λ in Section 4.5.2.4). The local search procedure is repeated until no
improvements are found.
A series of perturbations (denoted by Ptb NoSplit) was carried out to improve
the solution and move it from the local minimum. In each perturbation, depots were
shifted to slightly different positions determined by perturbation angles and radii to
form a perturbed problem. The customers were still visited in the same sequence to
form a feasible solution to the perturbed problem. LS NoSplit was applied to the
feasible solution to get a local minimum solution to the perturbed problem. The
depots were then set back to their original positions. MD continued with LS NoSplit
to get a different and, hopefully better, local minimum to the original problem.
Ptb NoSplit was repeated until there was no improvement for five consecutive
perturbations. The perturbation radius was the average distance from the depot to
the first and the last customers on the route. The first perturbation angle was ran-
dom, but subsequent perturbation angles were set to 144 degrees counter-clockwise
to the previous one. This scheme made consecutive perturbations of a depot in
almost opposite directions. It had full coverage of the directions when it stopped
after five iterations with no improvement.
We now develop and add four operators to MD: cyclic transfer, one-point
move, two-point move, route destruction and reconstruction.
Cyclic transfer is not new to the VRP literature. Thompson and Psaraftis
[87] applied this operator to solve the min-sum VRP. The idea is to simultaneously
relocate k customers. Suppose we have routes R1, R2, . . . , and Rk serving customers
80
C1, C2, . . . , and Ck, respectively. After cyclic transfer, we may have C1 ejected on
R1 and C2 served, C2 ejected on R2 and C3 served, etc, and Ck ejected on Rk
and C1 served. To identify cyclic transfers that reduce the value of the objective
function, Thompson and Psaraftis first generated an auxiliary graph with each node
representing a customer. Denote by Rj the route serving customer Cj and by Rj\j
the route if Cj is removed. The cost of the arc from node i to node j was the
estimated least-cost increase of Rj if customer Ci was inserted while customer Cj
was removed. Thompson and Psaraftis proved that if the three least-cost insertion
positions of customer Ci onto Rj are r, s, and t with costs cr, cs, and ct, respectively,
and cr ≤ cs ≤ ct, the least-cost insertion position of Ci onto Rj\j is one of the four
positions, r, s, t, and j − 1. The authors developed an algorithm (see Table 4.1)
to compute all arc costs in O(N2) time, where N is the total number of customers.
Looking for cyclic transfers that reduce the objective function value amounted to
identifying negative cost cycles from the auxiliary graph. Thompson and Psaraftis
applied different modules to identify negative cost cycles. The modules may require
searching in a restricted neighborhood, e.g., cycles involving only two nodes, or
generating only part of the auxiliary graph, to reduce the computational burden. A
negative cost cycle signaled a likely decrease in the min-sum objective function value.
The magnitude of the negative cost indicated the extent to which the objective
function value was expected to decrease.
The cyclic transfer neighborhood may be useful in the min-max problem. If
the longest route is surrounded by other long routes, it is unlikely that LS NoSplit
can improve the solution any further, but the larger cyclic transfer neighborhood
81
Table 4.1: Estimated arc cost of the auxiliary graph for cyclic transfer [87]
Algorithm 1
For all customers i
For routes R that does not serve i
Calculate cr, cs, and ct
For all customers j on R
Calculate the increase in cost of R\j, ci(j), if i is inserted between j − 1 and j + 1
Denote the estimated cost of adding i onto R\j by cij
If j ∈ {r, r + 1}
If j = s+ 1
cij = min{ci(j), ct}
Else
cij = min{ci(j), cs}
Endif
Else
cij = min{ci(j), cr}
Endif
Endfor
Endfor
Endfor
82
0 1
2
3
4
5
6
100
100
100
100
100
100
129
129
129
(a) Solution before cyclic transfer
0 1
2
3
4
5
6
100
100
100
100
100
100
69
69
69
(b) Solution after cyclic transfer
Figure 4.3: Cyclic transfer
may help break away from the local minimum. An example is shown in Figure 4.3.
Six customers served by three vehicles are located at a distance of 100 from the
depot. The distances are given next to the edges. The solution in Figure 4.3(a) has
three routes of equal duration 329 that cannot be improved by LS NoSplit. But if
we invoke a cyclic transfer with customers 1, 3, and 5, the solution can be improved
to have three routes of duration 269, which is shown in Figure 4.3(b).
To adapt Thompson and Psaraftis’s cyclic transfer to handle our problem,
we construct an auxiliary graph with the number of nodes equal to the number of
customers. For every pair of customers Ci and Cj not on the same route, denote
the route that serves Cj to be route Rj. We estimate the duration of Rj\j + i, i.e.,
if customer Ci is added to the route and customer Cj is removed. If the duration is
expected to be greater than the maximum duration, arc (i, j) is not included in the
auxiliary graph. Otherwise, if Rj is among the longest routes, arc (i, j) is added to
the auxiliary graph and assigned cost −1. If Rj is not among the longest routes, arc
83
Table 4.2: Algorithm to generate the auxiliary graph for cyclic transfer in the min-
max problem
Algorithm 2
Initialize the auxiliary graph, Gaux, to have n nodes but no arcs
For all ordered pairs of customers Ci and Cj that are on different routes Ri and Rj
Estimate the duration of Rj\j, denoted by TRj\j
Estimate the cost increase, ∆ij, if Ci is inserted onto Rj\j,
using the algorithm in Table 4.1 and add the service time of Ci
If TRj\j + ∆ij < Tmax
If Rj is not a longest route
Add arc (i, j) with cost 0 to Gaux
Else
Add arc (i, j) with cost −1 to Gaux
Endif
Endif
Endfor
(i, j) is added to the auxiliary graph and assigned cost 0. Therefore, a negative cost
cycle signals a likely decrease in the min-max objective function value. In Table
4.2, we present the algorithm to generate the auxiliary graph. Since the resulting
auxiliary graph is usually sparse, we apply Tarjan’s algorithm [86] to decompose
it into strongly connected components. For each component, we find at most 10
negative cost cycles by a depth-first search. Not all of the cyclic transfers suggested
by these negative cycles will actually improve the min-max objective, because the
duration of Rj\j and the increase in duration when customer i is inserted onto Rj\j
are only estimates. We apply the cyclic transfers suggested by the negative cost
cycles one by one until we find an improved solution.
We also apply one-point and two-point moves to reduce the total duration of
the fleet provided they do not worsen the min-max objective function value. Even if
these two operators do not reduce the maximum duration directly, they may open
up opportunities for LS NoSplit later in our algorithm. In the one-point move, we
84
Table 4.3: One-point move
Algorithm 3
For every route RA in the solution (Loop A1)
For every customer CA on route RA (Loop A2)
Estimate the change in duration if CA is removed
∆TRA = p(CA)s(CA)− p(CA)CA − CAs(CA)− sA,
where p(CA) and s(CA) are nodes before and after CA
For every route RB that is different from RA in the solution (Loop B1)
Compute the allowed duration increase ∆Tallowed = Tmax − TRB
For every edge (CB1, CB2) on route RB (Loop B2)
Estimate the increase in RB’s duration ∆TRB = CACB1 + CACB2 − CB1CB2 + sA
If ∆TRB ≤ ∆Tallowed and ∆TRA + ∆TRB < 0
Relocate CA between CB1 and CB2
Continue with Loop A2
Endif
Endfor
Endfor
Endfor
Endfor
For every route R in the solution
Apply the LKH solver to optimize the route
Endfor
consider relocating a customer between two other customers (or the depot) that are
on a different route. In the two-point move, we consider exchanging the positions
of two customers not on the same route. The two operators are presented in Tables
4.3 and 4.4. The LKH solver [55] is used in both operators.
Route destruction and reconstruction applies the ruin-and-recreation principle
of Schrimpf et al. [84]. If a long route serves only a few customers, it may be an
inefficient route. We destroy the route and insert its customers onto other routes
in a least-cost way. Meanwhile, a route that adds a customer from the inefficient
85
Table 4.4: Two-point move
Algorithm 4
For every route RA in the solution (Loop A1)
For every customer CA on route RA (Loop A2)
For every route RB with an index larger than that of RA in the solution ((Loop B1))
For every customer CB on route RB (Loop B2)
Estimate RA’s duration, TRA,aft, after the swap
Estimate RB’s duration, TRB ,aft, after the swap
If max {TRA,aft, TRB ,aft} ≤ Tmax and TRA,aft + TRB ,aft < TRA,bfr + TRB ,bfr,
where TRA,bfr is the duration of RA before the swap
Swap CA and CB
Continue with Loop A2
Endif
Endfor
Endfor
Endfor
Endfor
For every route R in the solution
Apply the LKH solver to optimize the route
Endfor
86
Table 4.5: Route destruction and reconstruction
Algorithm 5
Set threshold δ = 20%, and the set of inefficient routes S = ∅
Number of empty routes is Nempty = 0
For every route R in the solution
Compute and store the average travel time per customer for route R, Tavg,R
If R is empty
Increment Nempty
Endif
Endfor
Compute the average of Tavg,R, not including the empty routes and denote the average by Tavg
For every route R in the solution
If Tavg,R > (1 + δ)Tavg
Add R to S
Endif
Endfor
For every route R ∈ S
For every customer C on R
Insert C onto some route R˜ /∈ S in a least-cost way
Eject the nearest customer to R’s depot from route R˜
Endfor
Form a new route with all the ejected customers
Endfor
route must eject a customer that is nearest to the depot of the inefficient route. A
new route is constructed from these ejected customers. At the end of the process,
we have the same number of routes in the solution, and each route has the same
number of customers as it previously had. The route destruction and reconstruction
algorithm is presented in Table 4.5 and the complete modified MD is presented in
Table 4.6.
87
Table 4.6: Modified MD
Algorithm 6
Initialize a solution, S0, using AP and LKH [55]
Local search LS NoSplit
Perturbation Ptb NoSplit
Cyclic transfer
Local search LS NoSplit
Perturbation Ptb NoSplit
Two-point move
One-point move
Local search LS NoSplit
Perturbation Ptb NoSplit
Record the solution S1
Route destruction and reconstruction
Local search LS NoSplit
Perturbation Ptb NoSplit
Record the solution S2
Report the better solution of S1 and S2
4.4.2 Cluster balance subroutine
Before we present the local search and perturbation used in the second stage
of MDS, we describe a cluster balance subroutine that is used repeatedly in the
second stage. We want to keep the cluster with the longest route balanced, i.e., all
routes in the cluster have the same duration. Otherwise, we can apply the service
transfer process in the proof of Property 1 to reduce the duration of the longest
route. In addition, we keep the other clusters in the intermediate solutions balanced
as well. Although we would like to have all clusters balanced, a balanced structure
is disrupted whenever we remove a customer or add a customer during the local
search procedure. Sometimes balance can be restored by transferring the service
88
time of the split customer from one route to another. For example, suppose that
in cluster 2 in Figure 4.2(b), the service requirement of customer C1 is 20, which is
split evenly between routes R2 and R3. The duration of each route is 100. Suppose
the duration of R3 falls to 90 after some customer other than C1 is removed. To
restore balance, we can transfer five time units of customer C1’s service from route
R2 to route R3 so that the duration of each route is 95 with R2 taking 25% of C1’s
service requirement. When balance cannot be restored, we break the cluster into
smaller ones. For example, suppose a customer, other than C1, from R3 is removed
and the duration drops from 95 to 80. The balance cannot be restored, because it
requires 7.5 time units of service to be transferred from R2 to R3, but R2’s share on
C1 is only five units. Therefore, we break cluster 2 into two clusters, each with a
single route, by transferring the remaining five units on R2 to R3. C1 is now served
in full by R3 with duration 85 and R2 has duration at most 90.
In the solution process, clusters are often much more complex and unbalanced
clusters arise very often. We need a subroutine to restore balance or break up a
cluster in a specific way if balance is not possible.
Our cluster balance subroutine is based on a network flow model. Each cluster
is represented by an auxiliary directed graph H (N,A), where N is a set of nodes
that correspond to the routes. Two nodes are connected by two arcs in opposite
directions if and only if the corresponding routes serve a customer in common. The
auxiliary graphs of the five clusters in Figure 4.2 are given in Figure 4.4. In Figure
4.2(a), cluster 1 has a single route, so that its auxiliary graph in Figure 4.4(a) has
a single node without any arcs. In Figure 4.2(b), cluster 2 has routes R2 and R3
89
splitting customer C1, so that the auxiliary graph in Figure 4.4(b) has two nodes
connected by two arcs. The two non-negative numbers, U2,3 and U3,2, on each arc
are the maximum flows in the arcs. In this cluster, the service time required by
customer C1 is U2,3 + U3,2. U2,3 is delivered by R2 and U3,2 is delivered by R3. In
Figure 4.2(c), cluster 3 has two split customers, C2 and C3. In Figure 4.4(c), the
arcs with maximum flow U4,5 and U5,4 are induced by customer C2, whereas the arcs
with maximum flow U5,6 and U6,5 are induced by customer C3. Cluster 4 in Figure
4.2(d) has three routes, all splitting the same customer C4, so that its auxiliary
graph in Figure 4.4(d) has three nodes. Every pair of nodes is connected by two
arcs in opposite directions. The labels on each arc give the maximum flows through
the arcs. In this example, U8,7 + U8,9 is the service time at C4 by R8. U7,8 + U7,9 is
the service time at C4 by R7. U9.7 + U9,8 is the service time at C4 by R9.
Whenever a cluster is modified, we carry out a cluster balance subroutine by
90
R1
(a) Graph of Cluster 1
R2 R3U2,3
U3,2
(b) Graph of Cluster 2
R4 R5 R6U4,5
U5,4
U5,6
U6,5
(c) Graph of Cluster 3
R8
R7
R9
U8,7
U7,8
U7,9
U9,7
U8,9
U9,8
(d) Graph of Cluster 4
R10
R11
R12
R13
U10,11
U11,10
U11,12
U12,11
U12,13
U13,12
U11,13
U13,11
(e) Graph of Cluster 5
Figure 4.4: Auxiliary graphs of the clustomers in Figure 4.2
solving the following LP repeatedly.
(LP) min z (4.5)
s.t. Ti = T˜i −
∑
j:(i,j)∈A
xij +
∑
j:(j,i)∈A
xji ∀i (4.6)
z ≥ Ti − T ∗ ∀i (4.7)
z ≥ T ∗ − Ti ∀i (4.8)
s
(i)
l ≥
∑
j:(i,j)∈A(l)
xij −
∑
j:(j,i)∈A(l)
xji ∀l, i∃j(i, j) ∈ A(l)
(4.9)
xij ≥ 0 ∀(i, j) ∈ A (4.10)
Ti ≥ 0 ∀i (4.11)
z ≥ 0 (4.12)
91
The nodes are indexed by i or j. In constraint (4.6), the parameter T˜i is the duration
of the route represented by node i before balancing. The decision variable xij gives
the amount of flow in the arc (i, j) ∈ A. Therefore, constraint (4.6) indicates that the
variable Ti is the duration of the corresponding route after balancing. In constraints
(4.7) and (4.8), the parameter T ∗ is the targeted route duration. Since the total
duration within a cluster is preserved unless the cluster breaks after balancing, we
can compute the target by dividing the total duration by the number of routes in
the cluster. Therefore, constraints (4.7) and (4.8), together with the minimization
objective, force z to be the maximum absolute deviation of the duration of the
routes from the target after balancing. In constraint (4.9), s
(i)
l =
∑
j:(i,j)∈A(l) Ui,j is
the service time spent by route i at customer l, and A(l) ⊂ A is a subset of arcs
induced by l. This constraint implies that the maximum net outflows from node i
through arcs induced by customer l cannot exceed the service delivered by route i
at customer l. Constraints (4.10) to (4.12) define the variable types. In fact, xij is
the only decision variable. When the values of xij are fixed, the values of Ti and zi
are fixed as well. Ti and zi are introduced to make the presentation of constraints
clearer. The objective function (4.5) minimizes the maximum absolute deviation
from the target duration after balancing. A zero value of the objective function
indicates that the cluster can be balanced; otherwise the cluster cannot be balanced
without breaking it up. Other objective functions are possible (see Section 4.4.2.1).
Even if balance cannot be achieved, we still apply the flows from the solution to
LP, and then determine how to break up the cluster. Initially, we attach a different
label to each route. If two routes share a customer, we take the union of all routes
92
with those two labels and attach the same label to them. All routes with the same
label form a new cluster.
If a cluster is broken up, the smaller clusters that are formed may not be
balanced. We solve LP again to balance the smaller clusters until all clusters are
balanced. It seems that restoring balance may take a lot of effort, but the size of LP
is usually very small. The number of nodes in the auxiliary graphs is equal to the
number of routes in the cluster. The number of edges is related to the number of
split customers. Although we may have a customer serviced by several routes, the
number of split customers is less than the number of routes as a result of Property
2.
4.4.2.1 Alternative objective functions in the cluster balance subrou-
tine
We discuss three objective functions (4.13), (4.14), and (4.15) that balance the
cluster if possible, and break up the cluster if balancing is not possible. We explain
why we have chosen (4.14).
min
n∑
i=1
|Ti − T ∗| (4.13)
min max
i
|Ti − T ∗| (4.14)
min
n∑
i=1
|Ti − T ∗|2 (4.15)
93
Objective function (4.13) minimizes the sum of absolute deviations from the target
duration. Objective function (4.14) minimizes the maximum absolute deviation
and is the same as (4.5). Objective function (4.15) minimizes the sum of absolute
deviations squared. Each function gives an optimal value of zero if the cluster
is balanced. However, each performs differently if balance cannot be achieved as
illustrated by the following two examples.
Example 13.
In the unbalanced cluster shown in Figure 4.5(a), there are four routes, R1,
R2, R3, and R4, with durations 70, 70, 10, and 10, respectively. Routes R1 and
R2 split customer C1. Routes R2 and R3 split customer C2. Routes R3 and R4
split customer C3. The number next to an arc indicates the maximum flow in that
arc. The target duration of a route is [70(2) + 10(2)]/4 = 40, so there has to be
a net outflow of 2(70 − 40) = 60 from nodes R1 and R2, and a net inflow of the
same amount into nodes R3 and R4 in order to balance the cluster. However, the
maximum flow in arc (R2, R3) is 10, so the cluster breaks with R3 serving C2 in
full. By inspection, the desired balanced two smaller clusters are shown in Figure
4.5(b), with R1 and R2 having the same duration 65, and R3 and R4 having the
same duration 15, assuming the savings from travel time is negligible.
Both objective functions (4.14) and (4.15) produce the desired clusters in Fig-
ure 4.5(b) in one call of the cluster balance subroutine. However, objective function
(4.13) requires three calls in the worst case. As long as R3 takes the entire C2,
objective function (4.13) is indifferent as to how to split C1 between R1 and R2,
94
R1 : 70
R2 : 70 R3 : 10
R4 : 10
20
20
10
2
6
6
C1
C2
C3
(a) Unbalanced cluster
R1 : 65
R2 : 65 R3 : 15
R4 : 15
15
25 1
11
C1 C3
(b) Balanced cluster
Figure 4.5: Example 13
or how to split C3 between R3 and R4, because the function value is constant at
100. We have to call the subroutine again to balance the smaller clusters. However,
functions (4.14) and (4.15) break the cluster and balance the smaller clusters at the
same time in this example.
Example 14.
As shown in Figure 4.6(a), the unbalanced cluster has three routes, R5, R6,
and R7. R5 and R6 have duration 50 and R3 has duration 20. The target duration
is 40. Therefore, there has to be a net outflow of 20 from nodes R5 and R6 and net
inflow of 20 into R7 to balance the cluster. However, because the maximum flow in
arc (R6, R7) is 10, the cluster has to break with R7, thereby servicing customer C5
in full. Figure 4.6(b) shows the desired balanced clusters, assuming that the savings
in travel time is negligible.
Only objective function (4.15) produces the desired clusters in one call to the
subroutine. Both functions (4.13) and (4.14) take two calls in the worst case. After
95
R5 : 50
R6 : 50
R7 : 2020
20
10
10
C4 C5
(a) Unbalanced cluster
R5 : 45
R6 : 45
R7 : 3015
25
C4
(b) Balanced cluster
Figure 4.6: Example 14
R7 takes C5, the value of function (4.13) remains constant at 20, and the value of
function (4.14) remains constant at 10, as long as neither R1 nor R2 has duration
less than 40.
It is not a coincidence that objective function (4.15) requires the fewest func-
tion calls to achieve balance, while objective function (4.13) has the most in these
examples. To explain this, we consider the change of variables
yi = Ti − T ∗ i = 1, 2, . . . , n. (4.16)
The objective functions then become
min
n∑
i=1
|yi| (4.17)
min max
i
|yi| (4.18)
min
n∑
i=1
|yi|2 (4.19)
96
subject to an additional constraint that
n∑
i=0
yi = 0. (4.20)
Geometrically, the contours of objective function (4.19) are concentric spheres
centered at the origin in Rn. The contours of (4.18) are cubes with edges parallel
to the axes. The contours of (4.17) are octahedrons with vertices on the axes. The
optimal solution occurs where the boundary of the feasible region is tangent to a
contour. Since constraint (4.20) specifies a hyperplane passing through the origin
that is normal to the vector (1, 1, . . . , 1)T in Rn, we need only consider points on
this plane, denoted by Π. The intersections of the octahedrons, the cubes, or the
spheres with the hyperplane Π are regular hexagons, equilateral triangles, or circles,
all centered at the origin, shown in Figures 4.7(a), 4.7(b), and 4.7(c). The feasible
region is a convex polygon on the same plane. If this region contains the origin,
the optimal solution is unique for all three formulations. If this region does not
contain the origin, the optimal solution to objective function (4.19) is still unique
because the feasible region is a convex polygon, which is enclosed by (straight) line
segments. The optimal solutions to functions (4.17) and (4.18) may not be unique
when the boundary of the feasible region has a line segment parallel to part of the
level curves. In addition, as shown in Figures 4.7(a) and 4.7(b), each of the three
sides of a equilateral triangle is parallel to one of the six sides of a regular hexagon,
but not vice verse. This implies that if (4.18) has infinitely many optimal solutions,
(4.17) is likely to have infinitely many optimal solutions as well.
97
Π(a) Objective function (4.17)
Π
(b) Objective function (4.18)
Π
(c) Objective function
(4.19)
Figure 4.7: Intersections of contours of objective functions (4.17), (4.18), and (4.19)
with Π
A thorough discussion of the three formulations is not within the scope of
this paper, but we use objective function (4.14) in our implementation because it
usually requires fewer function calls than (4.13) and can be easily linearized. It also
conforms with the overall min-max style objective.
4.4.3 Local search
The solution that has been generated so far does not involve any split service.
Using the local search procedure LS Split, we explore the possibility of splitting
some customers from the cluster containing the longest routes to further reduce
the min-max objective function value. A series of merge and balance restoration
operations are used.
The sequence in which the customers are considered for splits can affect the
local minimum that results. In LS Split, we consider an alternating sequence, i.e.,
the customers near the beginning or the end of the routes are explored first. The
motivation is that routes through the same depot are allowed to merge before routes
98
with different depots. We illustrate the alternating sequence with a cluster contain-
ing two routes that serve three and four customers respectively. Denote by (p, q) the
qth customer on the pth route. The alternating sequence explores the customers in
the order (1, 1)→ (2, 1)→ (1, 3)→ (2, 4)→ (1, 2)→ (2, 2)→ (2, 3). We have tried
two other sequences: (1) the order in which the customers are stored in a solution,
i.e., (1, 1) → (1, 2) → (1, 3) → (2, 1) → (2, 2) → (2, 3) → (2, 4) in the illustra-
tion, and (2) the order of decreasing service times. We found that the alternating
sequence performed best among the three.
Starting with the first customer in the sequence, we identify a position on a
route in a different cluster in which the customer can be inserted in the cheapest way.
Instead of removing this customer completely from the longest route and inserting
it onto a shorter route in a different cluster, we merge the two clusters into one with
that customer as a connection. Then we apply the cluster balance subroutine to
the newly formed cluster. As shown in Figure 4.8, the filled squares represent three
depots and circles represent customers. In Figure 4.8(a), suppose the cluster on the
left with two routes contains the longest routes. If the customer represented by the
filled circle is to be inserted onto routes in the other cluster in the least cost way,
it will be inserted between the two customers represented by circles with a dash.
Instead of removing the filled customer, we merge the three routes to form a larger
cluster shown in Figure 4.8(b). This cluster may not be balanced, so we apply the
cluster balance subroutine, which may result in breaking up this cluster, as shown
in Figure 4.8(c).
If the objective function value decreases after balance is restored, the merge is
99
(a) Before merge
(b) Merged cluster
(c) Balance restored
Figure 4.8: Illustration of cluster merge
100
accepted and we continue with the local search on the new cluster with the longest
route; otherwise the move is rejected and we explore the possibility of splitting the
next customer in the sequence.
4.4.4 Perturbation
The perturbation technique, Ptb Split, used in this stage is the same as
Ptb NoSplit, except we use LS Split instead of LS NoSplit as the local search oper-
ator.
4.4.5 Satisfying the minimum delivery requirement
The solution produced at the end of the perturbation step may not satisfy the
minimum delivery requirements. In the final clean-up stage, we satisfy the minimum
requirement of all split customers by solving LP with the added constraints (4.21)
and (4.22) shown below.
Suppose route i serves a fraction p of customer l’s demand, and p ∈ (0, 1
2
f
]
,
i.e., p is less than or equal to half the minimum delivery fraction (denoted by f). We
add constraint (4.21) to LP, so that customer l is completely removed from route i.
s
(i)
l =
∑
j:(i,j)∈A(l)
xij −
∑
j:(j,i)∈A(l)
xji (4.21)
If p ∈ (1
2
f, f
)
, we add constraint (4.22) to LP, so that route i serves at least fraction
101
R15 : 120
R14 : 120
R16 : 120
U15,14
U14,15
U14,16
U16,14
U15,16
U16,15
U14,15 + U14,16 ≤ 20
U15,14 + U15,16 ≤ 20
U16,14 + U16,15 ≤ 20
Figure 4.9: Large minimum delivery fraction causing infeasibility
f of customer l. ∑
j:(j,i)∈A(l)
xji −
∑
j:(i,j)∈A(l)
xij ≥ f ∗ tl − s(i)l (4.22)
Occasionally, these two constraints may render LP infeasible because f is
large and the split customer is serviced by three or more routes. We illustrate this
in Figure 4.9. In this situation, we revert to the non-split feasible solution at the
end of Stage 1 as the final solution.
Suppose we have a cluster before the final clean-up stage shown in Figure 4.9.
There are three routes of duration 120, each serving one-third of a customer whose
total demand is 60. The minimum delivery fraction f = 0.35. Since R14 delivers
only one-third of the customer demand which is greater than 1
2
f = 0.175, we add
constraint U15,14 + U16,14 − U14,15 − U14,16 ≥ 60× 0.35− 20 = 1. Solving LP results
in a cluster with durations of R14 = 121, R15 = 119.5, and R16 = 119.5, i.e., one
unit of service time is transferred from R15 and R16 to R14. With this arrangement,
R15 serves 19.5 units of service time or 0.325 > 0.175 of the customer’s demand, so
102
we add the constraint U14,15 + U16,15 − U15,14 − U15,16 ≥ 1 to LP. Solving LP results
in a cluster with the durations of R14 = 121, R15 = 121, and R16 = 118, i.e., two
units of service time is transferred from R16 to R14 and R15. With this arrangement,
R16 serves 18 units of service time or 0.3 > 0.175 of the customer’s demand, so we
add the constraint U14,16 + U15,16 − U16,14 − U16,15 ≥ 1 to LP. However, the three
constraints that we have added define an infeasible region.
4.5 Computational results
In this section, we present the computational results of our algorithm on three
sets of instances. The first set of 43 instances (with no service times) is from Wang et
al. [94]. The data can be found in Appendix B. We want to show that modified MD
produces better results on these instances than MD. The second set of 21 instances
was generated by modifying the instances in Chen et al. [25]. The data can be
found in Appendix C. Taking advantage of the geometric symmetry, we develop a
simple greedy algorithm to obtain good min-max solutions that can be compared
to the solutions produced by MDS. The third set of 258 instances was generated
based on the first set. We analyze the savings from split service and the patterns
of splits as we vary the average customer service time and the average number of
customers served by one route. In all instances, we assume that the travel time is
equal in magnitude to the Euclidean distance. All experiments were done with a
CPU of 2.20 GHz and RAM of 4.0 GB. The proposed method is coded in C++.
103
4.5.1 Test Set 1
The results of the modified MD algorithm (denoted by MMD) on the first set of
43 instances are shown in Table 4.7. The first column gives the problem identifiers.
The second to fourth columns describe the size of data. The fifth and sixth column
give the results of MD. The running times of instances MM21 to MM43 are not
reported in [94]. The seventh and the eighth columns give the results of MMD. The
objective function value for MMD is the best of four runs with λ = 0.3, 0.6, 0.8,
and 1.2. The running time for MMD is the sum of the running times of the four
runs. The last column gives the percentage improvement of MMD over MD. The
average improvement on the 43 instances is about 2%, but the magnitude varies
depending on the instance. The largest improvement is on MM31 (11.41%). There
are six instances with negative improvement. This may be due to the parameter λ
introduced in LS NoSplit and the initial random perturbation angles. The sum of
the running times of the first 20 instances for MMD is 6.8 times that of MD, but
we point out that MMD with different λ values can run in parallel if the machine
has four cores, so that the running time can be reduced significantly. Wang et
al. [94] divided 40 of the instances (MM1, MM6, and MM7 excluded) into four
groups according to the distribution of customer locations and the customer-to-
vehicle ratio. The average improvement of MMD over MD for each group is shown
in Table 4.8. MMD produces the largest improvement when the customers are not
uniformly distributed and the customer-to-vehicle ratio is small.
104
Table 4.7: Results of MD and MMD on Test Set 1
Size of data MD MMD
Number Number Number of Objective Objective Improvement of
Problem of of vehicles function Running function Running MMD
identifier depots customers per depot value time (s) value time (s) over MD (%)
MM1 3 10 1 170.91 1 170.91 7 0.00
MM2 10 200 1 130.80 11 128.25 97 1.95
MM3 5 200 1 238.94 18 236.14 147 1.17
MM4 5 395 1 479.68 18 468.54 2058 2.32
MM5 10 390 1 315.89 33 312.19 408 1.17
MM6 4 400 1 82.23 44.0 81.74 124 0.59
MM7 1 25 3 189.02 2 189.01 15 0.00
MM8 3 200 2 217.38 30 208.47 321 4.10
MM9 4 400 3, 2, 2, 1 153.74 112 150.14 760 2.34
MM10 5 50 1 197.39 4 194.31 37 1.56
MM11 10 100 1 102.35 3 102.35 23 0.00
MM12 15 100 1 78.90 3 73.80 28 6.47
MM13 10 150 1 121.87 5 121.07 58 0.66
MM14 10 200 1 134.61 8 133.13 87 1.10
MM15 15 200 1 99.81 5 96.23 76 3.58
MM16 20 500 1 101.68 23 99.59 201 2.06
MM17 2 350 2 248.59 235 249.68 2478 -0.44
MM18 2 400 1, 3 390.16 619 394.28 1953 -1.06
MM19 3 400 1, 1, 2 365.66 616 359.19 3200 1.77
MM20 3 500 1, 2, 2 339.92 360 333.99 2571 1.75
MM21 10 400 1 259.14 - 253.93 575 2.01
MM22 10 200 1 400.60 - 400.59 1471 0.00
MM23 5 50 1 374.97 - 376.40 463 -0.38
MM24 15 200 1 204.00 - 200.62 542 1.66
MM25 20 500 1 272.61 - 270.75 821 0.68
MM26 5 150 2 364.56 - 361.52 825 0.83
MM27 4 400 3 290.37 - 291.16 447 -0.27
MM28 5 350 3 354.31 - 354.34 2581 -0.01
MM29 3 200 2 364.01 - 368.96 670 -1.36
MM30 5 250 1 140.34 - 136.12 496 3.01
MM31 3 250 1 124.32 - 110.13 193 11.41
MM32 3 200 1 103.15 - 98.85 43 4.17
MM33 8 400 1 97.56 - 94.61 116 3.02
MM34 6 400 1 84.64 - 83.62 329 1.20
MM35 2 300 2 109.30 - 102.98 99 5.78
MM36 2 250 2, 3 155.99 - 145.07 1200 7.00
MM37 3 500 1, 2, 2 156.41 - 150.69 137 3.65
MM38 2 350 2 155.46 - 154.62 328 0.54
MM39 5 250 1 209.85 - 209.85 518 0.00
MM40 3 200 1 243.47 - 241.10 897 0.97
MM41 3 500 2 257.16 - 244.90 2174 4.77
MM42 2 450 2, 3 367.44 - 345.35 2651 6.01
MM43 2 350 2 375.16 - 365.21 1122 2.65
Average 2.06
105
Table 4.8: Average improvement of MMD over MD
Distribution of customer locations Customer-to-vehicle ratio Average improvement (%)
Uniform Small 2.26
Uniform Large 0.43
Non-uniform Small 3.87
Non-uniform Large 2.21
4.5.2 Test Set 2
4.5.2.1 Data generation
In the VRP literature, some benchmark test instances are generated with
symmetric customer locations, so that estimated solutions with high quality can be
visualized using geometric considerations. In particular, Chen et al. [25] provided
SDVRP instances with customers located on concentric circles centered at the depot.
By varying the number of customers per circle (denoted by A) and the number of
circles (denoted by B), the authors generated 21 test instances. In Figures 4.10(a)
and 4.10(b), we show instance SD1, with A = 4 and B = 2, and instance SD10,
with A = 16 and B = 4.
We modify the 21 instances from [25] and produce min-max SDVRP instances.
The parameters A and B are the same for the 21 instances generated in [25]. The
difference in the radius between adjacent circles is 100, and the customer service time
is 100. There are 3
2
A vehicles stationed at the depot (A is even in each instance).
106
0 1
2
3
4
5
6
7
8
(a) SD1
0 1
2
3
456
7
8
9
10
11
12 13 14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
(b) SD10
Figure 4.10: Example of instances
0 1
16
17
32
33
48
49
64
(a) A section of SD10
0 1
16
17
32
33
48
49
64
R1
R2
R3
(b) Estimated solution
Figure 4.11: Sub-problem of SD10 and its estimated solution
4.5.2.2 Estimated solution
A simple heuristic approach is used to find solutions to the 21 problems. We
partition the region into A
2
equal sectors. Each sector has 2B customers located
on two rays at an angle of θ = 360
◦
A
that emanate from the depot. There are three
vehicles. We solve the sub-problem over the sector. Figure 4.11(a) shows one sector
obtained from SD10. There are eight customers, four on each of the two rays from
the depot, and three routes. The angle between the two rays is 22.5◦.
107
Table 4.9: Algorithm to estimate the optimal solution
Algorithm 7
Denote the estimated optimal objective function value by Ze
For k = 1 to B
travel time of R1, TR(R1) = 200B
travel time of R3, TR(R3) = 200B
travel time of R2, TR(R1) = 200k(1 + sin(
θ
2
))
total service time, S = 200B
average duration, Dave = 200B +
200k
3
(1 + sin( θ
2
))
Dmax = 300B
Dmin = 300B − 100k
If Davg < Dmin
Z
(k)
e = Dmin
Elseif Dmin ≤ Davg ≤ Dmax
Z
(k)
e = Davg
Else
Z
(k)
e = 3Davg − 2Dmax
Endif
Endfor
Pick the k with the smallest Z
(k)
e which gives the best estimated solution
In the estimated solution to the sub-problem, the first (third) route travels
along the first (second) ray until it reaches the farthest customer, and returns to the
depot along the same path, serving some customers fully or partly along the way.
The second route travels along the first ray until it reaches the kth customer, then
visits the kth customer on the second ray, and returns to the depot along the second
ray. We expect that the first and the third routes have equal duration, which is
not less than the duration of the second route. The number k and the estimated
solution is determined by the algorithm in Table 4.9. In Figure 4.11(b), we show
the routes of the estimated solution to the sub-problem of SD10 with k = 2.
The estimated solutions are given in Table 4.10. The first column gives the
problem identifier. The second to fifth columns describe each instance. A is the
108
number of customers per circle, B is the number of concentric circles, n is the total
number of customers, and m is the number of routes. The sixth to ninth columns
describe the the estimated solutions. The Max column gives the duration of the
longest route, i.e., the objective function value in the estimated solution. The Min
column gives the duration of the shortest route. The Min/Max column gives the
ratio of shortest duration to the longest duration. Because of symmetry, there may
be more than one longest route in the estimated solution. The number of routes with
duration equal to the objective function value is given in the column with heading
l.
Next, we show that the estimated solutions of the first 12 instances and the
sixteenth instance are, in fact, optimal. The remaining estimated solutions (except
for SD21) are all within 2% of optimality. For SD21, the estimated solution is within
6.51% of optimality.
4.5.2.3 Mathematical model and exact solutions for Test Set 2
In this section, we formulate a mixed integer program (MIP) to solve instances
SD1 to SD21. We prove that the estimated solutions to 13 instances (SD1 to SD12
and SD16) are optimal. Another seven estimated solutions are within 2% of opti-
mality.
109
Table 4.10: Estimated solutions
Problem A B n m Max Min Min/Max l
SD1 4 2 8 6 513.81 513.81 1.00 6
SD2 4 4 16 6 1027.61 1027.61 1.00 6
SD3 8 2 16 12 500.00 476.54 0.95 8
SD4 12 2 24 18 500.00 451.76 0.90 12
SD5 8 4 32 12 1000.00 953.07 0.95 8
SD6 16 2 32 24 500.00 439.02 0.88 16
SD7 4 10 40 6 2569.04 2569.04 1.00 6
SD8 4 12 48 6 3082.84 3082.84 1.00 6
SD9 12 4 48 18 1000.00 903.53 0.90 12
SD10 16 4 64 24 1000.00 878.04 0.88 16
SD11 4 20 80 6 5100.00 4872.79 0.96 4
SD12 8 10 80 12 2500.00 2382.68 0.95 8
SD13 8 12 96 12 3000.00 2859.22 0.95 8
SD14 12 10 120 18 2500.00 2258.82 0.90 12
SD15 12 12 144 18 2987.45 2987.45 1.00 18
SD16 72 2 144 108 500.00 408.72 0.82 72
SD17 8 20 160 12 5000.00 4765.37 0.95 8
SD18 16 10 160 24 2478.04 2478.04 1.00 24
SD19 16 12 192 24 2957.71 2957.71 1.00 24
SD20 12 20 240 18 4923.13 4923.13 1.00 18
SD21 72 4 288 108 1000.00 817.45 0.82 72
A: number of customers per circle
B: number of concentric circles
n: total number of customers
m: number of routes
l: number of longest routes
110
(MIP) min z (4.23)
s.t.z ≥
∑
i,j∈I
cijx
(k)
ij +
∑
i∈I
ckixki +
∑
i∈I
cikxik +
∑
i∈I
s
(k)
i ∀k ∈ K (4.24)
y
(k)
i =
∑
j∈I
x
(k)
ji + xki ∀i ∈ I,∀k ∈ K (4.25)
1 =
∑
i∈I
xki ∀k ∈ K (4.26)
0 =
∑
j∈I
x
(k)
ji −
∑
j∈I
x
(k)
ij + xki − xik ∀i ∈ I,∀k ∈ K (4.27)
ti =
∑
k∈K
s
(k)
i ∀i ∈ I (4.28)
s
(k)
i ≤ tiy(k)i ∀i ∈ I,∀k ∈ K (4.29)
0 = x
(k)
ii ∀i ∈ I,∀k ∈ K (4.30)∑
i∈I
∑
j∈I
x
(k)
ij ≤ |S| − 1 ∀S ⊆ I, S 6= ∅,∀k ∈ K (4.31)
xki ∈ {0, 1}, xik ∈ {0, 1}, y(k)i ∈ {0, 1},∀i ∈ I,∀k ∈ K (4.32)
x
(k)
ij ∈ {0, 1} ∀i ∈ I,∀j ∈ I,∀k ∈ K (4.33)
s
(k)
i ≥ 0 ∀i ∈ I,∀k ∈ K (4.34)
z ≥ 0 (4.35)
Let I denote the set of customers and K denote the set of routes. The decision
variables are xki, xik, y
(k)
i , x
(k)
ij , s
(k)
i , and z. xki (or xik) is binary and equals 1 if and
only if customer i is the first (or last) customer on route k. y
(k)
i is binary and equals
1 if and only if customer i is served on route k. x
(k)
ij is binary and equals 1 if and
111
only if customer i proceeds customer j on route k. s
(k)
i is continuous and determines
the amount of service time delivered to customer i by route k. z is continuous and
is the duration of the longest route.
The objective function (4.23) minimizes the maximum duration. In constraints
(4.24), the parameters cij, cki, and cik denote the travel times from customer i to
j, from the depot to customer i, and from customer i to the depot. The first
three terms on the right-hand side of the inequality sum to the travel time of route
k, and the last term is the service time on route k. Constraints (4.24) together
with the minimization objective ensure that z is the duration of the longest route.
Constraints (4.25) imply that customer i is served (partly or fully) by route k if
and only if there is an incoming arc to i traveled by route k. Constraints (4.26)
imply that on every route, there is exactly one customer that is visited immediately
after the vehicle leaves the depot. In constraints (4.27), for every customer, the
number of incoming arcs of route k is equal to the number of outgoing arcs of route
k. Constraints (4.28) ensure that every customer is fully served. In constraints
(4.29), customer i receives some service from route k only if the customer is on the
route. Constraints (4.30) eliminate self loops. Constraints (4.31) are the sub-tour
elimination constraints. Constraints (4.32) to (4.35) define the variable types and
bounds. Note that (MIP) applies to the multi-depot problem as well.
We add valid inequalities to strengthen the formulation. Some of the inequal-
ities apply to general instances, and the other inequalities apply to only specific
instances.
First, from Corollary 1, every edge linking two customers is traversed at most
112
Solution 1 Solution 2
Vehicles Order of Customers Vehicles Order of Customers
1 5, 6, 7, 8 1 1, 2, 3, 4
2 1, 2, 3, 4 2 5, 6, 7, 8
Table 4.11: Two Symmetric Solutions
once, in either direction. We add
∑
k∈K
x
(k)
ij + x
(k)
ji ≤ 1 ∀i ∈ I,∀j ∈ I (4.36)
Second, we exploit the symmetry of the model. We realized that exchanging
the assignment of customers between any two vehicles produces an alternative solu-
tion. This increases the running time because the search tree spends time identifying
these solutions. To remove this type of symmetry, we introduce the following valid
inequalities:
∑
i∈I
ixki ≤
∑
i∈I
ixk+1,i ∀k ∈ {1, 2, . . . , K − 1} (4.37)
Essentially, this set of valid inequalities enforces a lexicographic order on the vehicles.
The index of the first customer on route k + 1 is at least as big as that of the first
customer on route k where k takes on values from 1 to K−1. Consider the example
in Table 4.11 where both solutions are feasible without constraints (4.37). After
enforcing this set of inequalities, only Solution 2 is feasible.
The second type of symmetry for a given route comes from switching the order
in which customers are visited. This is an alternative solution because the travel
113
cost is symmetric. We introduce the following valid inequalities:
∑
i∈I
ixki ≤
∑
i∈I
ixik ∀k ∈ K (4.38)
Here, we enforce a lexicographic order on each route such that the index of the last
customer is at least as large as that of the first customer. For example, Solution 2
in Table 4.11 could also have route 2 with the following order of customers: 8, 7, 6,
5. With the set of inequalities (4.38), 5, 6, 7, 8 is the only feasible order. However,
we cannot have this set of inequalities (4.38) if the travel costs are asymmetric.
Next, we present the third set of valid inequalities. Let S be a subset of I
and δ(S) = {(i, j) : i ∈ S, j /∈ S} denote the set of arcs leaving S. The sub-
tour elimination constraints are enough to prevent sub-tours in the solution. To
strengthen the formulation, we add the following set of inequalities:
∑
k∈K
∑
(i,j)∈δ(S)
x
(k)
ij ≥ 1 ∀S ⊂ I, |S| ≥ 2, (4.39)
where |S| is the cardinality of the set S. We refer to this set of inequalities as the
connectivity cuts. In order to ensure the connectivity of the solution, we need to
separate the sub-tour elimination constraints and the connectivity cuts. For the
separation of the sub-tour elimination constraints, we find connected components in
the supported graph and add violated constraints if there is more than one compo-
nent. For the connectivity cuts, we solve a maximum flow problem from each vertex
to the depot. We note that the sub-tour elimination constraints are separated for
114
integer solutions. The connectivity cuts are only separated in the root node for
fractional solutions.
For the fourth set of valid inequalities, we use the estimated solutions to con-
struct additional valid inequalities. For example, if the objective value of the esti-
mated solution is 500, we know that some pair of customers cannot be served on the
same route if the optimal objective function value of the traveling salesman problem
including three nodes, two customers and the depot is greater than 500. Similarly,
we prevent some groups of three customers from being served on the same route.
Therefore, we have constraints (4.40) and (4.41), where F1 (or F2) is the set of cus-
tomer pairs (or groups of three customers) that are not served on the same route in
the optimal solution.
y
(k)
i + y
(k)
j ≤ 1 ∀(i, j) ∈ F1 (4.40)
y
(k)
i + y
(k)
j + y
(k)
l ≤ 2 ∀k ∈ K, ∀(i, j, l) ∈ F2 (4.41)
Furthermore, if we regard F1 as the edge set of an auxiliary graph whose
vertices are I, and identify a clique in the graph, additional equality constraints
on y
(k)
i can be constructed. For example, as long as F1 6= ∅ , we have a clique
of two vertices. For example, if (i, j) ∈ F1, we can add four equality constraints,
y
(k1)
i = 1, y
(k2)
i = 0, y
(k1)
j = 0, y
(k2)
j = 1, fixing some k1, k2 ∈ K and k1 6= k2. For
these 21 instances, we find the maximum cardinality clique in the graph. If a clique
(denoted by CLQ) of customers, i1, i2, ..., i|CLQ|, is found, we add |CLQ|2 equality
115
Table 4.12: Results for Test Set 2
Problem Estimate
Shortest Two
Outermost
Customers
Slack Two
Outermost
Customers
Possible Service Gap (%)
SD1 513.81 682.84 0.00 113.81 0.00
SD2 1027.61 1365.69 0.00 227.61 0.00
SD3 500.00 553.07 0.00 100.00 0.00
SD4 500.00 503.53 0.00 100.00 0.00
SD5 1000.00 1106.15 0.00 200.00 0.00
SD6 500.00 478.04 21.96 100.00 0.00
SD7 2569.04 3414.21 0.00 569.04 0.00
SD8 3082.84 4097.06 0.00 682.84 0.00
SD9 1000.00 1007.06 0.00 200.00 0.00
SD10 1000.00 956.07 43.93 200.00 0.00
SD11 5100.00 6828.43 0.00 1100.00 0.00
SD12 2500.00 2765.37 0.00 500.00 0.00
SD13 3000.00 3318.44 0.00 600.00 0.95
SD14 2500.00 2517.64 0.00 500.00 1.87
SD15 2987.45 3021.17 0.00 587.45 1.56
SD16 500.00 417.45 82.55 100.00 0.00
SD17 5000.00 5530.73 0.00 1000 .00 1.16
SD18 2478.04 2390.18 87.86 478.04 1.99
SD19 2957.71 2868.22 89.49 557.71 1.40
SD20 4923.13 5035.28 0.00 923.13 0.62
SD21 1000.00 834.90 165.10 200.00 6.51
constraints. We fix |CLQ| distinct routes, k1, k2, ..., k|CLQ| and include:
y
(kq)
ip
=

1 if p = q
0 otherwise
∀p, q ∈ {1, 2, . . . , |CLQ|} (4.42)
in our model.
Finally, we make the following observations that allow us to add valid cuts
to instances in Test Set 2. We refer to the route that serves at least one of the
outermost customers as an outermost route.
116
Observation 1. From SD1 to SD20, there exists an optimal solution which has A
outermost routes (A is the number of customers per circle as shown in Table 4.10).
Proof. To serve the outermost customers, we can send out one vehicle for each
outermost customer. We have A outermost routes.
First, we will show that we need at least A outermost routes. For each instance,
we calculate the shortest possible distance for an outermost route. This can be
found in the column Shortest Two Outermost Customers in Table 4.12. For most
instances, this distance is longer than the estimated solution which is indicated as 0
in the column Slack Two Outermost Customers. There are six instances that have
positive slack. Except for SD21, the slack amount is small so that we have to use at
least three vehicles to serve two outermost customers if each vehicle serves at least
two outermost customers. So, there are at least A outermost routes.
Then, we have at most 1
2
A vehicles remaining. All outermost customers should
be satisfied already, so, we would no longer visit any outermost customers. Thus,
we do not need to assign any outermost routes.
Observation 2. From SD1 to SD20, there exists an optimal solution where the
travel time of each outermost route is 200×B (B is the number of concentric circles
as shown in Table 4.10).
Proof. In order to make the best use of these outermost routes, we can have all
outermost routes with a travel time of 200×B because the travel time between two
adjacent customers is 100. The travel time from the depot to the nearest customer
is also 100. In this way, the outermost route has the smallest possible travel time.
117
This allows us to assign each outermost route the largest possible amount of service
time before an outermost route exceeds the pre-specified bound. The total service
time is A×B× 100 because there are A×B customers and each has a service time
of 100. Then, the total service time of the remaining 1
2
A vehicles is the minimum
possible. Thus, the resulting solution is optimal.
Let O denote the set of outermost customers. Observation 2 tells us that the
vehicle on the outermost route travels along the ray. So, we can visit all customers
in an outermost route in the path leaving the depot because the travel costs are
symmetric. This leads to the following set of inequalities for SD1 to SD20 of Test
Set 2:
∑
k∈K
xik = 1 ∀i ∈ O (4.43)
We note that this set of inequalities (4.43) dominates constraint set (4.42).
We label a ray by the smallest index of those customers on it. Thus, in SD1,
ray 1 has customers 1 and 5. In SD10, ray 1 has customers 1, 17, 33, and 49. We
refer to customer rays 1 to A
2
as partition 1 and customer rays A
2
+1 to A as partition
2.
Observation 3. From SD1 to SD20, we can solve each instance by focusing on
partition 1 and 3A
4
vehicles.
Proof. Feasibility is satisfied by the geometric symmetry. We can mimic the routes
for customer rays A
2
+ 1 to A.
118
For optimality, we have A rays which is a multiplier of four. Hence, 3A
2
is an
even number. The number of vehicles (denoted by v) served in partition 1 should be
equal to the number in partition 2. v is an even number and the number of vehicles
that serves both partitions is also an even number. Furthermore, there exists an
optimal solution where no vehicles serve both partition 1 and partition 2 at the same
time. We call this a non-crossing solution. Those vehicles serving both partitions
need to travel across the space between ray 1 and ray A and the one between A
2
and A
2
+ 1 in order to serve all customers. Thus, the total travel time is not smaller
than that of the non-crossing solution. Hence, the non-crossing solution is at least
as good as the solution with crossing given that the total service time is fixed.
Observation 4. For SD21, 934.90 is a valid lower bound on the optimal value.
Proof. The objective value of the best found solution is 969.98 for SD21. If we
assign each outermost route one outermost customer, then the optimal value is 1000
which can be verified by solving the IP formulation. It exceeds the incumbent value
of 969.98. Thus, we cannot have an optimal solution where each outermost route
serves only one outermost customer.
Therefore, we have at least one outermost route visiting two outermost cus-
tomers. The smallest possible traveling time is 834.90. The service time is at
least 100 because we have less than 72 outermost routes given that we have some
routes visiting more than one outermost customer. Therefore, the lower bound is
934.90.
MIP was solved using CPLEX 12.6.0 with a time limit of two hours. The exact
119
solver was able to find optimal solutions to the first 12 instances and the sixteenth
instance. All 13 optimal solutions are the same as the estimated solutions in Section
4.5.2.2. The exact solver shows that the estimated solution to the largest instance
(SD21) is within 6.51% of optimality. In addition, for the the largest instance
(SD21), the best solution found by the exact solver has an objective function value of
969.98 which is within 3.62% of optimality. The estimated solutions to the remaining
seven instances are all within 2% of optimality.
4.5.2.4 MDS solution
We tested MDS with 16 different λ values from 0.0 to 1.5 and chose λ =
0.3, 0.6, 0.8, and 1.2 based on results from the 21 instances. The solutions from
MDS are presented in Table 4.13. The first column gives the problem identifiers. The
second and the third columns give the number of customers and routes. The fourth
column gives the known optimal solutions. The fifth column gives our estimated
solutions. The sixth and seventh columns give the best solutions of four runs of
MDS with λ = 0.3, 0.6, 0.8, and 1.2. The running time is the sum of the times of
the four runs. The eighth column gives the percentage gaps of the MDS solutions
with respect to the estimated solutions. The average gap is 1.5% on the 21 instances.
The ninth column gives the best solution of the 16 runs of MDS with different λ
values. Six solutions were not generated by the four specified λ values (0.3, 0.6, 0.8,
1.2). The tenth column shows that the average gap from the estimated solution is
1.31%.
120
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4.5.3 Test Set 3
The 43 instances supplied by Wang et al. [94] have both uniform and non-
uniform distributions of customer locations. The number of customers in an instance
ranges from 10 to 500, and the number of depots from 3 to 20. For each instance,
we generate six instances with a service time requirement according to the following
procedure, while keeping the locations of customers and depots unchanged.
1. Supply every customer with a service time uniformly distributed over (1, 10).
This is the short service time scenario.
2. Multiply every service time by 10 to construct the medium service time sce-
nario; if a customer requires a service time of 1.5 in the short service scenario,
the requirement is 15 in the median service scenario.
3. Multiply every service time by 100 to construct the long service time scenario;
if a customer requires a service time of 1.5 in the short service scenario, the
requirement is 150 in the long service scenario.
4. For each of the three instances, we double the number of vehicles at each
depot. Therefore, we derived six instances from one of the 43 instances in
Wang et al. [94].
There are 258 instances in total with 86 instances in each service time category.
We can categorize the instances according to the customer-to-vehicle ratio, denoted
by rctv, which indicates the average number of customers per route in a solution.
122
Table 4.14: Savings (in %) from the non-split solutions
Short route Medium route Long route Average
Short service 1.07 0.48 0.24 0.62
Medium service 2.94 1.08 0.34 1.50
Long service 2.74 0.79 0.19 1.29
Average 2.25 0.78 0.26 1.14
The short route scenario has rctv < 20 and there are 90 instances in this category.
The medium route scenario has 20 ≤ rctv < 50 and there are 90 instances in this
category. The long route scenario has 50 ≤ rctv ≤ 100 and there are 78 instances
in this category. Since there are no other procedures available for comparison, we
compare the solutions produced by MDS to the non-split solutions from MMD.
We show the savings from the non-split solutions in each scenario with no min-
imum delivery requirement in Table 4.14. From the second column to the fourth col-
umn, the customer-to-vehicle ratio increases. From the second row to the fourth row,
the service time increases. The average savings is given by (0.62 + 1.50 + 1.29)/3 =
1.14%, or by [90(2.25) + 90(0.78) + 78(0.26)]/258. We observe that the savings de-
creases as the average number of customers per route increases. This observation
is expected. The savings from the non-split solution comes from reducing the time
spent at a particular customer (the split customer). If there is a large number of
customers on a route, it is unlikely that reducing the time spent at just one customer
will result in a large percentage decrease in the total duration. The trend in percent-
age savings is less straightforward as we vary the service times. The results suggest
that instances with a medium level of service time produce the largest savings.
123
Table 4.15: Average savings (in %) from splitting with four minimum delivery frac-
tions and three service times
Minimum delivery fraction
0.0 0.1 0.2 0.3 0.4
Short service* 0.62 0.58 0.49 0.38 0.26
Medium service 1.50 1.35 1.05 0.74 0.39
Long service 1.29 1.06 0.69 0.42 0.22
Average 1.14 1.00 0.74 0.52 0.29
* 86 instances in each service time category
Table 4.16: Average savings (%) from splitting with four minimum delivery fractions
and three rctv values
Minimum delivery fraction
0.0 0.1 0.2 0.3 0.4
Small rctv
* 2.25 1.97 1.43 0.97 0.57
Medium rctv 0.78 0.70 0.55 0.39 0.21
Large rctv 0.26 0.22 0.18 0.11 0.07
Average 1.14 1.00 0.74 0.52 0.29
* 90, 90, 78 instances in the three rctv cate-
gories, respectively
In Tables 4.15 and 4.16, we give the average savings from splitting with min-
imum delivery fractions 0.0 to 0.4. The formats of the two tables are similar. The
first column specifies how the 258 test instances are grouped. Table 4.15 categorizes
the instances by the level of service time. Table 4.16 categorizes the instances by the
magnitude of the customer-to-vehicle ratio. The second to the sixth columns give
the average savings from splitting with minimum delivery fraction 0.0 to 0.4. The
bottom row gives the weighted average of the savings. In both tables, the savings
decreases as the minimum delivery requirement increases. We observe that medium
service times and smaller customer-to-vehicle ratios result in larger savings with all
minimum delivery fractions.
124
We also study how customers are split in the solutions. In general, customers
do not prefer multiple visits, and they will favor solutions with fewer splits and
splits into no more than two deliveries. In Table 4.17, we show the distribution of
the splits by the number of times a customer is visited. For example, the second
column shows that, with no minimum delivery amount, 84.77% of the splits results
in two services, and 0.43% of the splits results in five or more splits. As the minimum
delivery fraction increases, the total number of splits decreases from 1878 to 573.
The percentage of splits into two parts increases to 100% when the minimum delivery
fraction is 0.4.
When several vehicles visit a customer, one of them delivers the smallest
amount. In general, customers do not prefer very small deliveries, and they will
prefer a solution with a few large deliveries. In Table 4.18, we present the distri-
bution of splits by the smallest amount. For example, the second column shows
that, with no minimum delivery amount, 39.35% of the splits deliver less than 10%
of a customer’s demand. Only 10.92% of the splits have minimum delivery 40% to
50% of a customer’s demand. We observe that, for fractions 0.1 to 0.4, the largest
percentage occurs where the minimum delivery fraction falls. When the fraction is
0, 39.35% of the splits have the smallest delivery less than 10%. When the fraction
is 0.1, about half of the splits have the smallest delivery between 10% and 20%.
The running time depends on the level of service time used to generate the
instances. On average, the initialization with the modified MD, the local search,
and the perturbation constitute more than 95% of the running time. For the short
service time scenario, these three procedures take about 13.6 minutes on average for
125
Table 4.17: Split distribution (in %) by the number of times a customer receives
service
Minimum delivery fraction
0 0.1 0.2 0.3 0.4
Split into two 84.77 92.17 95.76 97.70 100.00
Split into three 13.37 7.42 4.24 2.30 0.00
Split into four 1.44 0.34 0.00 0.00 0.00
Split into five or more 0.43 0.07 0.00 0.00 0.00
Total number of splits 1878 1469 1155 868 573
Table 4.18: Split distribution (in %) by the smallest portion a customer receives
Minimum delivery fraction
0 0.1 0.2 0.3 0.4
< 10% 39.35 0.00 0.00 0.00 0.00
10% - 20% 23.59 48.06 0.00 0.00 0.00
20% - 30% 14.54 21.03 59.65 0.00 0.00
30%- 40% 11.61 15.86 19.57 74.54 0.00
40% - 50% 10.92 15.04 20.78 25.46 100.00
Total number of splits 1878 1469 1155 868 573
the 86 test instances. For the medium service time scenario, these three procedures
take about 8.3 minutes on average. For the long service time scenario, these three
procedures take about 3.6 minutes on average. We run MDS with λ = 0.3, 0.6, 0.8,
and 1.2 in serial, so the total running time is the sum of the times of the four runs.
4.6 Conclusions
We developed a heuristic procedure (MDS) to solve the min-max Split Delivery
Multi-Depot Vehicle Routing Problem with Minimum Service Time Requirement.
MDS has three stages. In the first stage, we improved an existing procedure to
initialize a good solution without any service splits. In the second stage, we explored
126
the opportunity to improve solutions by splitting service, but ignored the minimum
service time requirement. In the third stage, we applied a post-processor to ensure
the minimum service time requirement is met.
We tested MDS on three sets of instances. On the first set of 43 instances,
the first stage of MDS outperformed the existing procedure by 2% on average. The
second set of 21 instances have good estimated solutions. The solutions produced by
the first two stages of MDS are, on average, 1.5% away from the estimated solutions.
On the third set of 258 instances, we showed that the savings from splitting service
is more substantial when the average number of customers per route is small with
a medium level of average customer service time.
127
Chapter 5: The Vehicle Routing Problem with Drones
5.1 Introduction and motivation
The Vehicle Routing Problem (VRP) is a well-studied problem [45, 90]. In its
simplest form, it seeks to route a fleet of homogeneous vehicles to deliver identical
packages from a depot to a number of customer locations while minimizing the total
travel cost. Following recent advancements in drone technology, Amazon [12, 77],
DHL [35], Federal Express [14], and other large companies with an interest in package
delivery, have begun investigating the viability of incorporating drone delivery into
their commercial package delivery services.
Drone delivery (from trucks) would enable trucks to visit customers located
centrally on the route and drones to visit farther-away customers. In other words,
trucks would get ”close enough” to more distant customers and then dispatch drones.
Drone delivery could reduce the number of required trucks and drivers on the road.
Perhaps more significantly, drones might speed up delivery.
In 2013, Jeff Bezos, CEO of Amazon, expressed his desire to use drones to
offer delivery to Amazon’s elite customers within 30 minutes of ordering [82]. This
is a primary motivation for our work. Given Amazon’s focus on speed of delivery,
we think the most appropriate objective function here is to minimize the time until
128
the last delivery. However, since all vehicles have to return to the depot, we seek to
minimize the completion time. This is a good approximation to the time until last
delivery when the last customer is close to the depot.
To date, there has been very little research on drone delivery of packages from
trucks. Three recent papers are Murray and Chu [71], Agatz et al. [1], and Gambella
et al. [43]. All of these focus on developing computational techniques (either exact
or heuristic) for solving a variant of this problem. As far as we know, our paper is
the first to study the problem from a worst-case point of view. Given the emerging
status of drone and truck delivery technology, we think our results are especially
valuable. They indicate, in a quantitative way, that the maximal potential savings
relative to a traditional truck-based model to companies like Amazon and others
are very substantial. Actualizing even a fraction of the maximal potential savings
would likely justify the cost of adopting this technology.
The remainder of the chapter is organized as follows. In Section 5.2, we de-
scribe our problem in detail and give the common notation we used throughout the
chapter. In Section 5.3, we formulate and prove our main worst-case theorems for
the simple VRPD model. Next, in Section 5.4, we extend our model and prove three
additional results. Finally, in Section 5.5, we conclude the chapter and give some
directions of future work.
129
5.2 Problem description
Suppose there are n customers to be served by a homogeneous fleet of m trucks,
each carrying k drones. Every customer demands one parcel, which can be delivered
by either a truck or a drone. A truck has a capacity of C parcels and a drone can
carry at most one parcel while in the air. Further, we assume that the drone has
a battery life of U time units, which initially is unrestrictively large. (Later, in
Theorem 19, we explicitly consider a restrictive battery life U .) We assume that the
driver keeps a number of fully charged batteries on board and replacing a battery
is instantaneous. The speed of the drone is α times the speed of the truck, and
both the drone and the truck follow the same distance metric. More specifically, we
assume that the truck and drone must travel from a to b along the street network.
(Later, in Theorem 20, we relax this assumption so that the drone can travel as
the crow flies.) A drone launched from a truck must be picked up by the same
truck. The truck can dispatch and pick up a drone only at a node, i.e., the depot
or a customer location. The truck can continue serving customers after a drone is
dispatched and pick up the drone at, possibly, a different node. The vehicle (truck
or drone) that arrives at the pick-up node first has to wait for the other one. There
is no service time for a delivery. The objective is to minimize the completion time,
i.e., from the time the trucks are dispatched from the depot with the drones to the
time when the last truck or the last drone returns to the depot.
We will refer to this new vehicle routing problem as the Vehicle Routing Prob-
lem with Drones, denoted by VRPDm,α, where m is the number of trucks in the
130
fleet and α is the ratio of the drone speed to the truck speed. Common notation
used in the remainder of this paper is listed below:
• Z(P ): The optimal objective function value of problem P (e.g., TSP, VRPDm,α)
• Zf (P ): The objective function value of a feasible solution to the problem P
(the feasible solution will be specified whenever the notation is used)
• Lr: The length of route r
• T vehr : The travel time by vehicle veh (veh=trc for truck, and veh=drn for
drone) on route r
• W vehr : The waiting time by vehicle veh on route r
• Dvehr = T vehr +W vehr : The duration of route r by vehicle veh.
5.3 Main results
Before a company like Amazon commits to a delivery strategy predicated on
the utilization of drones, it might want to know the answer to a key question: At
maximum, how much time could be saved, in the best case, using trucks and drones
vs. using trucks only? If we look at this question from another angle, it becomes:
How much longer will deliveries take with trucks only? This is commonly referred
to as worst-case analysis.
In this section, our goal is to provide theoretical bounds on the benefit from
using drones. In each of the theorems presented, we compare two related problems
Pt and Ptd. The two problems have the same set of customers, but different fleets.
131
In Pt, the fleet consists of trucks only. In Ptd, the fleet consists of trucks and drones.
The fleet in Ptd can serve the customers faster (due to parallelization). That is, we
expect Z(Ptd) ≤ Z(Pt). We want to determine the lowest upper bound on the ratio
Z(Pt)
Z(Ptd)
. For example, in the theorem below, we compare the TSP (traveling salesman
problem) with VRPD1,1.
Theorem 12. If the triangle inequality is valid,
Z(TSP)
Z(VRPD1,1)
≤ k + 1,
and the bound is tight.
Remark 6. Theorem 12 is a special case of later theorems; nonetheless, we present
a proof here because it serves as an easy-to-follow template for the other proofs. We
remind the reader that k is the number of drones per truck throughout this paper.
Proof of Theorem 12. We start with the optimal VRPD1,1 solution, and construct
a closed (not necessarily simple) walk of all the nodes. We then convert the closed
walk to a feasible TSP solution with bounded duration.
A VRPD1,1 solution can be decomposed into k+1 routes: one truck route and
k drone routes. Figures 5.1 and 5.2 illustrate the decomposition of a solution with
k = 2. The square labeled 0 represents the depot and the eight circles labeled 1 to
8 represent the customers. The black line represents the path followed by the truck
and the red and blue lines are paths followed by the two drones, respectively. The
dashed red (or blue) lines are paths of the drone while in the air and the solid red
132
(or blue) lines are paths of the drone while it is on the truck. Therefore, the red
drone is launched from the truck at customer 1 to serve customer 2, and picked up
at customer 5 where it is immediately launched again to serve customer 7. The red
drone is finally picked up at customer 4 and returns to the depot with the truck.
The blue drone is dispatched from the depot to serve customer 8 and picked up at
customer 4. This VRPD solution can be decomposed into three routes as shown in
Figure 5.2. The truck route is shown in Figure 5.2(a). Its duration is the sum of
the travel time of cycle 0 → 1 → 6 → 5 → 3 → 4 → 0 and the waiting time at
customer 5. The red drone route is shown in Figure 5.2(b). Its duration is the sum
of the travel time of cycle 0 → 1 → 2 → 5 → 7 → 4 → 0 and the waiting time at
customer 4. The blue drone route is shown in Figure 5.2(c). Its duration is the sum
of the travel time of cycle 0→ 8→ 4→ 0 and the waiting time at customer 4. All
three routes have the same duration, which is equal to the objective function value.
Given an optimal VRPD1,1 solution, we decompose it into k + 1 routes, and
construct a giant route, denoted by R, that traverses the k + 1 routes, one after
another. In the example shown in Figure 5.1, the sequence that the nodes are
traversed in R is 0 → 1 → 6 → 5 → 3 → 4 → 0 → 1 → 2 → 5 → 7 → 4 → 0 →
8 → 4 → 0. Every node is visited at least once in R and some are visited multiple
times. In particular, the depot is always visited k + 2 times, if we include both the
start and the end of the route. We have the travel time of R,
T trcR ≤ DtrcR = (k + 1)Z(VRPD1,1). (5.1)
133
01 2
34
5
6
7
8
Truck waits
Drones wait
Figure 5.1: A VRPD1,1 solution with k = 2
0
1
34
5
6
Truck waits
(a) Truck route
0
1 2
4
5
7
Drone waits
(b) Red drone route
0
48
Drone waits
(c) Blue drone route
Figure 5.2: Decomposition of a VRPD1,1 solution
134
01 2
34
5
6
7
8
Figure 5.3: A feasible TSP solution from the optimal VRPD solution
A feasible TSP solution can be obtained from R by deleting repeated customers and
keeping depots only at the beginning and the end. For the example shown in Figure
5.1, the feasible TSP solution is 0 → 1 → 6 → 5 → 3 → 4 → 2 → 7 → 8 → 0 as
shown in Figure 5.3. Since the triangle inequality is valid, we must have Zf (TSP) ≤
T trcR . Therefore,
Z(TSP) ≤ Zf (TSP) ≤ (k + 1)Z(VRPD1,1) (5.2)
or
Z(TSP)
Z(VRPD1,1)
≤ (k + 1). (5.3)
To show that the bound is tight, we consider an example with k+1 customers,
135
0c0
c1
c2
(2) (2)
(2)
(1)
(1)(1)
(a) Problem
0
c0
c1
c2
(b) Feasible VRPD1,1 solu-
tion
0
c0
c1
c2
(c) Optimal TSP solution
Figure 5.4: A worst-case VRPD1,1 example with k = 2
c0, c1, . . . , ck. All customers are located at a distance 1 from the depot. The distance
between every pair of customers is 2. (See Figure 5.4(a) for the case with k = 2.
The distances are given in parentheses next to the edges.) Both the truck and the
drones travel at a speed of 1. The capacity of the truck C = k + 1 and the battery
life of a drone is 2 time units. An optimal TSP solution visits the customers c0 to ck
in sequence, and Z(TSP) = 2(k + 1). A feasible VRPD1,1 solution serves customer
c0 with the truck and serves each of the remaining customers using a drone, which is
launched at the depot and picked up at the depot. All vehicles return to the depot
at the same time with Zf (VRPD1,1) = 2. In this example,
Z(TSP)
Z(VRPD1,1)
≥ Z(TSP)
Zf (VRPD1,1)
=
2(k + 1)
2
= k + 1. (5.4)
136
Theorem 13. If the triangle inequality is valid and α ≥ 1,
Z(TSP)
Z(VRPD1,α)
≤ αk + 1,
and the bound is tight.
Remark 7. Theorem 13 uses the same construction procedure as in Theorem 12
and generalizes Theorem 12.
Proof of Theorem 13. Without loss of generality, we assume the truck speed is 1
and the drone speed is α (since we are interested in only the ratio of the objective
function values). As in our proof of of Theorem 12, we decompose an optimal
VRPD1,α solution into k + 1 routes and traverse them one after another to form a
giant route R. If R is traveled by the truck, the travel time
T trcR =
k∑
j=0
T trcrj = T
trc
r0
+
k∑
j=1
Lrj
1
≤ T trcr0 +
k∑
j=1
αT drnrj . (5.5)
In equation (5.5), we have the length of a drone route Lrj ≤ αT drnrj , but not Lrj =
αT drnrj , because some part of Lrj is traveled at the truck speed. But since α ≥ 1, the
inequality always holds. After we remove the revisited customers and depots in the
middle of R, because of the triangle inequality, we obtain Zf (TSP). This yields
Z(TSP) ≤ Zf (TSP) ≤ T trcR ≤ T trcr0 +
k∑
j=1
αT drnrj . (5.6)
137
Therefore,
Z(VRPD1,α) = max{Dtrcr0 , Ddrnr1 , . . . , Ddrnrk } (5.7)
≥ max{T trcr0 , T drnr1 , . . . , T drnrk } (5.8)
≥ 1
αk + 1
(T trcr0 +
k∑
j=1
αT drnrj ) (5.9)
≥ Z(TSP)
αk + 1
(5.10)
Inequality (5.8) is valid because travel time on a route is never greater than the
duration of the route. Inequality (5.9) is valid because the maximum is never less
than any weighted average. Inequality (5.10) is due to inequality (5.6). Rearranging
the terms, we have,
Z(TSP)
Z(VRPD1,α)
≤ αk + 1. (5.11)
To show the tightness of the bound, we consider an example with k + 1 cus-
tomers, c0, c1, . . . , ck. c0 is at a distance of 1 from the depot and cj, j > 0, is at a
distance of α from the depot. The distance between c0 and cj, j > 0, is 1 + α and
the distance between ci and cj, i 6= j and i, j > 0, is 2α. (An example with k = 2 is
shown in Figure 5.5.) The truck speed is 1 and the drone speed is α. The capacity
of the truck C = k + 1, and the battery life of a drone is 2 time units. An optimal
TSP solution serves c0 to ck in sequence and Z(TSP) = 2αk+2. A feasible VRPD1,α
solution serves customer c0 with the truck and each of the other customers using
a drone, which is launched at the depot and picked up at the depot. All vehicles
138
0c0
c1
c2
(2α)
(1 + α)
(1 + α)
(α)
(1)
(α)
(a) Problem
0
c0
c1
c2
(b) Feasible VRPD1,α solu-
tion
0
c0
c1
c2
(c) Optimal TSP solution
Figure 5.5: A worst-case VRPD1,α example with k = 2
return to the depot at the same time with Zf (VRPD1,α) = 2. In this example,
Z(TSP)
Z(VRPD1,α)
≥ Z(TSP)
Zf (VRPD1,α)
=
2αk + 2
2
= αk + 1. (5.12)
Suppose the drone can travel 50% faster than the truck and that the truck
carries k = 2 drones. Then, Theorem 13 tells us that completion time can be up to
4 times as long without using drones as it is with drones. Based on this, it is easy
to understand the widespread interest in drones for package delivery.
The next theorem does not involve drones in particular, but its proof uses the
same approach as in the proofs of Theorems 12 and 13. We decompose an optimal
VRPD solution into several routes and traverse them one after another to form
a giant route R, from which we construct a feasible TSP solution with bounded
objective value.
139
Theorem 14. Let n customers be served by a fleet of m trucks of different speeds,
v1, v2, . . . , vm, such that the combined speed, V =
∑m
i=1 vi. Denote the optimal
(min-max) objective function value by Z(VRP*). If these customers are served by
one truck with speed v and of sufficient capacity, the optimal objective function value
is denoted by Z(TSPv). If the triangle inequality is valid, we have
Z(TSPv)
Z(VRP*)
≤ V
v
and the bound is tight.
Proof of Theorem 14. We use the truck with speed v to traverse the giant route R
formed by joining the m routes in the optimal VRP* solution, one after another.
The length of route R is denoted by LR. There is no waiting time in a VRP*
solution. Denote the travel time of the ith truck in the optimal VRP* solution by
Ti. We have
Z(VRP*) = max{T1, T2, . . . , Tm} (5.13)
≥ v1T1 + v2T2 + · · ·+ vmTm
v1 + v2 + · · ·+ vm (5.14)
=
LR
V
(5.15)
=
LR
v
v
V
. (5.16)
Again (5.14) is valid because a weighted average never exceeds the maximum. Since
we assume that the triangle inequality is valid, after we skip the depots in the middle
140
of R, we have a feasible TSP solution such that LR ≥ vZ(TSP). Therefore,
Z(VRP*) ≥ Z(TSP) v
V
, (5.17)
i.e.,
Z(TSP)
Z(VRP*)
≤ V
v
. (5.18)
To show the tightness of the bound, we construct an example of m customers,
c1 to cm (an example with m = 3 is shown in Figure 5.6). The distance from ci to
the depot is vi. The distance between ci and cj, i 6= j, is vi + vj. An optimal TSP
solution has objective function value Z(TSP) = 2(v1 + v2 + · · ·+ vm)/v = 2V/v. A
feasible VRP* solution serves customer ci on a dedicated route by the truck with
speed vi. All trucks finish their routes with the same travel time 2. The objective
function value is Zf (VRP*) = 2. Therefore, in this example,
Z(TSP)
Z(VRP*)
≥ Z(TSP)
Zf (VRP*)
=
V
v
. (5.19)
In view of Theorem 14, we have an alternate proof of the inequality in Theorem
13. There are two differences between VRPD1,α and VRP*. First, in VRP*, there
is no waiting time, but in VRPD1,α, duration is the sum of travel and waiting times.
Second, in VRP*, every route i is traversed at a constant speed, vi, but in VRPD1,α,
a drone route is traversed at the truck speed when the drone is on the truck and
traversed at the drone speed when the drone is in the air. We introduce average
141
0c1
c2
c3
(v2 + v3)
(v1 + v2)
(v1 + v3)
(v2)
(v1)
(v3)
(a) Problem
0
c1
c2
c3
(b) Feasible VRP* solution
0
c1
c2
c3
(c) Optimal TSP solution
Figure 5.6: A worst-case VRP* example with m = 3
speeds in looking at the optimal solution to the VRPD1,α so that it can be converted
into a feasible VRP* solution. The average speed on a route is the ratio of the route
length to the route duration. The average speed of the truck route r0 is v0 ≤ 1
because of possible waiting time by the truck. (We normalize the vehicle speed so
that the truck speed is always 1). The average speed on a drone route rj is vj ≤ α,
j > 0, because of lower truck speed and possible waiting by the drone. Therefore,
the optimal VRPD1,α solution can be viewed as a feasible VRP* solution with a
combined speed as defined in Theorem 14, V ≤ 1 + αk. Therefore,
Z(TSP)
Z(VRPD1,α)
=
Z(TSP)
Zf (VRP*)
≤ Z(TSP)
Z(VRP*)
≤ 1 + αk. (5.20)
The worst-case example is the same as in the original proof.
Remark 8. We generally expect that the drone travels faster than the truck, i.e.,
α > 1, but we also consider the case in which drones travel slower because of possible
regulatory rules. Both the original and the alternate proof encounter difficulty if we
relax the assumption α ≥ 1 in Theorem 13. In the original proof, the inequality in
142
(5.5) fails. In the alternate proof, the average speed of drone route rj, vj, j > 0, may
be greater than α, and therefore, the combined speed, V , as defined in Theorem 14,
may be greater than 1 + αk. Nevertheless, the worst-case bound still holds even if
we drop the assumption α ≥ 1 because of the following theorem.
Theorem 15. If the triangle inequality is valid,
Z(TSP)
Z(VRPD1,α)
≤ αk + 1,
and the bound is tight.
Proof of Theorem 15. We consider regular feasible solutions such that the truck and
the drone never both simultaneously wait at a pick-up node. This is a reasonable
assumption because any irregular solution is dominated by another regular feasible
solution (i.e., dispatch the truck immediately after the drone is picked up).
We start with the truck route, denoted by r0, in the optimal VRPD1,α and
add customers served by the drones to form a feasible TSP solution.
We denote the duration of the truck route byDtrcr0 . (Note thatD
trc
r0
= Z(VRPD1,α).)
We add all the customers served by the first drone to r0. The goal is to show the
increase in duration is not greater than αDtrcr0 . Suppose customer k is served by the
first drone that is dispatched at node i and picked up at node j. Denote, by Dtrcij ,
the time taken from the drone dispatchment at i to the truck’s arrival at j. Denote,
by W trcj , the possible waiting time of the truck at j. Denote the lengths from i to
k and from k to j by Lik and Lkj, respectively. Let the possible waiting time of the
143
drone at j be W drnj . We must have
Dtrcij +W
trc
j =
Lik + Lkj
α
+W drnj . (5.21)
Both sides of equation (5.21) measure the time elapsed from the launch of the drone
to the pick-up of the drone. The left-hand side measures it from the perspective of
the truck and the right-hand side measures it from the perspective of the drone.
In a regular solution, either W trcj = 0 or W
drn
j = 0.
Case 1 (W drnj = 0): Equation (5.21) becomes D
trc
ij +W
trc
j =
Lik+Lkj
α
, or
Lik + Lkj = α(D
trc
ij +W
trc
j ). (5.22)
If Lik ≤ Lkj, we loop customer k at i to form part of the route i− k − i− · · · − j.
We have the duration of this part of the route
2Lik +D
trc
ij +W
trc
j ≤ (Lik + Lkj) +Dtrcij +W trcj (5.23)
≤ α(Dtrcij +W trcj ) +Dtrcij +W trcj (5.24)
≤ (1 + α)(Dtrcij +W trcj ). (5.25)
Inequality (5.23) is due to the assumption that Lik ≤ Lkj. Inequality (5.24) is due to
equation (5.22). From (5.25), the additional duration is bounded by α(Dij +W
trc
j ).
If Lik > Lkj, we loop customer k at j to form the partial route i− · · · − j − k − j,
and the argument is the same.
144
Case 2 (W trcj = 0): If Lik ≤ Lkj, we still loop customer k at i to form part of the
route i− k − i− · · · − j. We have the duration of this part of the route
2Lik +D
trc
ij ≤ (Lik + Lkj) +Dtrcij
≤ α(Dtrcij −W drnj ) +Dtrcij
≤ (1 + α)Dtrcij .
The additional duration is bounded by αDtrcij . If Lik > Lkj, we loop customer k at
j to form the partial route i− · · · − j − k − j, and the argument is the same.
In Figure 5.7(a), we show a typical part of an optimal VRPD1,α solution. The
truck route is in black and the drone route is in red. At customer 1, the drone is
launched to visit customer 8. At customer 4, the truck waits to pick up the drone,
which is then launched at customer 5 to serve customer 6. The drone reaches and
waits at customer 7, where it is picked up. In Figure 5.2(b), we show part of the
intermediate route when customers 8 and 6, previously served by the drone, are
added to the truck route. Since customer 1 is nearer than customer 4 to customer
8, we form a loop 1 → 8 → 1 around customer 1. Similarly, we loop customer 6
around customer 7, instead of customer 5. (After all drone customers, including
those served by other drones, are inserted, we skip the revisited customers 1 and 7
to get part of the feasible TSP solution shown in Figure 5.7(c).)
For a particular drone, there is no overlap of the truck path on which this
drone is not with the truck. For example, in Figure 5.7(a), the path 1→ 2→ 3→ 4
and 5 → 9 → 10 → 7 do not overlap. Therefore, we can add all the customers
145
1 2 3 4 5 6 7
8 9 10
Truck waits Drone waits
(a) Part of a VRPD1,α solution
1 2 3 4 5 6 7
8 9 10
(b) Part of the intermediate route
1 2 3 4 5 6 7
8 9 10
(c) Part of the feasible TSP solution
Figure 5.7: Adding drone customers to truck route
served by a drone in the same manner such that the additional duration is bounded
by αDtrcr0 .
We then add the customers served by the second drone, and the third, and
so on until the kth drone. Each time the increase in duration is bounded by αDtrcr0 .
After all customers served by the drones are added to the truck route, the duration
is no greater than (1 + αk)Dtrcr0 . A feasible TSP solution is generated by removing
all the truck-related waiting time and revisits to customers. The objective function
value is also bounded by (1 +αk)Dtrcr0 and we have shown that the inequality holds.
To show the bound is tight, consider a VRPD1,α with k + 1 customers. Cus-
tomer c0 is located at a distance of 1 from the depot. Customers c1, c2, . . . , ck are
located at a distance of α from the depot. The distances between c0 and cj, j > 0
are 1 + α. The distances between any two customers ci and cj, i > 0, j > 0, are 2α.
146
01 2
34
5
6
7
8
(a) Proofs of Theorems 12 and 13 (black→
red → blue)
0
1 2
34
5
6
7
8
(b) Proof of Theorem 15
Figure 5.8: Comparison of the intermidate routes in TSP route construction
The speed of the truck is 1. An optimal TSP solution is to visit the customers in
the sequence c0, c1, . . . , ck, so Z(TSP) = 2(1 +αk). A feasible VRPD1,α solution is
to dispatch the k drones at the depot to serve customers c1 to ck, while the truck
serves customer c0. All vehicles will return to the depot at the same time, after 2
time units. Therefore, Zf (VRPD1,α) = 2. So
Z(TSP)
Z(VRPD1,α)
≥ Z(TSP)
Zf (VRPD1,α)
= 1+αk.
Remark 9. We constructed different TSP solutions from the same optimal VRPD1,α
solution. We compare the construction using the example shown in Figure 5.1. The
giant route in the proofs of Theorems 12 and 13 and the intermediate route in the
proof of Theorem 15 are shown in Figure 5.8. The feasible TSP solutions are shown
in Figure 5.9.
In the next theorem, we consider VRPDm,α with m trucks, each carrying k
drones.
147
01 2
34
5
6
7
8
(a) Proofs of Theorems 12 and 13(black→
red → blue)
0
1 2
34
5
6
7
8
(b) Proof of Theorem 15
Figure 5.9: Comparison of the TSP solutions constructed in the proofs
Theorem 16. If the triangle inequality is valid,
Z(TSP)
Z(VRPDm,α)
≤ m(αk + 1),
and the bound is tight.
Proof of Theorem 16. Given an optimal VRPDm,α solution, we can discompose the
problem into m subproblems. Let Si be the set of customers served by either the
ith truck or a drone on the ith truck. The ith subproblem is a VRPD1,α on the set
of customers Si. The optimal VRPDm,α solution gives feasible solutions to all m
subproblems. If we denote the TSP on Si by TSP
(i), by Theorem 15, we have
Z(TSP(i)) ≤ (αk + 1)Z(VRPD(i)1,α) ≤ (αk + 1)Zf (VRPD(i)1,α). (5.26)
We join the TSP solutions to subproblems to form a giant route that serves all
148
the customers and then we skip the visits to the depots in the middle of the route.
The result is a feasible TSP solution over all the customers. Therefore,
Z(TSP ) ≤
m∑
i=1
Z(TSP (i)) (5.27)
≤
m∑
i=1
(αk + 1)Zf (VRPD
(i)
1,α) (5.28)
≤ (αk + 1)
m∑
k=1
Z(VRPDm,α) (5.29)
= m(αk + 1)Z(VRPDm,α). (5.30)
Inequality (5.27) holds because its right-hand side is the duration of a route that
visits every customer exactly once and visits the depot m+1 times. Inequality (5.28)
holds because of inequality (5.26). Inequality (5.29) holds because Z(VRPDm,α) =
maxi{Zf (VRPD(i)1,α)}.
Rearranging the terms, we prove the inequality in Theorem 16. To prove that
the bound is tight, we consider a VRPDm,α with m(k + 1) customers, c
(i)
j , where
i ∈ I = {1, 2, . . . ,m} and j ∈ J = {0, 1, . . . , k}. The truck capacity is C = m(k+ 1)
parcels and the battery life of a drone is 2. The speeds of the trucks and the drones
are 1 and α, respectively. The distance metric is described below:
• Distance between the depot and customer c(i)0 is 1, ∀i ∈ I
• Distance between the depot and customer c(i)j is α, ∀i ∈ I,∀j ∈ J\{0}
• Distance between customers c(i1)0 and c(i2)0 is 2, ∀i1, i2 ∈ I, i1 6= i2
• Distance between customers c(i1)0 and c(i2)j is 1 +α, ∀i1, i2 ∈ I and ∀j ∈ J\{0}
149
• Distance between customers c(i1)j1 and c(i2)j2 is 2α, ∀i1, i2 ∈ I,∀j1, j2 ∈ J\{0}, (i1, j1) 6=
(i2, j2)
An example with m = 2 and k = 2 is illustrated in Figure 5.10. The example is in-
tentionally constructed as a symmetric example with perfect synchronicity between
trucks and drones by placing “drone nodes” at distance α and “truck nodes” at dis-
tance 1 from the depot. In addition, the triangle inequality always holds at equality.
This allows for zero wait time, constant utilization of all vehicles, and knowledge
that we are utilizing the most direct routes possible.
An optimal TSP solution has duration Z(TSP) = 2m(1+αk). In fact, serving
the customers in any sequence will result in duration of 2m(1 + αk). A feasible
VRPDm,α solution dispatches all drones at the depot. The j
th drone on the ith
truck serves customer c
(i)
j . The i
th truck serves customer c
(i)
0 on a dedicated route.
All vehicles return to the depot at the same time and Zf (VRPDm,α) = 2. Therefore,
in this example, we have
Z(TSP)
Z(VRPDm,α)
≥ Z(TSP)
Zf (VRPDm,α)
=
2m(1 + αk)
2
= m(1 + αk). (5.31)
In the next theorem, we compare the VRPDm,α to the min-max VRP with a
fleet of m trucks and no drones.
150
0 c
(1)
0
c
(1)
1c
(1)
2
c
(2)
0
c
(2)
1 c
(2)
2
(1 + α)
(2α)
(1 + α)
(1 + α)
(2α)
(1 + α)
(2α) (2α)
(1)
(α)(α)
(1)
(α) (α)
(a) Problem
0 c
(1)
0
c
(1)
1c
(1)
2
c
(2)
0
c
(2)
1 c
(2)
2
(b) Feasible VRPDm,α solution
0 c
(1)
0
c
(1)
1c
(1)
2
c
(2)
0
c
(2)
1 c
(2)
2
(c) Optimal TSP solution
Figure 5.10: A worst-case VRPDm,α example with k = 2
151
Theorem 17. If the triangle inequality is valid,
Z(VRP*)
Z(VRPDm,α)
≤ αk + 1,
and the bound is tight.
Proof of Theorem 17. The proof relies on the same decomposition used in the proof
of Theorem 16. Denote the set of customers served by the ith truck or a drone on the
ith truck by Si. The route in the optimal VRPDm,α solution that serves customers
in Si is feasible to the subproblem VRPD
(i)
1,α. We denote the TSP on Si by TSP
(i)
and reproduce inequality (5.26) below.
Z(TSP(i)) ≤ (αk + 1)Zf (VRPD(i)1,α). (5.32)
The optimal objective function value of the min-max VRP is never greater
than the maximum of the Z(TSP(i))s; otherwise we have a better VRP* solution
consisting of the routes from the optimal TSP(i) solutions.
Z(VRP*) ≤ max{Z(TSP(1)), Z(TSP(2)), . . . , Z(TSP(k))} (5.33)
≤ (αk + 1) max
i
{Zf (VRPD(i)1,α)} (5.34)
= (αk + 1)Z(VRPDm,α). (5.35)
Rearranging the terms, we have the inequality in Theorem 17.
To show that the bound is tight, we consider the same example of m(k + 1)
152
customers as in the proof of Theorem 16. In the optimal VRP solution, we serve
the customers c
(i)
j , ∀j ∈ J , by the ith truck. All routes have the same duration and
Z(VRP*) = 2(1+αk) is the optimal objective function value because if Z(VRP*) <
2(1+αk), we will have a TSP solution over all the m(k+1) customers and the depot
with Z(TSP) < 2m(1 +αk). A feasible VRPDm,α solution described in the proof of
Theorem 16 has Zf (VRPDm,α) = 2. Therefore, in this example,
Z(VRP*)
Z(VRPDm,α)
≥ Z(VRP*)
Zf (VRPDm,α)
=
2(1 + αk)
2
= 1 + αk. (5.36)
The next theorem compares VRPDm,α and VRPDm,β, i.e., VRPD with differ-
ent drone speeds. The idea is to address the following question: If a more advanced
(and faster) set of drones becomes available, how much time can we save in delivering
all packages?
Theorem 18. Let α < β. If the triangle inequality is valid, we have
Z(VRPDm,α)
Z(VRPDm,β)
≤ β
α
,
and the bound is tight.
To prove Theorem 18, we first introduce a lemma that is true for all regular
feasible solutions of VRPD, i.e., a truck leaves a pick-up node as soon as it picks up
the drone. Suppose an ant crawls onto the truck just before it is dispatched from
the depot. The ant can crawl from a drone to the truck or from the truck to a drone,
153
only when the drone is on the truck. It stays on one of the vehicles (the truck or a
drone) until the fleet is back to the depot.
Lemma 1. For every regular feasible solution to the VRPD, there is a strategy for
the ant to always stay on a vehicle that is in motion.
Proof of Lemma 1. The ant crawls onto the truck just before the truck leaves from
the depot. Whenever a drone is about to launch, the ant has a choice to crawl onto
this drone or to stay on the truck. If, at the pick-up node of this drone, the truck has
to wait, the ant chooses to crawl onto the drone; otherwise, it stays on the truck. In
a regular feasible solution, the truck and the drone never both wait at the pick-up
node. The ant crawls back to the truck whenever the drone is picked up if the ant
is on the drone. Following this strategy, the ant will never stay on a vehicle that is
waiting.
We illustrate the ant’s strategy using the example in Figure 5.1. When the
truck is dispatched from the depot, the blue drone is launched. Since the truck will
not wait at customer 4 where the blue drone is picked up, the ant chooses to stay
on the truck. At customer 1, the red drone is launched for the first time. Since
the truck will have to wait at customer 5 to pick up the red drone, the ant crawls
onto the drone. When the truck picks up the red drone at customer 5, the ant
crawls back to the truck. The red drone is launched for the second time at 5, but
the ant stays on the truck this time because the truck does not have to wait at the
pick-up node 4. The ant stay on the truck until it is back at the depot. The ant
route is 0(on the truck) → 1(crawls onto the red drone) → 2(on the red drone) →
154
5(crawls back onto the truck)→ 3(on the truck)→ 4(on the truck)→ 0(on the truck).
There is no waiting time on this route. In addition, the ant route can be partitioned
according to the vehicle that the ant stays on. In the proceeding example, the
elements of partition are 0 → 1 on the truck, 1 → 2 → 5 on the drone, and
5→ 3→ 4→ 0 on the truck.
With Lemma 1 proved, we now prove Theorem 18.
Proof of Theorem 18. We start with a fleet with only one truck with k drones and
show first
Z(VRPD1,α)
Z(VRPD1,β)
≤ β
α
. (5.37)
Suppose we have an optimal VRPD1,β solution. We construct a feasible VRPD1,α
solution by following the same routing plan, but serving the customers with the α
drones. In this VRPD1,α solution, there is a strategy for the ant to always stay
on a moving vehicle by Lemma 1. The ant never waits, so its travel time is the
duration of the ant route (Rα), which is also the objective value of the solution to
the VRPD1,α. The ant route can be partitioned into segments based on the vehicle
the ant is on. On the other hand, if the ant chooses the same path (Rβ) in the
optimal VRPD1,β solution, there may be waiting times. Rβ has the same length
as Rα but different duration because of shorter travel times and possible waiting
times. Rβ can be partitioned in exactly the same way as Rα. For every element of
the partition, if the path is traveled with the truck speed, the travel time on that
path in both the VRPD1,α and VRPD1,β solutions are equal; if the path is traveled
by the drone, the travel time of that path in the VRPD1,α solution is no more than
155
β
α
times the travel time of the path in the VRPD1,β solution. Therefore, the total
travel time by the ant in the VRPD1,α solution is no more than
β
α
times the travel
time in the VRPD1,β solution. Because of possible waiting times on route Rβ and
because there is no waiting time on route Rα, the duration of Rα is no more than
β
α
times the duration of Rβ. Hence, inequality (5.37) holds.
To generalize inequality (5.37) to problems with multiple trucks, we partition
the VRPDm,β into m subproblems of VRPD1,β according to the optimal VRPDm,β
solution. Let Si be the set of customers served by either the i
th truck or a drone on
the ith truck, where i ∈ I = {1, 2, . . . ,m}. The problem of serving all customers in
Si using one truck and k β drones is the i
th subproblem, denoted by VRPD
(i)
1,β. We
assume the ith route in the optimal VRPDm,β solution also solves the subproblem
VRPD
(i)
1,β optimally. (If not, we can always replace the i
th route of the VRPDm,β
solution with the optimal solution to the VRPD
(i)
1,β without increasing the objective
function value of the VRPDm,β solution.) We solve the i
th subproblem using the α
drones to obtain an optimal solution whose objective function value is denoted by
Z(VRPD
(i)
1,α). By inequality (5.37), we have
Z(VRPD
(i)
1,α) ≤
β
α
Z(VRPD
(i)
1,β) (5.38)
max
i∈I
Z(VRPD
(i)
1,α) ≤
β
α
max
i∈I
Z(VRPD
(i)
1,β) =
β
α
Z(VRPDm,β). (5.39)
We put the optimal solutions to the m subproblems VRPD
(i)
1,α together to form a
156
feasible solution to the VRPDm,α. This yields the desired inequality:
Z(VRPDm,α) ≤ Zf (VRPDm,α) = max
i∈I
Z(VRPD
(i)
1,α) ≤
β
α
Z(VRPDm,β). (5.40)
To show the bound is tight, we consider two cases. If 1 ≤ α < β, Let customer
c0 be the only customer, which is at a distance of 1 from the depot. Since, the
drones travel faster than the truck in both VRPD1,α and VRPD1,β, it is optimal
to have a drone to serve c0. Z(VRPD1,α) =
1
α
and Z(VRPD1,β) =
1
β
. Therefore,
Z(VRPD1,α)
Z(VRPD1,β)
= β
α
in this example.
If α < 1, we consider an example with the number of drones per truck k ≥ 1
α
.
Let the number of customers be k + 1. Customer c0 is at a distance of 1 from the
depot and customers c1 to ck are at a distance of β from the depot. The distance
between c0 and cj with j > 0 is 1+β and the distance between ci and cj with i, j > 0
is 2β. A feasible solution, denoted by Sα, to VRPD1,α is to serve c0 by the truck and
c1 to ck by the drones. The objective function value of Sα is
2β
α
. 2β
α
is also a lower
bound of all feasible solutions to VRPD1,α. If a customer cj with j > 0 is served by
a drone, it is on a route with duration at least 2β
α
. If all customers cj with j > 0 are
served by the truck, the duration of the truck route is at least 2kβ ≥ 2β
α
. Therefore,
Sα is also the optimal solution and Z(VRPD1,α) =
2β
α
. A feasible solution to the
VRPD1,β is to have the truck serving c0 and the drones serving cj with j > 0 and
the objective function value is Zf (VRPD1,β) = 2. Therefore, in this example,
Z(VRPD1,α)
Z(VRPD1,β)
≥ Z(VRPD1,α)
Zf (VRPD1,β)
=
β
α
157
Remark 10. If we can replace our current set of drones with an advanced set of
drones which travel twice as fast, we can reduce the delivery completion time by up
to 50%.
5.4 Extending our model
So far, in this paper, we have ignored cost, assumed that the truck and the
drone follow the same distance metric, and ignored the limited battery life of a
drone. In this section, we begin to relax these simplifications and provide some
initial results for others to build upon.
The next theorem takes into account explicitly the limited battery life (in time
units), U , of a drone, which we essentially ignored in the previous section. A lower
bound on Z(VRPD1,α) is given by Theorem 19.
Theorem 19. If the triangle inequality is valid, then
Z(VRPD1,α) ≥ Z(TSP)− nUα, (5.41)
where n is the number of customers served by drones in the optimal VRPD1,α solution
and U is the battery life of a drone.
Remark 11. The maximal amount we can save by adding drones to trucks, i.e.,
nUα, is directly proportional to drone range and the number of drone deployments.
In other words, long range drones and high utilization rates both could help reduce
158
costs.
Remark 12. Theorem 19 gives a lower bound to Z(VRPD1,α). An upper bound on
Z(VRPD1,α) is Z(TSP ). In the worst case, none of the drones are deployed. This
could happen when customers are located far apart and the drone range is small.
Proof of Theorem 19. We construct a feasible TSP solution from the optimal VRPD1,α
solution using the same procedure presented in the proof of Theorem 15. We insert
the customers served by drones one by one onto the truck route whose duration
equals Z(VRPD1,α). If a drone is launched at node i to service customer k and is
then picked up at node j, the distance covered by the drone is Lik + Lkj ≤ αU . If
Lik ≤ Lkj, we insert k just after node i on the truck route. If Lik > Lkj, we insert
k just after node j on the truck route. The increase in the duration of the truck
route is no more than αU if the triangle inequality is valid. After all n customers
served by the drone are added, the increase in duration is no more than nαU , i.e.,
Zf (TSP) ≤ Z(VRPD1,α) + nαU . Since Z(TSP) ≤ Zf (TSP), we have
Z(VRPD1,α) ≥ Z(TSP)− nUα
after rearranging the terms.
Remark 13. The inequality Z(VRPD1,α) ≥ Z(TSP)1+αk from Theorem 15 is still valid
if the drones have limited battery life. Considering both Theorems 15 and 19, we
have Z(VRPD1,α) ≥ max{Z(TSP)1+αk , Z(TSP)− nUα}.
In the above theorems, the drones and the trucks follow the same distance
159
metric. In practice, we expect the drones to (typically) travel via the crow-fly
distance and the trucks to be restricted to the street network. Therefore, the above
worst-case ratios are conservative in practice. Of course, this dichotomy ignores
the reality of high-rise buildings and other barriers. We show what happens to
the worst-case result if the drone and the truck follow different distance metrics
in the following theorem. The distance matrices followed by a truck and a drone
are denoted by Qt and Qd, respectively. The (i, j)
th entry of Qt (Qd), denoted by
Qt(i, j) (Qd(i, j)), is the distance traveled by the truck (drone) from node i to node
j. Denote the duration of the optimal TSP solution by Z(TSP, Qt) and the optimal
VRPD1,α solution by Z(VRPD1,α, Qt, Qd).
Theorem 20. Let B be the least upper bound on Qt(i,j)
Qd(i,j)
, ∀(i, j), and B ≥ 1, then
Z(TSP, Qt)
Z(VRPDm,α, Qt, Qd)
≤ Bm(αk + 1).
Remark 14. If the truck is restricted to the street network and the drone travels
via the crow-fly distance, B ≥ 1. In effect, if the crow-fly distance is much more
direct than the road network, in places, i.e., B is large, then we can potentially save
even more by utilizing drones.
Proof of Theorem 20. Let Q∗ be another distance metric defined by Q∗ = Qt/B.
Since B ≥ 1, we have Q∗(i, j) ≤ Qt(i, j), ∀(i, j). Since Qt(i, j)/Qd(i, j) ≤ B, we
have Q∗(i, j) = Qt(i, j)/B ≤ Qd(i, j), ∀(i, j). Therefore,
Z(VRPDm,α, Q∗, Q∗) ≤ Z(VRPDm,α, Qt, Qd) (5.42)
160
because at worst, the same routes can be utilized and traversed more quickly. Yet
Z(VRPDm,α, Q∗, Q∗) = Z(VRPDm,α, Qt, Qt)/B (5.43)
because these two quantities are derived from the same problem, except for a scalar
multiple of B in both of the distance metrics.
Previously we showed in Theorem 16 that
Z(TSP,Qt) ≤ m(αk + 1)Z(VRPDm,α, Qt, Qt), (5.44)
so from (5.43) and (5.44)
Z(TSP, Qt) ≤ B(m(αk + 1))Z(VRPDm,α, Q∗, Q∗), (5.45)
and now by (5.42)
Z(TSP, Qt) ≤ B(m(αk+1))Z(VRPDm,α, Q∗, Q∗) ≤ B(m(αk+1))(VRPDm,α, Qt, Qd),
(5.46)
which yields the desired result.
The next example illustrates, not surprisingly, that when trucks and drones
follow different distance metrics, we can do better than the bound in Theorem 15.
In Figure 5.11, there are seven customers located on two concentric circles with radii
one and two. There are four edges of length one that link the two circles (see Figure
161
0c1
c2
c3
c4
c5c6
c7
(a) Problem
0
c1
c2
c3
c4
c5c6
c7
(pi2 )
(pi2 )(
pi
2 )
(pi2 )
(
√
5− 2√2)
(
√
5− 2√2)
(
√
5− 2√2)
(
√
5− 2√2)(
√
5− 2√2)
(
√
5− 2√2)
(
√
5− 2√2)
(
√
5− 2√2)
(b) Optimum VRPDc1,α solution
Figure 5.11: Truck and drone follow different distance metrics
Node
Polar coordinates Distance from the depot
Radial Angular Edge restriction Crow-fly
0 1 −pi/2 0 0
c1 1 0 pi/2
√
2
c2 1 pi/2 pi 2
c3 1 pi pi/2
√
2
c4 2 −pi/4 1 + pi/2 5− 2
√
2
c5 2 pi/4 1 + pi 5 + 2
√
2
c6 2 3pi/4 1 + pi 5 + 2
√
2
c7 2 −3pi/4 1 + pi/2 5− 2
√
2
Table 5.1: Positions of the depot and the customers in Figure 5.11(a)
5.11(a)). The seven customers are served by one truck carrying one drone. The
speed of the truck is one and the speed of the drone is α = 4
pi
√
5− 2√2 ≈ 1.876.
The polar coordinates of the depot (node 0) and the seven customers and their
distances from the depot are given in Table 5.1.
We assume the drones can fly as the crow flies, but the truck is restricted to
the edges shown in Figure 5.11(a). For example, the distance between customer
c1 and the depot is
pi
2
≈ 1.571 for the truck, but √2 ≈ 1.414 for the drone using
162
the coordinates given in Table 5.1. The crow-fly distance between points (r1, θ1)
and (r2, θ2) is calculated by
√
r21 + r
2
2 − 2r1r2 cos(θ1 − θ2). We denote the optimal
objective function value by Z(VRPDc1,α). From a geometric point of view, we serve
the four customers on the outer circle by the drone and the three customers on the
inner circle by the truck. The optimal solution is shown in Figure 5.11(b). The drone
is dispatched from the depot to serve customer c4 while the truck travels to serve
c1. The two vehicles arrive at c1 at the same time when the drone is immediately
launched to serve c5, and so on. Eventually, the two vehicles arrive at the depot
simultaneously with Z(VRPDc1,α) = 2pi ≈ 6.283.
If we serve all the customers using only the truck, Z(TSP ) = 2+ 11
2
pi ≈ 19.279.
The path followed by the truck is 0 → c1 → c5 → c4 → c7 → c6 → c2 → c3 → 0
(optimal solution obtained using Gurobi solver [52]). In this example, we have
Z(TSP)
Z(VRPDc1,α)
=
2+ 11
2
pi
2pi
≈ 3.068 > 1 + αk ≈ 2.876. Incidentally, if the drone also
follows only the edges shown in Figure 5.11(a), we think the optimal solution is
Z(VRPD1,α) =
pi(2+pi)√
5−2√2
≈ 10.961. The routes are similar to the routes in the
optimal solution in which the drone flies as the crow flies. The drone is dispatched
from the depot to serve customer c4 while the truck travels to serve c1. The truck
arrives at c1 earlier and waits for the drone for time
pi(2+pi)
4
√
5−2√2
− pi
2
. The drone is
immediately launched to serve c5, and so on. The ratio of objective function values
is about 1.759, less than 2.876.
While minimizing the completion time is the primary objective, a company
may want to look at aspects of economic cost as well. In the next theorem, we
combine the completion time and the variable costs of using the truck and drone to
163
form a new objective function, denoted by Y . Therefore, the new objective function
value of the optimal TSP solution is calculated by Y (TSP ) = Z(TSP )+θX(TSP ),
where X(TSP) denotes the variable cost of truck usage and θ gives weights to
the two components of the objective function. When θ = 0, we are minimizing
the completion time. When θ is very large, we are minimizing the sum of the
variable costs. The new objective function value of the optimal VRPD1,α solution is
calculated by Y (VRPD1,α) = Z(VRPD1,α) + θX(VRPD1,α), where X(VRPD1,α) =
Xt +Xd, the sum of truck and drone usage costs. We assume the cost per unit time
of the drone is a times the cost per unit time of the truck. a is expected to be much
less than 1. The drone usage cost is incurred only when the drone is in the air. We
ignore the fixed costs for now.
Theorem 21. If the triangle inequality is valid, then
Y (VRPD1,α) ≥ Y (TSP)−
[α
a
+
(α
a
− 1
)
θ
]
Xd,
where Xd is the variable cost of k drones in the optimal VRPD1,α solution.
Remark 15. The coefficient
[
α
a
+
(
α
a
− 1) θ] is positive if α > a. The potential
savings from using a drone is large if α, θ, and Xd are large while a is small. We
also point out the similar structure of the inequalities in Theorems 19 and 21 and
in Theorems 16 and 20.
Remark 16. An upper bound on Y (VRPD1,α) is Y (TSP ).
Proof of Theorem 21. Without loss of generality, we assume the truck speed is 1
164
and the drone speed is α. We further assume that the truck usage cost is 1 per unit
time and the drone usage cost is a per unit time, so that X(TSP) = 1 × Z(TSP).
If not, we can modify the parameter θ to normalize the usage costs of the vehicles.
Note also that Y (TSP) = Z(TSP) + θX(TSP) = (1 + θ)Z(TSP). Therefore, a TSP
solution that minimizes duration also minimizes the total cost Y .
We want to find a lower bound for Y (VRPD1,α) in terms of Y (TSP), similar
to what we did in Theorem 19. Given an optimal VRPD1,α solution with dura-
tion Z(VRPD1,α), we can construct a feasible TSP solution with duration no more
than (1 + αk)Z(VRPD1,α) using the construction process described in the proof of
Theorem 15. Therefore, an upper bound of Z(TSP) is given by
Z(TSP) ≤ (1 + αk)Z(VRPD1,α). (5.47)
Using the same construction process, we can show that an upper bound of the
truck usage cost is given by
X(TSP) ≤ Xt + Xd
a
α, (5.48)
where Xt and Xd are the truck and drone usage costs of the optimal VRPD1,α
solution. The factor Xd
a
gives the sum of drone usage time. Multiplying it by the
drone speed α gives the maximum total distance covered by the k drones. Since the
truck has unit speed and unit usage cost, the term Xd
a
α also gives the additional
truck usage cost when we convert the optimal VRPD1,α to a feasible TSP solution.
165
In inequalities (5.47) and (5.48), Z(TSP) = X(TSP), and 1× Z(VRPD1,α) =
Xt. Comparing these two equations, a tighter upper bound for Z(TSP) is Xt +
Xd
a
α
because Xd
ak
≤ Xt
1
, as the average usage time per drone is never greater than the
usage time of the truck.
Now,
Y (TSP) = (1 + θ)Z(TSP)
≤ (1 + θ)
(
Xt +
α
a
Xd
)
= Xt + θ(Xt +Xd) +
[α
a
+
(α
a
− 1
)
θ
]
Xd
= Y (VRPD1,α) +
[α
a
+
(α
a
− 1
)
θ
]
Xd
which yields the desired result.
5.5 Conclusions and future work
The idea of delivering packages by drones (from trucks) as well as directly
from trucks, as is the common practice, is intriguing and is being seriously con-
sidered by numerous prominent companies in the U.S. and in Europe. There are,
however, numerous technological and regulatory obstacles to overcome. In order for
the commercialization of this idea to make sense, the potential savings in delivery
completion time must be considerable.
After describing the VRPD and defining notation, we prove several worst-case
theorems. Each result reveals the amount of time that could be saved, in the best
166
case, as a result of using trucks and drones rather than trucks alone in delivering
packages to customers. For example, suppose a drone travels 50% faster than a
truck, there are m trucks, and at most two drones per truck. Theorem 17 tells us
that, in the best case, we can reduce delivery completion time by 75%.
For each of the first seven theorems, we proved worst-case bounds and showed
that these bounds are tight. Next, we extended our model in three key directions.
First, we explicitly included a limited battery life for the drones. Second, we took
into account that trucks travel over a street network, whereas drones travel from
one point to another as the crow flies. Third, we sought to incorporate cost, in
addition to delivery completion time, into our model. For each of these extensions,
we proved an additional inequality.
These extensions represent an initial attempt to add greater realism to the
basic model. There is much more work to be done in terms of worst-case analysis.
For example, can Theorems 19 and 21 be generalized to the m-vehicle case? In
addition, there is a need for smart exact and heuristic approaches to solve the
VRPD and simulation studies that aim to determine the expected benefits of using
drones and trucks to deliver packages rather than trucks alone.
Overall, we think the VRPD represents a very exciting new direction in logis-
tics. We expect to see substantial progress on this problem in both the academic
literature and in practice over the next decade. Furthermore, we expect the aca-
demic and practitioner communities to feed off of one another. What we have shown
represent bounds on maximal savings. Further research could give us better indica-
tions of actual savings in real-life settings.
167
Chapter 6: The Min-Max Close-Enough Vehicle Routing Problem
6.1 Introduction
We have seen many cases where advancements in technology motivate new
problems in operations research. The notion of close-enough routing is one of these
new problems. Traditionally, both the simpler Traveling Salesman Problem (TSP)
and the more complex Vehicle Routing Problem (VRP) require cities and customers
to be visited exactly at their locations. For example, utility companies send their
workers to read the meters at every household. With radio frequency identification
(RFID) technology, meters can be read from a distance. Instead of visiting every
customer, workers need only get close enough to a customer to read the meter.
Another application of close-enough routing problem arises when a pilot (or a drone)
surveys several ground targets. The drone does not have to fly directly above the
targets but only has to get close enough to survey them.
The basic form of close-enough routing, the Close-Enough Traveling Salesman
Problem (CETSP), was introduced by Gulczynski et al. [51]. The CETSP is,
typically, defined on a Euclidean plane. The salesman must start from and end at
the depot. Every customer has a service range. A customer has been visited when
the salesman comes within the customer’s service range. The objective is to visit
168
all customers and return to the depot in the shortest distance traveled. When all
customer service ranges are equal to zero, the CETSP reduces to the TSP. A positive
service range changes the geometry of the problem. The TSP can be described as
finding the shortest Hamiltonian cycle in a complete graph. However, in the CETSP,
the nodes of the routes are not known in advance. A CETSP solver must not only
determine the sequence in which the customers are visited, but also the locations
at which these customers are served. Since Gulczynski et al.’s work on heuristics
for the CETSP, several papers have appeared in the literature. Three papers have
focused on heuristics [24, 70, 85] and two papers have developed exact approaches
and lower bounds [24, 32].
A natural extension to the CETSP is the Close-Enough Vehicle Routing Prob-
lem (CEVRP). Instead of only one route traveled by one salesman, a number of
routes are traveled by a fleet of vehicles that make deliveries to meet the demand
of customers. The vehicles do not have to visit the customers at their locations;
they only need to get close enough to the customers. The total demands delivered
on a route cannot exceed the capacity of a truck. The CEVRP can model pack-
age delivery when customers are willing to travel some distance to pick up their
packages. For example, in disaster routing, we can drop rescue packages near the
affected villages. Mennell [70] developed Steiner-zone-based heuristics to solve the
CEVRP. Steiner zones are explained in Section 6.2.2.
We propose a new variant of the CEVRP called the min-max Close-Enough
Vehicle Routing Problem (MMCEVRP). Instead of minimizing the total distance
traveled by the fleet, we minimize the distance of the the longest route. In other
169
words, we focus on the completion time. When a task requires several routes to be
traveled in parallel, the task is finished only when the last route is completed. For
example, if we launch several drones to survey the destruction on major roads after
a natural disaster, then the survey is completed only when the last drone returns
to its base. Some complex problems can be formulated using the MMCEVRP as
a subproblem. For example, suppose that drones are used to take readings from
meters. The drones are loaded onto a truck. We may want to park the truck
in a particular neighborhood and then dispatch the drones to take the readings.
Only when the last drone returns can the truck leave and reposition to a different
neighborhood. The min-max objective can also be used to balance the route lengths.
If the length of the longest route is minimized, the variability of the route lengths
tends to be small.
In the MMCEVRP, we have to fix the number of vehicles in the fleet in advance;
otherwise, the optimal solution simply requires that the number of vehicles equals
the number of customers and each vehicle serves one specific customer. In addition,
we do not consider the capacity constraint because most applications of close-enough
routing problems pertain to service rather than the delivery of physical commodities.
The rest of the chapter is organized as follows. In Section 6.2, we describe
the MMCEVRP in the Euclidean plane and explain the concept of Steiner zones.
In Section 6.3, we develop our heuristic algorithm (denoted by MMSZ) for the
MMCEVRP. In Section 6.4, we present the performance of MMSZ on CETSP and
MMCEVRP instances. Finally, in Section 6.5, we give our concluding remarks and
mention directions for future work.
170
6.2 MMCEVRP
6.2.1 Problem description
The MMCEVRP is defined on a Euclidean plane. The set of points, V =
{v0, v1, v2, . . . , vn}, gives the locations of the depot (v0) and the customers (vi, i > 0).
Customer i has service range ri. For customer i, there is a disk centered at vi with
radius ri. We want to construct K cycles (routes) that pass through v0 such that
all disks defined by the customers are serviced by at least one of the routes. The
objective is to minimize the longest distance of the K routes.
An example of the MMCEVRP with 11 customers is shown in Figure 6.1. The
depot is at the bottom left labeled D. The circles represent the disks defined by the
11 customers. Assuming the fleet has two vehicles, we show two feasible routes (one
with a solid red line, one with a dashed green line).
6.2.2 Steiner zone
If a route passes through a disk defined by a customer, then that customer
is served. If a route passes through an overlap between two disks, both customers
are served. If we can identify the overlapping regions, and then pick a point from
each of these regions and disks defined by customers that are not already accounted
for by the overlaps, the problem becomes a standard routing problem. This is the
motivation of what we call Steiner-zone-based methods.
A Steiner zone is the overlap of disks. We define the disks themselves to be
171
D
C1
C2
C3
C4
C5 C6
C7
C8
C9
C10
C11
C12
Figure 6.1: An MMCEVRP example with 11 customers and routes for two vehicles
172
special cases of Steiner zones. If a Steiner zone is contained in at most k disks, it
has degree k. Therefore, a disk that is not contained in any other disk has degree
1. Intuitively, Steiner zones of high degree are desirable because a route that passes
though it serves multiple customers at the same time. We note that a Steiner zone
with very high degree usually has a small area, which limits our choice of a point from
it (we term the point a Steiner point) in both the construction and improvement
procedures in Section 6.3.
In Figure 6.2, we show examples of Steiner zones. Their degrees are given in
the captions of the subgraphs. Observe that a degree k Steiner zone is enclosed by
at most k arcs. We use the set notation to denote the Steiner zones. For example,
{C4, C5} denotes a Steiner zone that is contained in the disks defined by C4 and C5
and not other customers.
The boundary of a Steiner zone consists of one or more arcs. In general, if
the boundary has more than one arc, we define the center of the Steiner zone to be
the average of the endpoints of these arcs, i.e., the x (y) coordinate of the center
is the average of the x (y) coordinates of the endpoints. In the special case where
the Steiner zone is bounded by a circle, we define its center to be the center of the
circle. All Steiner zones are convex because they are formed by the intersection of
convex disks. Therefore, a center point of a Steiner zone always lies in the zone. In
Figures 6.2(a) and 6.2(d), the centers of Steiner zone {C2, C3} and {C6, C7, C8} are
marked by an x.
173
C2 C3x
(a) {C2, C3} has degree two
C4 C5
(b) {C4, C5} has degree two
C1
(c) {C1} has degree one
C6
C7
C8
x
(d) {C6, C7, C8} has degree
three
Figure 6.2: Steiner zones of various degrees
174
6.3 Algorithm
MMSZ is a hybrid composite algorithm that combines both tour construction
and tour improvement phases. The construction phase has four steps. The improve-
ment phase has intra-route and inter-route moves. An overview of the algorithm is
given in Table 6.2.
6.3.1 Construction procedures
6.3.1.1 Customer pruning
We observe that not all customers need be considered explicitly to construct
a feasible solution. For example, in Figure 6.3, there are 11 customers with various
radii. The depot is represented by the square labeled D on the bottom left. We
can eliminate customer C3 because its disk contains the disk defined by C12; any
route that serves C12 also serves C3. Similarly, we can eliminate customer C1 on the
bottom left because the depot is within its service range.
We may also remove customer C9. If all service ranges are zero, there always
exists an optimal solution with all routes lying within the convex hull defined by
V , the locations of the depot and the customers. If not, we can identify a path
starting from the first time and ending at the second time when the route crosses
the boundary. Since all routes start and end at the depot, which is in the convex
hull, such a path always exists. Replace the path with a straight-line segment. The
solution is feasible because no customers lie outside the convex hull. The solution
175
D
C1
C2
C3
C4
C5 C6
C7
C8
C9
C10
C11
C12
Figure 6.3: Customer pruning
176
is never worse because the triangle inequality holds on a Euclidean graph.
We can apply the same concept when some service ranges are positive. We
hypothesize that there always exists an optimal solution with all routes in the convex
hull defined by the depot and customer locations. The convex hull is drawn using
the dashed line in Figure 6.3. A rigorous proof is required because it is possible that
a route visits a customer (for example, C11) outside the convex hull (although we
believe such a route is not optimal).
The convex hull intersects the circles defined by the boundary customers, i.e.,
C5, C6, and C8, at the dashed arcs. In an optimal solution, if a route visits a
boundary customer, it will visit a point on the arc. Therefore, any customer that
defines a disk containing the dashed arcs can be removed (for example, C9).
To summarize, a customer may be removed if it defines a disk that contains
(A) the depot or (B) a disk defined by another customer. From our computational
experience, a pre-processing procedure that considers these two pruning criteria
both reduces total running time and improves solution quality. A customer may
also be removed by (C) the convex hull argument; however, the effects are mixed.
In general, removal of a customer by (C) reduces running time, but it may or may
not improve solution quality (solution quality could be worse). Removal by (C)
requires further research and a more rigorous argument. In Section 6.4, we report
only results with customer pruning based on criteria (A) and (B).
177
6.3.1.2 Steiner zone construction
A naive approach to construct the Steiner zones would examine every subset
of customers and determine if the disks they define overlap. This method has an
exponential running time. One way to reduce the running time is limiting the degree
of Steiner zones constructed to at most three, as suggested in [70]. However, we do
not want to limit the search space of Steiner zones, so we implement a sweep line
algorithm [83]. From our computational experience, this algorithm is fast.
The sweep line algorithm is illustrated with seven customers shown in Figure
6.4(a). The labels t1 to t12 on the horizontal axis are x values such that t1 <
t2 < · · · < t12. Similarly, the labels l1 to l11 on the vertical axis are y values such
that l1 < l2 < · · · < l11. Every customer is represented by a circle, which is then
approximated by a pair of horizontal line segments (Figure 6.4(b)). If the center of
the circle is at (x, y) and the radius is r, the two line segments are (x−, y−)(x+, y−)
and (x−, y+)(x+, y+), where x± = x ± r and y± = y ± r. Therefore, the seven
customers in Figure 6.4(a) can be approximated by seven pairs of line segments in
Figure 6.4(c).
Imagine a vertical line that sweeps from left to right so that the horizontal
axis represents time. Every pair of horizontal line segments that approximates a
customer at (x, y) will cut the sweep line and register an interval [y−, y+] from time
x− to time x+. Whenever the sweep line detects an overlap of registered intervals
(we term it a child interval), it will calculate possible Steiner zones. If a new Steiner
zone is found, the child interval is also registered, and is not removed until one of
178
C1
C2
C3
C4
C5
C6
C7
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
l1
l2
l3
l4
l5
l6
l7
l8
l9
l10
l11
x
y
(a) Customer locations
(x, y)
(x−, y−) (x+, y−)
(x−, y+) (x+, y+)
r
(b) Customer approximation
C1
C2
C3
C4
C5
C6
C7
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
l1
l2
l3
l4
l5
l6
l7
l8
l9
l10
l11
x
y
(c) Line segments representation
Figure 6.4: Sweep line algorithm
179
the parents is removed.
Table 6.1: Status of the sweep line
Time Registered interval Steiner zone
[t1, t2] [l4, l9] {C1}
[t2, t3] none none
[t3, t4] [l6, l11] {C2}
[t4, t5]
[l6, l11] {C2}
[l2, l7] {C3}
[t5, t6] [l2, l7] {C3}
[t6, t7]
[l2, l7] {C3}
[l1, l6] {C4}
[l2, l6] {C3, C4}
[t7, t8] [l1, l6] {C4}
[t8, t9] none none
[t9, t10]
[l5, l10] {C5}
[l3, l8] {C6}
[l5, l8] {C5, C6}
[t10, t11]
[l5, l10] {C5}
[l3, l8] {C6}
[l4, l9] {C7}
[l5, l9] {C5, C7}
[l4, l8] {C6, C7}
[l5, l8] {C5, C6, C7}
[t11, t12] [l4, l9] {C7}
The status of the sweep line as it sweeps across the customers in Figure 6.4(c)
is recorded in Table 6.1. The first column gives the time interval. The second
column gives the registered interval over each time interval. The third column gives
the Steiner zones corresponding to the registered intervals. If there is more than
one Steiner zone corresponding to an interval, we record only the interval with
the highest degree. Over the time interval [t4, t5], although the registered intervals
[l6, l11] and [l2, l7] overlap, upon checking, the disks defined by customers C2 and C3
180
do not overlap, so the child interval [l6, l7] is not registered on the sweep line. Over
the time interval [t10, t11], the registered interval [l5, l8] points to two Steiner zones
({C5, C6}, {C5, C6, C7}). Only the Steiner zone {C5, C6, C7} is registered because it
has degree three, while the Steiner zone {C5, C6} has degree two.
6.3.1.3 Set covering
After we have determined the set of Steiner zones, we solve a Set Covering
Problem (SCP) that determines the fewest Steiner zones to cover all customers.
Specifically, the following Binary Integer Program (BIP1) is solved.
(BIP1) min
∑
j∈M
xj (6.1)
s.t
∑
j∈M
sijxj ≥ 1 ∀i ∈ N (6.2)
xj ∈ {0, 1} ∀j ∈M (6.3)
where M = {0, 1, . . . ,m} is the set of indices for the Steiner zones and N =
{0, 1, . . . , n} is the set of indices for the customers. The binary decision variable
xj equals 1 when Steiner zone j is selected. In the objective function (6.1), we
minimize the number of Steiner zones selected. In constraints (6.2), the binary pa-
rameter sij equals 1 when Steiner zone j is contained in the disk defined by customer
i; therefore, customer i is served by visiting Steiner zone j. The constraints force
every customer to be served. Constraints (6.3) define a binary decision variable.
181
We observe that the optimal solution is often not unique. For example, if n = 4
and we have four Steiner zones of degree at least two ({1, 2}, {1, 2, 3}, {2, 3}, {2, 3, 4}),
both {1, 2} & {3, 4} and {1, 2, 3} & {2, 3, 4} cover all four customers with two Steiner
zones. The combination {1, 2} and {3, 4} is desirable because the union of the two
low-degree Steiner zones contains the union of the two high-degree Steiner zones.
In view of the above observations, we modify BIP1 with a new objective func-
tion (6.4) and an additional constraint (6.5). We denote the modified model by
BIP2.
(BIP2) min
∑
j∈M
djxj (6.4)
s.t
∑
j∈M
xj ≤ L (6.5)
∑
j∈M
sijxj ≥ 1 ∀i ∈ N (6.6)
xj ∈ {0, 1} ∀j ∈M (6.7)
In the objective function (6.4), dj is the degree of Steiner zone j. The objective
function minimizes the total degree of the selected Steiner zones. In constraints
(6.5), L is the optimal objective function value found in solving BIP1.
Both BIPs are solved using the general purpose optimization software Gurobi
[53]. Even though the SCP is NP complete, our computational experience shows
that both BIPs are solved quickly in all test instances. If the problem size is too
large for a solution to be produced in a reasonable amount of time, the following
three modifications may be used:
182
1. Use an exact solver specifically designed to solve the SCP;
2. Reduce m, the number of Steiner zones considered; for example, by excluding
some degree two or degree three Steiner zones;
3. Use a heuristic solver for the SCP instead of an exact solver.
6.3.1.4 MMVRP solver
We choose a Steiner point from every Steiner zone. We do not make arbitrary
choices, but identify the Steiner point that is closest to the depot. These Steiner
points together with the depot constitute a min-max VRP that is solved using the
MMD solver developed by Wang et al. [95]. An initial feasible solution to the
MMCEVRP is produced.
6.3.2 Improvement procedures
The key difference between the standard VRP and the CEVRP lies in the
location where a customer can be served. In the standard VRP, there is a unique
location where a customer has to be visited whereas, in the CEVRP, a customer can
be served at any point in the disk defined by that customer. As long as the radius
of the disk is greater than zero, the number of choices is infinite. These choices
increase the complexity of the routing problem but they also lead to savings. Both
the intra-route and inter-route improvement procedures seek to exploit the choices
of the locations to visit.
183
6.3.2.1 Intra-route improvement
For a specific route, we want to shorten its length by re-selecting Steiner points.
An optimal choice may be found using second order cone programming [70], however
this procedure is time consuming. We apply a greedy heuristic, GREEDYSR, that
alternates between selection of Steiner points and routing of these points.
We examine the Steiner points in the sequence that they are visited on a
specific route. For every Steiner point q0, we fix its predecessor p and successor s, and
choose a point q from the Steiner zone where q0 is located to minimize d(p, q)+d(q, s),
where d(p, q) denotes the Euclidean distance from p to q. In particular, if the line
segment ps crosses the Steiner zone, there are infinite number of choices, and we
choose one of the two points at the boundaries arbitrarily.
Figure 6.5 illustrates one iteration of the selection process. Let a route serve
two customers C1 at (1, 1) and C2 at (2, 0). Both customers have a service range of
0.25. The depot is at the origin. Initially, as shown in Figure 6.5(a), the route visits
points A1(0.8232233, 0.8232233) and B1(1.75, 0) that are within the respective disks
and are closest to the depot. The length of this route is about 4.15. To improve the
selection of Steiner points, we first fix points D and B1 on the route, and choose a
point A on the disk defined by C1, such that d(D,A) + d(A,B1) is minimized. The
point is A = A2(0.984492, 0.750481) as shown in Figure 6.5(b). Next, we fix points
A2 and D on the route, and choose a point B on the disk defined by C2, such that
d(A2, B) + d(B,D) is minimized. The point is B2(1.763626, 0.0814086). The new
route has length 4.03.
184
C1
C2D
A1
B1
(a) Before
C1
C2D
A1 A2
B1
B2
(b) After
Figure 6.5: One pass of the selection process
We repeat the selection process until no improvement can be found. The Lin-
Kernighan-Helsgaun (LKH) TSP solver [56] is called to optimize the routing. The
improvement procedure alternates between the Steiner points selection process and
the LKH solver until no improvement can be found.
Next, we perturb the route by a random selection of Steiner points. Each
Steiner point has a probability of 0.5 to be replaced with the center point of
its Steiner zone. We expect the new route to increase in length. We apply the
GREEDYSR to search for a new local minimum. The routing should precede the
selection process this time; otherwise we may undo the perturbation. If the new
route is shorter, it replaces the old route. In our implementation, perturbation is
carried out 10 times.
6.3.2.2 Inter-route improvement
The construction procedures and the intra-route improvement procedures de-
pend on the choice of Steiner zones from solving BIP1 and BIP2. However, such
a choice may not be optimal. We use two strategies to break away from a local
185
optimum.
The first strategy does not consider any Steiner zone of degree greater than
one. For every customer location, we find its closest point (called a foot) on the
feasible routes. Ties are broken arbitrarily. The feet together with the depot form
a min-max VRP that can be solved using the MMD solver. The solution remains
feasible because it visits all feet. It is at least as good as the original solution that
visits all feet. The intra-route improvement procedures are then applied to decrease
the objective function value.
The second strategy uses new Steiner zones. In the current version of MMSZ,
we compute the feet as described in the first strategy. These points serve as candi-
date Steiner zone points. For each foot, we identify the customers with disks that
contain the point in order to generate a new set of Steiner zones. From the new set,
we select the least number of Steiner zones using BIP1 and BIP2. The MMD solver
solves the min-max VRP on the selected points.
The second strategy may be modified by considering other points on the routes
that are different from the feet. We can construct new Steiner zones using the
feasible routes as a guide. Further research may develop insight on how to choose
the new Steiner points.
In Table 6.2, we give an overview of the MMSZ algorithm.
186
Table 6.2: Overview of MMSZ
Algorithm 1
Construction phase
1. Customer pruning
Remove customers with disks that contain the depot or disks defined by other customers
2. Steiner zone construction
Use sweep line algorithm
3. Set covering
Solve BIP1 and BIP2
4. Solution initialization
Use the min-max VRP solver MMD
Improvement phase
5. Intra-route improvement
5a For every route in the solution
Do
Alternate between Steiner point selection and re-routing
While there is improvement
5b Do 10 times
Perturb Steiner point selection
Do
Alternate between re-routing and Steiner point selection
While there is improvement
If route length shortened
Update route
Endif
End
Endfor
6. Inter-route improvement
Do
6a Select feet for all customers on its nearest route
Use the min-max VRP solver MMD
Apply Intra-route improvement
6b Select a subset of feet that covers all customers
Use the min-max VRP solver MMD
Apply Intra-route improvement
while there is improvement
187
6.4 Computational results
Because the MMCEVRP is a new problem that has not been studied in the lit-
erature, there are no benchmark instances. We modify existing CETSP and CEVRP
instances to produce benchmark instances. We test the performance of MMSZ us-
ing 14 instances taken from [70]. The number of customers ranges from 99 to 1000.
Some instances have customer locations that are uniformly distributed; some have
locations that are clustered. The instances can be found in the Appendix. We im-
plement MMSZ using C++ and perform our computational experiments on a Linux
machine with a 2.2GHz processor and 4G RAM. The running time of an instance is
the average of 10 runs.
6.4.1 CETSP
In this section, we report the performance of MMSZ on CETSP. When there is
one route, the MMD solver in MMSZ reduces to a LKH solver. We compare MMSZ
to the heuristic solvers developed in [70]. The results are presented in Table 6.3. The
first column gives the instance names. The second column gives the best solution
produced by these heuristics. The third column gives the gap (%) between the results
produced by MMSZ and the best solutions. The fourth to seventh columns give the
gap (%) between the seven heuristics developed in [70] and the best solutions. In the
last three rows, we calculate the average gap, the average running time per instance,
and the number of best solutions produced. Mennell [70] developed 10 heuristics;
the three heuristics with an average gap greater than 10% and no best solutions are
188
not reported in Table 6.3.
MMSZ finds four new best solutions. In terms of average gap, MMSZ is not
the best among the heuristics; MMSZ’s average gap of 3.22% is reasonable given its
short running time compared to the other algorithms (note these algorithms were
run on different machines). SZ1 is faster than MMSZ but produces an average gap
of 7.78%. SZ1 produces three results that have a deviation of 10% or more from the
best solution. The results of MMSZ on these 14 instances indicate that MMSZ needs
improvement. The fact that MMSZ has a short running time makes it a promising
heuristic.
6.4.2 MMCEVRP
We present the results of MMSZ on the MMCEVRP in Table 6.4. The cus-
tomer locations and service ranges are exactly the same as those in the CETSP
instances. We assume that there are six routes in each instance. The first col-
umn in Table 6.4 gives the names of the test instances. The second and the third
columns give the objective function values and running times produced by MMSZ.
The average running time is 140.5 seconds. In the fourth and fifth columns, we
solve each instance as a min-max VRP using MMD, i.e., assuming all customer
service ranges are zero. Comparing the second and the fourth columns, the differ-
ence in the objective function values produced by MMSZ and MMD is the benefit
we obtain from close-enough routing. The percentage savings is computed in the
sixth column. The average savings is 27.6%. Comparing the third and the fifth
189
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190
columns, we observe that MMSZ generally takes less computational time to solve
an MMCEVRP instance than MMD takes to solve the corresponding min-max VRP
instance. Most likely, this is due to the customer pruning strategies. Even though
MMSZ calls MMD several times, the instances solved are smaller than the min-max
VRP. Further research is required to construct lower bounds on these MMCEVRP
instances to examine the performance of the MMSZ algorithm.
6.5 Conclusions and future work
In this chapter, we proposed a new problem, the MMCEVRP, by combining
the work on the CETSP, the CEVRP, and the min-max VRP. We developed a
heuristic, MMSZ, based on the idea of Steiner zones and showed that it performed
reasonably well on CETSP instances.
There are several modifications that can be considered such as using the convex
hull argument in customer pruning and using the Steiner zone selection in the inter-
route improvement procedures. We hope that these modifications will improve the
MMSZ solver. We would like to run the solver on additional CETSP instances and
develop lower bounds on the MMCEVRP instances.
191
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192
Chapter 7: Conclusions and future work
In this dissertation, we studied several variants of the VRP with the min-
max objective function. Instead of minimizing the total distance traveled by all the
vehicles, we minimize the distance of the longest route.
We used both theoretical and computational approaches. We performed worst-
case analyses that compared optimal solutions to the min-max and min-sum prob-
lems. We showed that the optimal solutions with respect to one objective function
can be very poor with respect to the other objective function. This observation
motivated our development of heuristics that solved the min-max VRPs.
We studied the MMMDVRP and developed a heuristic algorithm (MD). We
compared MD to two alternative heuristics that we developed and to an existing
method from the literature on a set of 20 test instances. MD produced 15 best
solutions and was the top performer. Additional computational experiments on in-
stances with uniform and non-uniform distributions of customers, varying customer-
to-vehicle ratios, and real-world data further demonstrated MD’s effectiveness in
producing high-quality results.
We generalized the MMMDVRP to the MMSDMDV-MSTR by incorporating
customer service times, service splits, and minimum service requirements. We de-
193
veloped a heuristic (MDS) for this problem. We demonstrated the effectiveness of
MDS on 21 instances whose near optimal solutions can be estimated using geome-
try. We also investigated the savings from split service and the split patterns as we
varied the required service times, the average number of customers per route, and
the minimum service time requirements.
We proposed the VRPD. The problem was motivated by several influential
companies currently investigating the use of commercial drones for package delivery.
We performed worst-case analyses to reveal the amount of delivery time that could
be saved at most as a result of using a fleet with trucks and drones instead of using
a traditional fleet with only trucks. The maximum speed up is a function of the
number of drones loaded onto one truck and the speed of a drone relative to the
speed of a truck.
We proposed the MMCEVRP which is motivated by RFID technology. We
developed a heuristic (MMSZ) for this problem. On 14 CETSP instances from the
literature, MMSZ produced four new best solutions. MMSZ had fast running times
and produced results that were comparable in quality to the results of the existing
heuristics for the CETSP. We also generated 14 new MMCEVRP instances and
used MMSZ to demonstrate the savings that could be obtained when vehicles are
required only to get close enough to the customers.
We raised new research questions that can be explored in future work. First,
we compared the min-max and min-sum objective solutions from a worst-case per-
spective. What happens in average cases? One approach would be to solve the
benchmark VRP instances with the min-max objective function and compare the
194
solutions to the best-known min-sum solutions. However, almost all benchmark
VRP instances involve the delivery of goods instead of services. Therefore, we
would need to modify MD and MDS to handle the delivery of goods. Second, we
showed the benefit from using drones in the VRPD from a theoretical point of view.
What happens in practice? Can we run a simulation of the VRPD? This requires
a computational approach for the VRPD. Third, we have already mentioned sev-
eral modifications that can be considered to improve the MDSZ algorithm for the
CETSP and MMCEVRP. We would like to demonstrate the effectiveness of MDSZ
over a larger set of test instances. Finally, real-life routing is more complicated
than merely deciding to use a min-sum or min-max objective function. Routing
may involve a combination of the two objective functions. We need to consider
constructing routes that minimize the total distances but are balanced at the same
time. Besides having a weighted sum in the objective function, a unifying scheme
might consider minimizing the p-norm of the route lengths, or equivalently, to mini-
mize Lp1 +L
2
2 + · · ·+Lpm, where L1, L2, . . . , Lm are the lengths of the routes. It would
be worthwhile to explore how the value of the parameter p changes the solutions.
195
Appendix A: The MD algorithm illustration
In this appendix, we illustrate the MD algorithm using an instance with three
depots, with each depot having one vehicle and 10 customers. (We denote this
problem by MM1. The coordinates of the customers and depots are given in the
online appendix.) The locations of customers and depots are shown in Figure A.1.
Customers are represented by circles and depots are represented by stars.
A.1 Initialization
Customers 1, 9, 5, and 2 are assigned to depot 1. Customers 7, 3, and 4 are
assigned to depot 2. Customers 10, 6, and 8 are assigned to depot 3. The LKH
solver generates a TSP on each route. This gives the initial solution that is shown
in Figure A.2.
The number next to a line segment is the length between neighboring nodes.
The number in parentheses next to a depot is the total length of the route passing
through that depot (170.778 for depot 1, 143.072 for depot 2, and 219.02 for depot
3).
196
A.2 Local search
The maximal route passes through depot 3 and has a length of 219.02. There
are three customers on this route. The savings produced by removing a customer
from this route are given in Table A.1.
The customer with the largest savings (customer 10) is removed from the
maximal route. It may be inserted onto the route passing through depot 1 or onto
the route passing through depot 2. The increase in route length is estimated by
inserting customer 10 between every pair of adjacent nodes on the route. These
costs are given in Table A.2.
Customer 10 is inserted in the least–cost way (27.837) between customer 7 and
customer 3 on route 2 that passes through depot 2. The TSP solution on routes 2
and 3 are calculated again using the LKH solver. The following solution is produced
after iteration 1 (see Figure A.3). Route 1 passes through depot 1 with customers 1,
9, 5, and 2 and a length of 170.778. Route 2 passes through depot 2 with customers
7, 10, 3, and 4 and a length of 170.909. Route 3 passes through depot 3 with
customers 8 and 6 and a length of 127.098.
The objective function value decreased from 219.02 to 170.909, so the proce-
dure continues. The maximal route is the second route with four customers. The
savings from removing a customer are given in Table A.3.
197
Figure A.1: Locations of customers and depots
100
90
80
70
60
50
40
30
20
10
1009080706050403020100
Customer1
Customer2
Customer3
Customer4
Customer5
Customer6
Customer7
Customer8
Customer9
Customer10
Depot1
Depot2
Depot3 Customer
Depot
Customer 10 is removed and inserted onto route 1 or route 3. The insertion
costs are given in Table A.2 and Table A.4.
If customer 10 is inserted onto route 3, the estimated increase in route length
is 91.922. If it is inserted onto route 1, the estimated increase in route length is
88.507 (see Table A.2). So we try to insert customer 10 onto route 1. After solving
Table A.1: Savings if a customer is removed from route 3
Customer removed Savings
Customer 10 91.922
Customer 6 10.282
Customer 8 0.606
198
Figure A.2: Initial solution
100
90
80
70
60
50
40
30
20
10
1009080706050403020100
80
35.056
22.361
10
22.361
(170.778)
22.361
56.569
14.142
50
(143.072)
94.34
53.852
10
60.828
(219.02)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
Table A.2: Cost of inserting customer 10 onto routes 1 and 2
Route Position of insertion between nodes Cost of insertion
Passing through depot 1
depot and customer 1 89.706
Customer 1 and 9 88.507
Customer 9 and 5 103.602
Customer 5 and 2 140.214
Customer 2 and depot 154.734
Passing through depot 2
Depot and customer 7 70.908
Customer 7 and customer 3 27.837
Customer 3 and customer 4 28.284
Customer 4 and depot 141.421
199
Figure A.3: Iteration 1
100
90
80
70
60
50
40
30
20
10
1009080706050403020100
80
35.056
22.361
10
22.361
(170.778)
36.056
14.142
56.569
14.142
50
(170.909)
53.852
10
63.246
(127.098)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
Table A.3: Savings if a customer is removed from route 2
Customer removed Savings
Customer 7 1.203
Customer 10 27.837
Customer 3 0
Customer 4 0
Table A.4: Cost of inserting customer 10 onto route 3
Route Position of insertion between nodes Cost of insertion
Passing through depot 3
Depot and customer 8 100.488
Customer 8 and 6 110.828
Customer 6 and depot 91.922
200
the TSP on routes 1 and 2 using the LKH solver, the new objective function value
is 238.877, which is greater than 170.909. There is no improvement if customer 10
is removed from the maximal route (i.e., route 2)
We go back to Table A.3 and consider removing customer 7. The increase in
route length is estimated by inserting customer 7 between every pair of adjacent
nodes on routes 1 and 3. These costs are given in Table A.5.
Customer 7 is inserted in the least-cost way between customers 9 and 5 on
route 1. After solving the TSP on routes 1 and 2 using the LKH solver, the new
objective function value is 203.438, which is greater than 170.909. The solution is
not updated.
We go back to Table A.3 and consider removing customers 3 and 4. Neither re-
moval produces a smaller objective function value, so the solution with the objective
function value of 170.909 (Figure A.3) is retained.
A.2.1 Improvement by perturbation
For each of the three depots, we compute the average of the distances to its
preceding and succeeding customers. This is the radius of the first perturbation.
The angle of the first perturbation is generated randomly. The new positions of the
depots after perturbation are given in Table A.6. The sequence of nodes on each
route is unchanged and the feasible solution to the new problem is shown in Figure
A.4. The objective function value is 240.507.
We apply our local improvement procedure to the problem with the perturbed
201
Figure A.4: A feasible solution to the perturbed problem
100
90
80
70
60
50
40
30
20
10
0
−10
−20
−30
−40
1009080706050403020100−10−20
(190.720)
(152.271)
(240.507)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
202
positions of the depots. When the local improvement procedure ends, we have a
solution with an objective function value of 175.466. This solution is shown in Figure
A.5.
The depots are then set to their original positions with the sequence of nodes
on each route given by the perturbed solution (see Figure A.6). This solution is
feasible and has an objective function value 227.925. We apply the local improve-
ment procedure to this solution and obtain another feasible solution with objective
function value 226.275 in Figure A.7. The first perturbation does not result in a
better solution, and we continue with the second to the fifth with the angles of
perturbations shown in Table A.7. None of these improves the current solution, so
MD stops. The final solution has an objective function value of 170.909.
203
Table A.5: Cost of inserting customer 7 onto routes 1 and 3
Route Position of insertion between nodes Cost of insertion
Passing through depot 1
Depot and customer 1 34.031
Customer 1 and 9 33.945
Customer 9 and 5 33.695
Customer 5 and 2 68.482
Customer 2 and depot 84.097
Passing through depot 3
Depot and customer 8 59.394
Customer 8 and customer 6 96.569
Customer 6 and depot 56.569
204
Figure A.5: Solution to the perturbed problem after local search
100
90
80
70
60
50
40
30
20
10
0
−10
−20
−30
−40
1009080706050403020100−10−20
(175.466)
(173.963)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
205
Figure A.6: A feasible solution to the original problem
100
90
80
70
60
50
40
30
20
10
1009080706050403020100
(223.467)
(227.924)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
206
Figure A.7: The feasible solution generated after one perturbation
100
90
80
70
60
50
40
30
20
10
1009080706050403020100
(220.564)
(226.274)
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
D1
D2
D3 Customer
Depot
207
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208
Appendix B: Min-Max Multi-Depot Vehicle Routing Problem test
instances
In this appendix, we present the problem data for the Min-Max Multi-Depot
Vehicle Routing Problem defined in Chapters 3 and 4. There are 43 instances. Each
instance is presented in two Tables. For example, instance MS1 is given in Tables
B.2 and B.1. The first tables presents information of the depots. The first column
gives the indices of the depots. The second and third columns gives the x and y
coordinates. The fourth column gives the number of vehicles available at the depot.
The second table presents the customer information. The first column gives the
indices. The first column gives the indices of the depots. The second and third
columns gives the x and y coordinates. The fourth column gives the service time
required by the customer in short service scenario. For moderate and long service
scenarios, multiply the service time in the fourth column by 10 and 100, respectively.
For problems with no service as defined in Chapter 3, assume the service time to be
zero.
209
Table B.1: Depot locations and number of vehicles for MS1
Depot index x-coordinate y-coordinate Number of vehicles
1 10.0000 20.0000 1
2 20.0000 30.0000 1
3 30.0000 10.0000 1
Table B.2: Customer locations and service time for MS1
Customer index x-coordinate y-coordinate Service time (short)
1 10.0000 100.0000 8.3325
2 20.0000 40.0000 9.1521
3 70.0000 80.0000 2.1429
4 30.0000 40.0000 9.2204
5 20.0000 50.0000 6.6912
6 90.0000 30.0000 1.8779
7 50.0000 70.0000 3.5065
8 80.0000 30.0000 5.9219
9 30.0000 70.0000 9.6176
10 80.0000 90.0000 9.6840
210
Table B.3: Depot locations and number of vehicles for MS2
Depot index x-coordinate y-coordinate Number of vehicles
1 21.2888 52.2043 1
2 59.2391 43.7700 1
3 22.9666 68.5444 1
4 39.1410 46.6052 1
5 68.7562 47.9356 1
6 39.5161 7.6577 1
7 68.0789 73.3489 1
8 55.8174 17.9064 1
9 57.6268 24.4486 1
10 63.9899 9.8381 1
Table B.4: Customer locations and service time for MS2
Customer index x-coordinate y-coordinate Service time (short)
1 42.3717 21.0719 2.4185
2 38.1346 96.6976 9.7353
3 96.0173 63.5615 9.6145
4 53.2372 42.5230 5.3684
5 52.9380 22.6214 8.2025
6 97.0738 93.2507 2.2770
7 24.2893 74.2582 4.7959
8 25.6262 51.3310 9.2416
9 77.1841 54.1750 8.1299
10 93.4500 21.4326 9.6354
11 56.0222 80.0675 6.9017
12 41.3510 62.7991 1.3214
13 96.8513 9.0680 8.6422
14 74.4064 81.2102 9.4059
15 71.9163 9.6782 7.1086
16 75.8901 19.2165 7.8197
17 94.1169 6.3931 7.6882
18 6.6357 49.6881 4.5300
19 97.5356 46.1870 6.8993
20 33.5305 87.3451 2.5407
21 83.3950 76.1189 7.3544
22 24.7385 68.3413 1.2865
23 77.2984 31.9094 3.4923
24 73.3318 36.2518 1.4155
25 11.6293 86.7636 1.8742
26 4.2015 35.9457 8.4111
Continued on next page
211
Table B.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
27 71.5816 31.5702 7.2535
28 19.9927 89.6961 3.8539
29 71.3789 67.9739 9.5520
30 33.9053 59.6417 1.3100
31 64.4098 88.2395 4.9487
32 54.5410 37.1641 4.4340
33 83.3633 72.3460 7.8897
34 0.0955 24.5134 8.1568
35 33.6509 99.5646 2.6819
36 83.5126 57.9980 5.4079
37 48.1385 42.7319 5.0103
38 79.1647 30.6400 6.8168
39 23.7766 93.6280 7.3843
40 93.7347 75.9613 7.7922
41 77.7377 68.3942 3.4842
42 96.2453 92.2266 7.1173
43 22.4053 96.7950 6.8959
44 91.3288 44.2740 2.4635
45 65.5203 76.4083 2.0710
46 42.4624 99.5223 5.4853
47 68.3758 10.9553 9.6377
48 2.6470 6.0943 4.0635
49 9.8981 69.9627 6.2674
50 77.7062 11.3505 3.0143
51 34.0485 8.0255 7.7614
52 59.4066 19.0212 3.2959
53 92.3058 65.8970 5.5536
54 62.2910 14.8163 7.2917
55 9.6147 66.5420 9.0181
56 16.7153 71.4803 9.6336
57 38.2046 77.6560 5.9249
58 85.6429 85.8575 2.2476
59 12.6112 73.1837 2.3436
60 2.3018 9.1639 3.3176
61 10.2421 34.7997 8.5665
62 44.8135 31.9384 3.2885
63 75.6650 80.1556 8.3286
64 19.5197 67.8249 3.1917
65 25.5492 17.8588 9.3634
66 55.0357 69.9585 4.1499
67 29.5891 11.0002 2.7694
Continued on next page
212
Table B.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
68 25.2060 73.4743 3.2598
69 90.6318 23.8128 6.5444
70 30.0720 54.3313 5.2596
71 38.8312 40.4830 4.1649
72 13.4515 86.0942 8.4775
73 58.9769 89.9728 6.2674
74 72.3640 36.8535 5.9475
75 54.9162 94.0927 9.2547
76 5.5910 24.2092 3.5726
77 85.7959 7.7676 7.8148
78 46.0143 48.2620 7.7836
79 78.4601 71.5383 4.4240
80 90.9931 20.7262 6.1104
81 68.2374 60.4949 1.6827
82 36.9523 11.6687 1.4856
83 14.5552 86.0910 5.7772
84 64.5500 94.7755 8.0125
85 8.1966 50.9360 9.4061
86 39.9162 67.2787 2.1692
87 50.5978 30.7904 6.1194
88 76.1888 88.4342 5.2245
89 9.2827 95.3463 1.1071
90 84.8672 51.5999 4.0341
91 93.0101 8.3152 2.4596
92 13.7636 5.3947 8.1486
93 33.2069 42.0601 3.8009
94 74.8078 0.1772 5.7568
95 54.1435 82.3773 2.4908
96 62.9500 84.0450 6.4178
97 65.7024 1.4281 3.3667
98 65.0223 34.0155 6.8867
99 29.9930 61.0280 7.2029
100 46.5959 60.3401 7.7334
101 63.3036 29.0540 5.0549
102 18.4229 35.1736 1.7544
103 54.2073 78.8436 3.0608
104 64.0933 83.3867 9.2200
105 52.0235 74.2476 2.3714
106 72.7472 24.2331 8.4324
107 37.8189 46.6308 5.8451
108 75.6411 57.9820 9.9652
Continued on next page
213
Table B.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
109 26.0032 64.0590 1.7036
110 69.0846 56.5915 4.9841
111 81.2258 17.8132 1.9599
112 22.2669 62.8717 9.6571
113 40.2015 97.7549 1.0417
114 82.4689 3.1487 7.9742
115 83.5833 36.7082 8.3557
116 65.2170 31.8721 8.8183
117 12.9822 84.7061 1.7599
118 10.4784 4.7148 4.5980
119 6.3152 46.9795 3.3388
120 81.1699 23.6665 8.2006
121 66.9589 82.7761 4.8827
122 65.4007 14.9655 9.1958
123 56.7773 93.9456 2.6366
124 36.6892 91.7089 3.3742
125 27.1541 15.1045 2.3099
126 36.9662 21.7908 2.2246
127 69.8461 40.8888 8.8236
128 89.6409 4.7775 6.2173
129 11.2503 53.0036 5.9487
130 44.7073 8.2384 2.3046
131 31.4107 44.4389 8.6773
132 87.2632 32.3204 6.5985
133 80.8371 68.7854 4.1586
134 82.3874 95.1422 5.6192
135 6.4314 18.0002 4.6163
136 81.8890 86.6141 1.6837
137 53.8426 47.3724 3.1592
138 90.7878 94.5270 2.1099
139 40.1263 46.6021 2.6552
140 57.7198 39.6023 3.1596
141 48.3229 72.1113 4.7554
142 95.6106 87.1121 1.4469
143 90.0032 5.0789 9.1244
144 40.8929 37.4761 9.5031
145 72.9129 89.6216 5.4178
146 48.5348 35.8281 5.4033
147 56.0211 2.5580 4.0395
148 28.9788 4.9546 9.1005
149 68.6327 6.1254 4.3232
Continued on next page
214
Table B.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
150 65.6304 24.0635 2.0008
151 88.6036 33.5977 8.0223
152 30.7436 46.4527 4.5076
153 9.3165 25.3369 3.1752
154 3.0666 40.7277 4.6352
155 96.3846 0.2616 1.8681
156 35.8780 59.9087 2.1878
157 45.3830 92.6853 9.4785
158 10.1330 9.0371 9.6052
159 95.6642 72.6462 6.1769
160 89.8242 16.3304 1.5380
161 40.2470 20.8568 3.1130
162 73.7383 5.9784 4.1784
163 75.7725 25.7072 8.3907
164 57.3396 2.9404 1.1386
165 88.9068 25.3356 1.3872
166 89.5288 2.1035 2.5209
167 11.8599 54.6317 6.8420
168 90.6514 23.5580 7.5855
169 62.7801 69.5762 6.8297
170 27.3630 0.4912 5.0583
171 68.9240 25.0002 5.9231
172 77.4322 34.2250 3.6669
173 50.2278 81.4333 7.7022
174 5.4367 0.6760 2.7006
175 56.4215 48.4245 7.1810
176 98.7090 90.5716 2.6516
177 50.1543 18.6850 4.3164
178 88.3348 65.7118 6.6306
179 87.4595 13.4362 8.0220
180 61.7789 80.8280 1.7301
181 96.1064 33.0440 9.3645
182 72.6070 0.5962 7.9814
183 29.1658 76.7126 5.3811
184 46.6497 74.4982 4.9227
185 94.3889 55.5933 5.0211
186 9.4327 24.7474 3.7571
187 1.1900 17.7821 5.5766
188 37.2270 81.8080 5.5969
189 35.4200 17.4567 8.3586
190 8.2033 7.4115 8.1535
Continued on next page
215
Table B.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
191 31.0937 21.1644 6.7989
192 25.5754 37.6355 4.4075
193 10.4812 41.1446 8.3042
194 29.0293 32.4128 5.7954
195 49.8504 47.0981 4.1565
196 82.0490 56.4202 9.4510
197 30.7409 52.8335 8.8835
198 77.1465 79.3498 5.9514
199 20.2639 69.4421 6.6023
200 93.9600 5.4612 6.2834
216
Table B.5: Depot locations and number of vehicles for MS3
Depot index x-coordinate y-coordinate Number of vehicles
1 51.7495 16.6061 1
2 5.9168 24.4048 1
3 45.3517 22.9581 1
4 71.5177 97.2638 1
5 16.3892 54.9787 1
Table B.6: Customer locations and service time for MS3
Customer index x-coordinate y-coordinate Service time (short)
1 65.9347 13.9814 2.8697
2 7.6244 79.7171 3.7112
3 6.5731 62.8122 5.2383
4 42.2126 69.4265 3.0744
5 38.8115 92.4552 8.5988
6 68.7263 35.3737 2.7529
7 32.2607 47.2219 3.0333
8 98.7039 45.2264 2.5364
9 95.5273 40.0173 3.0490
10 9.2997 19.1013 4.9213
11 20.6722 74.7603 3.7999
12 63.5399 49.9023 9.3104
13 63.2667 62.8860 4.8719
14 80.9434 60.7898 2.6633
15 0.7111 18.6862 9.1439
16 49.9912 84.8929 9.8177
17 24.3640 91.6986 4.9498
18 79.4765 71.4256 2.0001
19 83.0204 62.8923 3.3226
20 81.1405 38.7679 4.6785
21 54.5647 93.7111 6.3541
22 21.4328 75.5154 3.3599
23 49.7063 9.2986 6.4256
24 15.3895 7.5649 7.4009
25 42.4834 69.3362 2.9957
26 88.3003 33.2948 2.0568
27 1.1494 40.3969 3.6701
28 90.2812 50.2277 3.8690
29 3.1320 61.1400 4.8175
30 53.3081 6.7816 5.5707
31 30.1657 90.0306 1.7696
Continued on next page
217
Table B.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
32 35.3248 64.7544 3.3623
33 9.2645 35.1265 8.2091
34 57.8233 16.9696 1.2630
35 82.6313 99.5440 9.3597
36 41.6470 99.8797 7.5730
37 29.9607 93.4010 5.3975
38 62.0015 85.0375 6.2067
39 40.6180 57.5657 3.1356
40 1.1030 58.3901 5.1296
41 25.7348 22.9469 9.6678
42 57.3268 65.9794 5.9213
43 6.2108 9.7641 5.6902
44 23.1410 95.9846 3.0843
45 24.5214 87.9156 5.4001
46 61.6664 48.5627 6.6165
47 63.3129 13.9200 7.1122
48 65.2097 95.2913 4.5596
49 24.0897 71.1530 4.3069
50 5.3875 27.0574 9.8918
51 11.8316 61.7139 1.3396
52 96.2430 87.4157 8.9665
53 63.2148 56.4725 9.2196
54 97.8891 68.7579 8.1657
55 14.3761 28.7705 1.8884
56 24.7022 8.4721 3.3568
57 42.5798 37.2627 4.0182
58 39.4624 87.0338 7.1176
59 47.7660 36.1793 2.2290
60 48.4300 27.0830 7.4910
61 20.6074 80.9024 1.9609
62 49.4130 58.4027 6.8838
63 56.4975 49.2220 5.4476
64 14.8381 35.4672 8.0115
65 24.3911 30.8156 7.4353
66 98.7911 66.0646 9.1335
67 23.1601 66.5199 9.0183
68 95.7599 83.5580 4.0075
69 38.8064 69.4215 7.2887
70 28.5808 48.0228 2.7803
71 20.1051 36.5955 1.2749
72 49.0074 93.3398 7.6967
Continued on next page
218
Table B.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
73 46.7727 41.8866 5.5002
74 57.2927 85.0163 5.3193
75 16.4220 39.6474 9.1425
76 11.9291 62.9770 6.4888
77 24.9008 1.1356 6.5590
78 34.0818 97.8530 8.7350
79 57.7463 69.6665 8.2494
80 56.5399 50.5062 6.1905
81 87.9296 84.1013 2.6463
82 22.2513 80.8307 3.1594
83 76.8688 35.6211 8.9786
84 1.9344 40.5730 1.2581
85 71.1380 53.4484 5.4091
86 22.1543 46.6015 2.5113
87 93.5079 78.1585 9.8081
88 75.0565 84.1438 7.4143
89 93.1089 19.1518 5.5042
90 64.6096 38.4546 5.2398
91 25.7552 42.4601 1.5366
92 68.1301 36.0579 7.1377
93 63.4657 43.5454 1.3819
94 82.9543 23.0787 1.6430
95 31.7206 40.8781 5.6948
96 83.3590 53.4587 1.8706
97 78.5742 32.2458 8.3633
98 5.9935 93.3967 8.3579
99 29.4875 76.6433 7.5020
100 73.1582 50.9890 2.3488
101 12.9750 91.4705 6.9364
102 50.7740 20.7177 5.6674
103 34.7406 97.4828 9.7568
104 31.2918 43.4434 6.8409
105 38.7898 52.2879 8.2030
106 16.3543 40.9691 5.0842
107 35.0749 94.9436 4.8915
108 7.0657 53.7740 8.4278
109 40.2958 43.4379 1.7512
110 4.3994 95.2502 2.1985
111 25.7205 83.9927 2.5605
112 54.3179 76.0495 4.5184
113 75.8951 33.2688 8.4824
Continued on next page
219
Table B.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
114 90.7364 26.4182 8.2303
115 53.7900 66.3277 1.5442
116 83.7320 19.9492 4.5933
117 51.0974 19.2698 5.7419
118 90.1519 15.8271 4.7512
119 59.2997 9.5270 6.9117
120 12.4853 54.0009 6.6518
121 25.2374 17.1285 3.6279
122 86.0886 28.7830 4.8849
123 91.0325 61.9415 1.1394
124 7.4769 42.3282 9.8566
125 52.0687 36.4475 2.5045
126 84.5190 28.8201 1.9559
127 8.0212 39.0486 4.3517
128 62.9930 82.6206 2.7831
129 6.7775 4.9362 5.4072
130 29.4878 39.9111 4.0554
131 24.9314 55.4772 9.5647
132 58.6656 84.2038 9.2830
133 33.5036 91.2324 1.4741
134 34.5026 90.5755 7.6407
135 96.5250 79.2366 3.4221
136 61.2938 1.8262 4.8055
137 63.0190 90.4577 5.9308
138 14.8569 60.4558 9.4846
139 34.8968 54.5496 4.7597
140 67.4349 22.2294 9.8475
141 21.3657 58.3887 3.7131
142 61.6199 43.6148 7.3099
143 67.4303 46.9643 6.9970
144 96.4090 58.2727 5.8521
145 98.1139 82.3507 7.2829
146 65.6092 66.0335 6.9988
147 96.3105 16.0012 2.6032
148 17.0134 60.1479 2.1521
149 17.3919 30.1151 9.9917
150 41.0605 12.9844 2.5401
151 43.9775 47.6483 1.2934
152 99.4172 71.7430 6.0508
153 95.2514 86.9517 8.9368
154 94.8587 1.9623 7.0226
Continued on next page
220
Table B.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
155 1.9617 65.3235 2.7139
156 64.4344 72.3402 4.3202
157 14.0724 13.0591 5.1465
158 35.7299 4.4767 9.8347
159 63.1400 29.3383 2.4076
160 66.4236 10.1468 8.6997
161 70.8748 73.1358 6.8029
162 90.7964 42.7851 4.3864
163 91.6963 25.3390 2.7183
164 57.7239 0.5453 4.8543
165 44.1691 65.2593 5.3382
166 18.4609 35.5386 2.0855
167 42.3110 81.7361 6.3056
168 53.2011 90.0074 3.0357
169 30.2541 69.9039 4.4616
170 94.3200 66.3982 6.2469
171 5.6019 70.3227 3.2663
172 26.2895 88.9624 3.6140
173 24.1409 12.3061 6.5538
174 14.5428 44.7442 3.3875
175 31.6316 48.0949 8.4194
176 76.4449 58.9633 9.8440
177 10.7543 86.1450 7.5722
178 77.3199 5.7134 4.0949
179 50.8148 92.5009 6.2566
180 0.7758 39.1215 1.9699
181 70.2742 90.5410 9.1568
182 89.1321 84.3112 8.9169
183 17.1201 99.3738 8.3598
184 30.5219 25.5909 3.3466
185 90.4901 2.5831 6.3492
186 42.8127 70.7142 1.2026
187 43.5558 38.2540 4.8273
188 50.2604 51.9665 3.8145
189 28.5803 22.1361 2.4534
190 39.6735 91.1996 2.6089
191 96.3475 72.3820 4.8060
192 84.0355 64.1584 1.8481
193 35.3905 49.3433 6.3867
194 41.6860 20.0757 5.2383
195 89.4717 11.4777 7.2635
Continued on next page
221
Table B.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
196 55.3785 60.3113 7.2990
197 80.6704 36.7337 6.7468
198 19.6683 31.9498 1.3024
199 67.8038 62.8998 1.6193
200 77.6332 90.0649 3.8764
222
Table B.7: Depot locations and number of vehicles for MS4
Depot index x-coordinate y-coordinate Number of vehicles
1 63.6348 72.0529 1
2 53.2735 39.9964 1
3 20.8717 39.4036 1
4 67.3728 41.1502 1
5 24.1908 14.9744 1
Table B.8: Customer locations and service time for MS4
Customer index x-coordinate y-coordinate Service time (short)
1 41.0432 46.1949 5.7778
2 72.6150 166.6222 6.8900
3 100.6177 76.6355 4.6686
4 89.9108 21.6288 8.3798
5 129.7186 73.1642 7.4652
6 89.0872 33.1108 9.7178
7 45.4358 89.9866 5.7820
8 129.4441 130.5741 3.9263
9 33.3562 16.0214 1.9507
10 89.9108 76.9025 6.4986
11 26.2183 78.5047 8.0092
12 51.7502 21.3618 4.8111
13 77.8312 125.5007 1.8174
14 7.1380 47.5300 3.3982
15 25.3946 117.7570 2.3829
16 81.6747 49.1322 3.5290
17 105.8339 118.2911 4.9608
18 31.7090 3.7383 5.7443
19 15.5113 35.7810 5.1168
20 153.3288 189.5861 8.8783
21 13.3105 60.0757 5.6625
22 72.0659 17.6235 9.4926
23 147.2889 140.4539 6.7394
24 102.8140 63.0174 9.6192
25 38.5724 20.0267 3.1664
26 48.7303 6.9426 7.0851
27 42.6905 46.4619 3.6016
28 95.9506 151.6689 7.0463
29 100.6177 101.4686 7.2563
30 138.2292 170.3605 1.6119
31 45.4358 15.2203 3.2931
Continued on next page
223
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
32 25.3946 58.7450 3.0164
33 19.3548 32.8438 7.0105
34 8.6479 43.5247 8.5995
35 117.6390 142.8571 4.1002
36 23.1984 69.4259 8.0247
37 30.6108 24.0320 7.0780
38 45.1613 15.4873 1.0604
39 113.5209 63.2844 6.4195
40 64.9279 18.9586 4.4809
41 28.4146 12.2830 9.2439
42 101.1668 76.1015 1.0104
43 58.8881 44.8598 5.1620
44 63.2807 28.0374 4.8191
45 34.7289 73.1642 5.1482
46 33.3562 5.3405 7.9314
47 1.7845 55.5407 3.9022
48 75.6349 44.0587 8.0627
49 42.9650 127.3698 5.2422
50 41.3178 7.7437 1.3219
51 105.8339 75.3004 2.5829
52 114.8936 70.2270 7.4958
53 70.9632 52.8660 5.2614
54 64.9279 67.5567 2.3745
55 39.3960 71.8291 4.0701
56 24.0220 17.6235 6.4665
57 0.0000 58.2109 2.7257
58 40.2196 22.9640 7.6458
59 7.2752 50.4673 3.1856
60 91.2835 51.8024 9.2568
61 66.3006 65.9546 3.4216
62 79.4784 80.1068 7.8895
63 36.9252 9.0788 2.6980
64 73.4386 60.3471 3.5875
65 79.4784 65.1535 1.8200
66 122.3061 64.0854 6.1859
67 143.4454 176.2350 7.1503
68 29.7872 32.5768 5.9193
69 48.7303 14.6862 4.8316
70 44.6122 26.7023 6.8000
71 108.5793 80.9079 6.8286
72 75.0858 31.5087 7.1112
Continued on next page
224
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
73 66.5752 25.9012 6.7221
74 41.5923 88.3845 9.5066
75 72.3404 33.3778 2.8804
76 24.2965 41.9226 7.3835
77 66.3006 71.0280 3.1261
78 90.7344 116.4219 2.0746
79 13.5896 35.5140 6.4657
80 52.5738 33.6449 5.0512
81 122.5806 165.2870 5.1285
82 83.5964 77.1696 6.9575
83 72.6150 21.8959 7.9326
84 79.4784 135.9146 4.1520
85 77.8312 39.2523 6.9581
86 38.5724 1.3351 4.7454
87 71.2423 22.1629 8.5774
88 86.8909 16.2884 8.4963
89 2.3336 51.5354 3.3080
90 57.2409 42.7236 6.5211
91 97.3233 100.4005 6.2402
92 47.0830 19.4927 5.8667
93 111.3246 169.2924 8.8295
94 95.6760 167.6903 3.3830
95 92.9307 108.1442 3.8627
96 58.3391 69.6929 2.0729
97 70.6932 42.4566 9.4585
98 39.6706 124.1656 6.8100
99 8.7348 37.8149 5.3152
100 92.6561 82.7770 6.7539
101 120.6589 61.4152 5.9024
102 65.2025 66.4887 6.8258
103 39.3960 23.7650 5.8950
104 70.6932 49.3992 7.4894
105 16.6095 54.7397 5.7025
106 92.3816 52.3364 9.9433
107 52.0247 25.3672 2.9681
108 80.0275 104.6729 1.9522
109 35.0034 81.7089 1.9873
110 170.8991 145.7944 1.5723
111 69.5951 22.4299 4.6412
112 67.3988 49.6662 5.0354
113 51.2011 55.8077 4.2923
Continued on next page
225
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
114 88.8126 70.4940 7.8715
115 21.5511 115.8879 6.6511
116 58.8881 32.0427 7.9478
117 78.9293 106.5421 9.3957
118 143.1709 186.1148 9.7547
119 80.8511 68.0908 2.7283
120 126.9732 143.6582 2.2499
121 108.0302 120.4272 7.2664
122 169.5264 146.5955 1.8444
123 106.9321 193.3244 5.7286
124 102.5395 103.8718 5.7731
125 117.1906 60.6898 8.7503
126 70.9677 45.1268 5.3637
127 14.6877 39.7864 4.5411
128 57.7900 28.5714 7.0429
129 36.6507 23.4980 7.6713
130 33.9053 4.5394 5.6805
131 118.7371 79.0387 4.1294
132 88.5381 47.7971 2.3500
133 56.1382 62.7503 6.2748
134 17.4331 41.1215 3.3593
135 69.3205 44.5928 1.4001
136 138.7783 152.2029 7.7944
137 106.6575 125.7677 3.1851
138 91.1004 39.1989 4.9816
139 119.2862 66.7557 7.1902
140 97.3233 105.4740 4.2331
141 157.7213 200.0000 7.6271
142 13.3150 51.0013 4.5524
143 75.3603 82.5100 7.1507
144 96.2251 65.4206 7.3364
145 28.9636 17.3565 4.9807
146 62.7316 67.0227 1.1762
147 57.2409 37.3832 3.9777
148 124.2279 128.1709 4.8188
149 33.3562 89.4526 3.4324
150 60.8099 91.8558 2.7735
151 41.0432 12.5501 8.3955
152 110.7756 122.2964 4.8693
153 121.4825 150.0668 8.9899
154 56.6918 123.6315 4.5206
Continued on next page
226
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
155 134.6603 138.3178 7.9220
156 44.0631 45.9279 4.5711
157 77.8312 90.7877 8.2766
158 63.2807 131.3752 7.7957
159 88.6250 36.7334 4.3966
160 64.3789 64.0854 2.9442
161 13.0405 38.4513 8.1137
162 46.5340 33.9119 9.5437
163 63.0062 25.6342 3.9481
164 74.2622 72.8972 7.0414
165 8.6479 43.7917 4.9478
166 83.5964 102.2697 8.5015
167 78.6548 80.3738 7.9197
168 63.5552 27.7704 2.5053
169 74.8113 109.2123 8.7578
170 122.8552 73.4312 9.9088
171 32.2581 47.2630 5.6298
172 66.5752 21.0948 8.9585
173 42.1414 113.4846 6.2922
174 42.9650 15.7543 2.3928
175 73.1640 20.2937 2.7988
176 57.7900 61.1482 4.6626
177 70.4187 20.5607 7.7384
178 32.5326 36.5821 8.4303
179 75.3603 17.8905 8.1097
180 36.1016 0.0000 3.8667
181 121.7570 77.9706 5.8066
182 91.0089 84.3792 1.8096
183 40.2196 65.6876 2.0054
184 50.1030 28.8385 2.2266
185 50.6520 48.0641 7.1079
186 113.7909 70.7610 5.4566
187 52.2992 40.3204 2.7074
188 53.9465 60.6142 5.4551
189 117.3644 71.2951 2.3285
190 90.4598 71.5621 1.4948
191 144.8181 139.9199 8.6564
192 31.9835 29.9065 6.0450
193 21.8257 63.2844 9.3665
194 56.1428 56.8758 7.2700
195 94.3034 74.7664 6.2451
Continued on next page
227
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
196 44.0631 84.1121 8.3386
197 90.7344 96.3952 8.9111
198 26.4928 29.6395 9.9002
199 45.7104 24.8331 1.0047
200 63.5552 13.0841 8.7889
201 49.8284 2.6702 6.5131
202 99.7941 60.0801 9.9096
203 157.7213 142.0561 5.7491
204 63.2807 87.5834 5.3157
205 55.0446 81.9760 8.2121
206 108.0302 69.4259 3.0506
207 42.1414 32.3097 5.4828
208 109.6774 68.8919 9.1077
209 92.9307 67.2897 6.1720
210 27.0419 66.2216 8.6066
211 117.0899 127.9039 7.6478
212 28.6891 24.5661 6.2739
213 21.5511 30.7076 3.2206
214 12.2169 43.2577 6.9977
215 65.7515 83.5781 1.7513
216 65.7515 112.1495 6.6336
217 109.6774 148.4646 6.9485
218 99.2450 99.5995 7.5678
219 82.2237 133.2443 9.0168
220 66.3006 37.9172 9.8407
221 88.5976 39.9599 7.9213
222 114.6191 63.8184 6.2330
223 44.0631 53.6716 9.3548
224 51.4756 14.4192 6.2208
225 99.5196 76.3685 1.1528
226 91.0089 34.1789 2.0877
227 109.9520 73.9653 8.7644
228 42.4159 97.1963 5.3587
229 103.1068 113.8852 8.6037
230 16.8840 71.2951 2.8846
231 192.3130 172.7637 5.9706
232 108.5793 79.3057 6.6690
233 23.4729 30.9746 1.2879
234 123.1297 160.7477 6.5324
235 108.5793 123.0975 4.2617
236 31.7090 70.7610 1.4458
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228
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
237 25.3946 30.4406 5.4061
238 13.8641 59.0120 2.7326
239 113.2464 65.6876 2.1078
240 65.4770 16.8224 2.8494
241 105.0103 57.6769 2.3186
242 52.5738 22.6969 2.7016
243 44.0631 21.6288 1.3839
244 123.8161 65.0200 6.7168
245 119.2862 141.2550 3.5368
246 152.5051 139.1188 5.8474
247 194.7838 178.1041 7.2565
248 58.6136 37.1162 5.4920
249 104.4612 84.9132 5.8222
250 2.0590 49.0654 5.0066
251 83.3219 95.8611 2.1154
252 143.7200 159.4125 5.4132
253 8.9224 42.1896 8.6770
254 46.5340 40.5875 8.8653
255 56.4173 25.1001 3.4326
256 102.5395 171.6956 2.8762
257 114.6191 153.8051 6.0848
258 11.9423 63.0174 6.7628
259 104.1867 61.9493 4.7533
260 64.9279 34.9800 2.8538
261 123.4043 78.5047 9.5314
262 61.6335 122.8304 1.7386
263 64.1043 62.4833 1.9514
264 51.7502 39.5194 2.2784
265 44.0631 131.9092 2.4981
266 190.3912 168.3578 6.5886
267 100.8922 155.6742 6.1634
268 22.6493 59.2746 1.4687
269 63.5552 53.9386 9.3808
270 8.6479 42.3231 7.5580
271 58.8881 13.8852 7.6406
272 53.6719 14.9533 1.5706
273 114.3445 75.5674 8.7440
274 152.5051 134.3124 9.4096
275 91.2835 124.4326 9.8596
276 30.3363 64.6195 8.7304
277 54.7701 19.2256 8.0700
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229
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
278 109.1283 116.9559 5.6204
279 63.8298 34.7130 2.5984
280 47.3576 26.4352 4.5873
281 94.8524 111.3485 2.2054
282 135.2093 161.8158 1.2780
283 69.5951 54.4682 9.4523
284 67.3988 69.1589 3.7118
285 103.6376 163.1509 3.6598
286 64.6534 64.8865 3.9964
287 48.4557 68.6248 5.2036
288 32.2581 48.8652 6.8338
289 25.9437 24.2991 1.2271
290 62.1826 31.7757 8.5799
291 30.8854 11.7490 6.0313
292 95.9506 130.0401 8.6869
293 91.8325 74.4993 4.1309
294 124.2279 126.3017 5.0142
295 28.6891 129.2390 1.4882
296 164.0357 150.6008 2.5940
297 76.4585 44.3258 6.9653
298 117.6390 127.6368 3.9775
299 55.0446 128.7049 9.0864
300 72.0659 55.0067 2.0634
301 49.5539 81.4419 9.8958
302 11.9423 48.3311 5.8598
303 162.6630 156.7423 7.3623
304 31.1599 31.2417 9.9954
305 73.4386 18.4246 3.5906
306 47.0830 10.1469 4.7307
307 31.1599 42.9907 5.1836
308 34.4544 66.7557 7.8756
309 53.9465 26.1682 8.3638
310 64.1043 63.5514 1.9020
311 93.7543 59.5461 2.6031
312 30.8854 23.2310 4.2367
313 103.6376 72.6302 1.5103
314 105.8339 73.6983 5.6970
315 81.4001 77.4366 4.0226
316 94.5779 95.0601 2.5810
317 112.1391 119.3280 2.8805
318 92.1071 48.3311 9.1464
Continued on next page
230
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
319 152.7797 144.4593 7.0785
320 90.5605 35.8790 5.2162
321 114.8936 64.6195 9.2092
322 72.6150 18.1575 1.9361
323 98.9705 74.2323 7.7099
324 78.1057 136.7156 7.6264
325 45.4358 11.2150 6.0568
326 116.2663 120.9613 2.6577
327 19.6294 61.4152 6.3749
328 73.7131 145.2603 3.6994
329 34.4544 34.1789 2.2071
330 61.3590 59.8131 2.9134
331 19.6294 72.0961 9.0545
332 14.4132 33.1108 1.6431
333 95.6760 56.0748 3.1824
334 112.1482 121.4953 1.4838
335 123.4043 124.9666 4.9755
336 124.5024 72.0961 1.1195
337 71.2423 48.5981 9.0747
338 3.9808 51.8024 2.7699
339 33.9053 67.8238 1.8403
340 55.0446 119.8932 3.7663
341 59.9863 92.6569 5.1045
342 43.5141 149.2657 1.9150
343 121.2080 34.4459 9.9585
344 120.3844 78.7717 3.9888
345 84.4200 79.8398 3.6761
346 54.7701 41.6555 1.5584
347 70.6932 82.2430 3.6842
348 200.0000 183.1776 1.4172
349 71.5168 114.8198 5.5489
350 68.7714 18.6916 7.8528
351 70.6932 60.8812 6.6796
352 125.6005 69.9599 1.8090
353 40.2196 53.4045 1.7278
354 18.5312 58.4780 7.9952
355 46.8085 12.8171 9.1462
356 41.3178 29.1055 5.8039
357 63.2807 85.9813 1.9824
358 29.2382 65.4206 8.4323
359 59.7117 13.3511 4.0429
Continued on next page
231
Table B.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
360 3.2944 50.5340 3.6458
361 53.1229 10.6809 7.7168
362 41.3178 45.3939 1.0930
363 22.3702 56.6088 1.4360
364 37.7488 68.3578 7.0112
365 115.9918 59.2790 6.4312
366 59.4372 28.3044 5.7349
367 7.2752 51.2684 7.5674
368 72.8895 62.2163 7.3653
369 89.0872 86.7824 8.0324
370 103.0885 80.6409 3.5918
371 34.1798 13.6182 7.2328
372 102.8140 158.3445 6.0100
373 31.1599 98.5314 4.5687
374 104.9417 110.3783 1.5543
375 31.9835 26.9693 8.0216
376 39.3960 77.7036 4.0383
377 5.7653 47.7303 6.4708
378 49.2793 9.6128 7.6713
379 28.6891 86.5154 1.9433
380 92.1071 41.3885 2.1510
381 73.7131 13.6182 5.9459
382 165.9574 174.3658 5.3671
383 30.0618 46.7290 9.0143
384 45.4358 115.3538 8.1906
385 33.9007 93.4579 7.6091
386 66.5752 112.9506 1.4620
387 46.8085 19.7597 1.6560
388 27.8655 63.8184 1.7967
389 26.4928 67.2897 8.1852
390 38.2979 30.1736 9.4871
391 33.6307 132.7103 7.1534
392 37.7488 27.2363 2.1887
393 77.5566 85.4473 7.5045
394 40.7687 17.0895 1.9932
395 92.1071 43.7917 2.0574
232
Table B.9: Depot locations and number of vehicles for MS5
Depot index x-coordinate y-coordinate Number of vehicles
1 33.7083 39.2445 1
2 57.5542 64.0354 1
3 61.0117 5.1591 1
4 95.1798 96.9469 1
5 78.8370 30.4870 1
6 25.7830 87.4796 1
7 58.1238 41.5663 1
8 56.5414 54.3891 1
9 78.1262 31.0382 1
10 86.8901 68.5936 1
Table B.10: Customer locations and service time for MS5
Customer index x-coordinate y-coordinate Service time (short)
1 41.0432 46.1949 6.7665
2 72.6150 166.6222 3.9593
3 100.6177 76.6355 6.8843
4 89.9108 21.6288 7.7422
5 129.7186 73.1642 6.2487
6 89.0872 33.1108 7.6603
7 45.4358 89.9866 3.1134
8 129.4441 130.5741 7.6146
9 33.3562 16.0214 9.7354
10 89.9108 76.9025 8.8024
11 26.2183 78.5047 1.7761
12 51.7502 21.3618 4.2979
13 77.8312 125.5007 4.3228
14 7.1380 47.5300 7.1653
15 25.3946 117.7570 6.3815
16 81.6747 49.1322 8.1043
17 105.8339 118.2911 4.3089
18 31.7090 3.7383 2.8543
19 15.5113 35.7810 1.7800
20 153.3288 189.5861 7.9474
21 13.3105 60.0757 2.8511
22 72.0659 17.6235 4.4944
23 147.2889 140.4539 5.9660
24 102.8140 63.0174 3.0606
25 38.5724 20.0267 6.7775
26 48.7303 6.9426 5.3603
Continued on next page
233
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
27 42.6905 46.4619 2.3666
28 95.9506 151.6689 8.0374
29 100.6177 101.4686 1.9055
30 138.2292 170.3605 3.6466
31 45.4358 15.2203 3.1364
32 25.3946 58.7450 5.7779
33 19.3548 32.8438 1.8235
34 8.6479 43.5247 4.6478
35 117.6390 142.8571 1.9436
36 23.1984 69.4259 2.0106
37 30.6108 24.0320 8.0599
38 45.1613 15.4873 3.6241
39 113.5209 63.2844 6.4318
40 64.9279 18.9586 9.6798
41 28.4146 12.2830 4.8924
42 101.1668 76.1015 7.2528
43 58.8881 44.8598 7.8229
44 63.2807 28.0374 4.8938
45 34.7289 73.1642 6.8995
46 33.3562 5.3405 1.9878
47 1.7845 55.5407 9.4038
48 75.6349 44.0587 2.6871
49 42.9650 127.3698 3.3956
50 41.3178 7.7437 8.1805
51 105.8339 75.3004 5.3884
52 114.8936 70.2270 7.9206
53 70.9632 52.8660 4.5641
54 64.9279 67.5567 3.4564
55 39.3960 71.8291 1.3351
56 24.0220 17.6235 7.0597
57 0.0000 58.2109 4.8661
58 40.2196 22.9640 5.0657
59 7.2752 50.4673 6.4887
60 91.2835 51.8024 1.5346
61 66.3006 65.9546 3.8423
62 79.4784 80.1068 7.9545
63 36.9252 9.0788 7.2679
64 73.4386 60.3471 2.1280
65 79.4784 65.1535 2.1714
66 122.3061 64.0854 1.8312
67 143.4454 176.2350 1.0704
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234
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
68 29.7872 32.5768 4.8080
69 48.7303 14.6862 6.9002
70 44.6122 26.7023 7.5063
71 108.5793 80.9079 5.7809
72 75.0858 31.5087 1.9794
73 66.5752 25.9012 6.6859
74 41.5923 88.3845 2.1385
75 72.3404 33.3778 2.2087
76 24.2965 41.9226 1.8873
77 66.3006 71.0280 2.2782
78 90.7344 116.4219 2.5143
79 13.5896 35.5140 2.7662
80 52.5738 33.6449 3.8573
81 122.5806 165.2870 3.8479
82 83.5964 77.1696 2.9581
83 72.6150 21.8959 3.2594
84 79.4784 135.9146 9.0363
85 77.8312 39.2523 7.3290
86 38.5724 1.3351 6.0016
87 71.2423 22.1629 2.6599
88 86.8909 16.2884 2.9083
89 2.3336 51.5354 1.6961
90 57.2409 42.7236 9.2242
91 97.3233 100.4005 7.3604
92 47.0830 19.4927 6.0201
93 111.3246 169.2924 3.8209
94 95.6760 167.6903 2.4958
95 92.9307 108.1442 6.6025
96 58.3391 69.6929 9.8914
97 70.6932 42.4566 2.5339
98 39.6706 124.1656 3.3201
99 8.7348 37.8149 4.5712
100 92.6561 82.7770 1.6660
101 120.6589 61.4152 7.1569
102 65.2025 66.4887 4.6215
103 39.3960 23.7650 9.8455
104 70.6932 49.3992 4.6197
105 16.6095 54.7397 6.5860
106 92.3816 52.3364 2.3893
107 52.0247 25.3672 4.4321
108 80.0275 104.6729 2.4502
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235
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
109 35.0034 81.7089 7.8230
110 170.8991 145.7944 8.8400
111 69.5951 22.4299 4.1570
112 67.3988 49.6662 7.1698
113 51.2011 55.8077 3.6473
114 88.8126 70.4940 5.7757
115 21.5511 115.8879 8.4918
116 58.8881 32.0427 6.3774
117 78.9293 106.5421 4.0178
118 143.1709 186.1148 3.6930
119 80.8511 68.0908 5.0733
120 126.9732 143.6582 4.8038
121 108.0302 120.4272 4.2365
122 169.5264 146.5955 6.0249
123 106.9321 193.3244 7.6829
124 102.5395 103.8718 4.8190
125 117.1906 60.6898 4.8642
126 70.9677 45.1268 2.1239
127 14.6877 39.7864 1.2199
128 57.7900 28.5714 3.6117
129 36.6507 23.4980 3.8577
130 33.9053 4.5394 6.8832
131 118.7371 79.0387 9.6124
132 88.5381 47.7971 9.4216
133 56.1382 62.7503 5.1210
134 17.4331 41.1215 3.1643
135 69.3205 44.5928 7.8751
136 138.7783 152.2029 7.8339
137 106.6575 125.7677 7.6658
138 91.1004 39.1989 7.6932
139 119.2862 66.7557 1.9533
140 97.3233 105.4740 7.1340
141 157.7213 200.0000 5.1693
142 13.3150 51.0013 2.9095
143 75.3603 82.5100 1.8867
144 96.2251 65.4206 8.4122
145 28.9636 17.3565 2.5751
146 62.7316 67.0227 2.4721
147 57.2409 37.3832 6.9939
148 124.2279 128.1709 9.0495
149 33.3562 89.4526 5.6490
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236
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
150 60.8099 91.8558 7.3243
151 41.0432 12.5501 2.3823
152 110.7756 122.2964 9.5811
153 121.4825 150.0668 5.8680
154 56.6918 123.6315 7.1176
155 134.6603 138.3178 1.3291
156 44.0631 45.9279 8.2828
157 77.8312 90.7877 7.7376
158 63.2807 131.3752 2.0817
159 88.6250 36.7334 5.7254
160 64.3789 64.0854 3.9325
161 13.0405 38.4513 5.9180
162 46.5340 33.9119 4.5899
163 63.0062 25.6342 4.7358
164 74.2622 72.8972 2.6266
165 8.6479 43.7917 3.2985
166 83.5964 102.2697 1.1848
167 78.6548 80.3738 9.3131
168 63.5552 27.7704 6.8833
169 74.8113 109.2123 9.3935
170 122.8552 73.4312 2.4716
171 32.2581 47.2630 9.2899
172 66.5752 21.0948 8.1519
173 42.1414 113.4846 6.1965
174 42.9650 15.7543 4.9603
175 73.1640 20.2937 3.3185
176 57.7900 61.1482 7.7675
177 70.4187 20.5607 3.0580
178 32.5326 36.5821 1.5777
179 75.3603 17.8905 7.9060
180 36.1016 0.0000 7.0408
181 121.7570 77.9706 7.4369
182 91.0089 84.3792 6.7785
183 40.2196 65.6876 4.7714
184 50.1030 28.8385 4.5169
185 50.6520 48.0641 8.3453
186 113.7909 70.7610 3.8569
187 52.2992 40.3204 8.3309
188 53.9465 60.6142 8.1017
189 117.3644 71.2951 8.6704
190 90.4598 71.5621 5.5507
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237
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
191 144.8181 139.9199 6.7210
192 31.9835 29.9065 9.5580
193 21.8257 63.2844 4.9957
194 56.1428 56.8758 1.5402
195 94.3034 74.7664 8.8007
196 44.0631 84.1121 6.6807
197 90.7344 96.3952 4.1957
198 26.4928 29.6395 9.9730
199 45.7104 24.8331 3.0175
200 63.5552 13.0841 6.8721
201 49.8284 2.6702 6.4449
202 99.7941 60.0801 4.4852
203 157.7213 142.0561 2.2797
204 63.2807 87.5834 1.2262
205 55.0446 81.9760 4.7900
206 108.0302 69.4259 2.6569
207 42.1414 32.3097 7.5320
208 109.6774 68.8919 4.3333
209 92.9307 67.2897 8.5740
210 27.0419 66.2216 7.6081
211 117.0899 127.9039 6.1392
212 28.6891 24.5661 2.5917
213 21.5511 30.7076 9.6165
214 12.2169 43.2577 3.3879
215 65.7515 83.5781 9.3212
216 65.7515 112.1495 3.0139
217 109.6774 148.4646 4.3621
218 99.2450 99.5995 1.7875
219 82.2237 133.2443 6.7610
220 66.3006 37.9172 2.6256
221 88.5976 39.9599 1.4055
222 114.6191 63.8184 7.5086
223 44.0631 53.6716 4.1269
224 51.4756 14.4192 6.9456
225 99.5196 76.3685 4.4548
226 91.0089 34.1789 6.6461
227 109.9520 73.9653 1.1948
228 42.4159 97.1963 9.1951
229 103.1068 113.8852 8.2050
230 16.8840 71.2951 7.7126
231 192.3130 172.7637 8.3180
Continued on next page
238
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
232 108.5793 79.3057 4.4498
233 23.4729 30.9746 6.5555
234 123.1297 160.7477 6.1795
235 108.5793 123.0975 5.7705
236 31.7090 70.7610 3.4756
237 25.3946 30.4406 3.2377
238 13.8641 59.0120 5.0647
239 113.2464 65.6876 3.0494
240 65.4770 16.8224 8.2400
241 105.0103 57.6769 9.8749
242 52.5738 22.6969 1.2699
243 44.0631 21.6288 5.8210
244 123.8161 65.0200 1.7837
245 119.2862 141.2550 8.2188
246 152.5051 139.1188 9.9023
247 194.7838 178.1041 1.6025
248 58.6136 37.1162 9.4546
249 104.4612 84.9132 1.1636
250 2.0590 49.0654 7.1545
251 83.3219 95.8611 8.0536
252 143.7200 159.4125 5.8072
253 8.9224 42.1896 8.9682
254 46.5340 40.5875 9.0910
255 56.4173 25.1001 6.6334
256 102.5395 171.6956 2.2408
257 114.6191 153.8051 2.9602
258 11.9423 63.0174 2.6393
259 104.1867 61.9493 1.3764
260 64.9279 34.9800 1.9625
261 123.4043 78.5047 6.5480
262 61.6335 122.8304 9.4569
263 64.1043 62.4833 4.1901
264 51.7502 39.5194 4.6957
265 44.0631 131.9092 9.8591
266 190.3912 168.3578 9.5102
267 100.8922 155.6742 7.0898
268 22.6493 59.2746 9.8947
269 63.5552 53.9386 7.9015
270 8.6479 42.3231 4.0303
271 58.8881 13.8852 6.9614
272 53.6719 14.9533 3.1975
Continued on next page
239
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
273 114.3445 75.5674 3.6596
274 152.5051 134.3124 7.1216
275 91.2835 124.4326 5.7506
276 30.3363 64.6195 4.7043
277 54.7701 19.2256 6.4237
278 109.1283 116.9559 7.7547
279 63.8298 34.7130 6.2518
280 47.3576 26.4352 5.9661
281 94.8524 111.3485 6.2521
282 135.2093 161.8158 5.6064
283 69.5951 54.4682 1.7433
284 67.3988 69.1589 7.4761
285 103.6376 163.1509 9.9654
286 64.6534 64.8865 4.1908
287 48.4557 68.6248 9.7413
288 32.2581 48.8652 4.1180
289 25.9437 24.2991 8.9789
290 62.1826 31.7757 5.0923
291 30.8854 11.7490 4.7208
292 95.9506 130.0401 2.9596
293 91.8325 74.4993 2.1309
294 124.2279 126.3017 3.7802
295 28.6891 129.2390 7.5349
296 164.0357 150.6008 8.0458
297 76.4585 44.3258 7.2441
298 117.6390 127.6368 1.0882
299 55.0446 128.7049 8.5889
300 72.0659 55.0067 9.3010
301 49.5539 81.4419 7.9386
302 11.9423 48.3311 1.3839
303 162.6630 156.7423 4.4037
304 31.1599 31.2417 7.3391
305 73.4386 18.4246 7.5656
306 47.0830 10.1469 3.0185
307 31.1599 42.9907 3.4215
308 34.4544 66.7557 7.0573
309 53.9465 26.1682 5.2974
310 64.1043 63.5514 6.6134
311 93.7543 59.5461 3.1280
312 30.8854 23.2310 2.5941
313 103.6376 72.6302 8.4668
Continued on next page
240
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
314 105.8339 73.6983 7.9023
315 81.4001 77.4366 9.4103
316 94.5779 95.0601 1.9710
317 112.1391 119.3280 2.6400
318 92.1071 48.3311 1.8919
319 152.7797 144.4593 5.4079
320 90.5605 35.8790 2.7392
321 114.8936 64.6195 9.0630
322 72.6150 18.1575 1.8918
323 98.9705 74.2323 1.3975
324 78.1057 136.7156 6.0157
325 45.4358 11.2150 7.9525
326 116.2663 120.9613 3.8075
327 19.6294 61.4152 2.6108
328 73.7131 145.2603 4.0506
329 34.4544 34.1789 2.8913
330 61.3590 59.8131 5.5914
331 19.6294 72.0961 9.1573
332 14.4132 33.1108 6.6603
333 95.6760 56.0748 1.9138
334 112.1482 121.4953 4.5177
335 123.4043 124.9666 1.4915
336 124.5024 72.0961 5.5115
337 71.2423 48.5981 4.8855
338 3.9808 51.8024 9.9780
339 33.9053 67.8238 8.3044
340 55.0446 119.8932 5.3709
341 59.9863 92.6569 9.0500
342 43.5141 149.2657 2.2379
343 121.2080 34.4459 4.5100
344 120.3844 78.7717 9.3462
345 84.4200 79.8398 9.2574
346 54.7701 41.6555 7.4222
347 70.6932 82.2430 6.5650
348 200.0000 183.1776 4.0896
349 71.5168 114.8198 9.4242
350 68.7714 18.6916 2.1230
351 70.6932 60.8812 7.5753
352 125.6005 69.9599 6.8183
353 40.2196 53.4045 8.4984
354 18.5312 58.4780 4.5845
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241
Table B.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
355 46.8085 12.8171 7.7484
356 41.3178 29.1055 8.5170
357 63.2807 85.9813 3.9021
358 29.2382 65.4206 5.9704
359 59.7117 13.3511 9.8122
360 3.2944 50.5340 5.9438
361 53.1229 10.6809 3.9738
362 41.3178 45.3939 6.5752
363 22.3702 56.6088 4.2457
364 37.7488 68.3578 7.8086
365 115.9918 59.2790 4.7251
366 59.4372 28.3044 5.4311
367 7.2752 51.2684 7.2527
368 72.8895 62.2163 9.7546
369 89.0872 86.7824 3.9498
370 103.0885 80.6409 8.5402
371 34.1798 13.6182 7.6517
372 102.8140 158.3445 9.5876
373 31.1599 98.5314 1.2873
374 104.9417 110.3783 4.2118
375 31.9835 26.9693 6.9639
376 39.3960 77.7036 3.5335
377 5.7653 47.7303 3.0734
378 49.2793 9.6128 7.4002
379 28.6891 86.5154 6.6212
380 92.1071 41.3885 6.3155
381 73.7131 13.6182 6.9439
382 165.9574 174.3658 1.4280
383 30.0618 46.7290 4.1391
384 45.4358 115.3538 5.0621
385 33.9007 93.4579 3.1681
386 66.5752 112.9506 7.4354
387 46.8085 19.7597 8.7056
388 27.8655 63.8184 3.5336
389 26.4928 67.2897 7.5795
390 38.2979 30.1736 2.2399
242
Table B.11: Depot locations and number of vehicles for MS6
Depot index x-coordinate y-coordinate Number of vehicles
1 25.0000 25.0000 1
2 75.0000 25.0000 1
3 75.0000 75.0000 1
4 25.0000 75.0000 1
Table B.12: Customer locations and service time for MS6
Customer index x-coordinate y-coordinate Service time (short)
1 35.0000 25.0000 8.5305
2 34.9799 25.6342 2.2474
3 34.9195 26.2659 6.2939
4 34.8193 26.8925 4.2954
5 34.6795 27.5115 8.2608
6 34.5007 28.1203 5.5340
7 34.2837 28.7166 5.4063
8 34.0293 29.2979 8.8934
9 33.7385 29.8620 4.1783
10 33.4125 30.4064 5.0450
11 33.0527 30.9291 9.6718
12 32.6604 31.4279 1.3807
13 32.2373 31.9008 9.7566
14 31.7851 32.3459 2.7029
15 31.3055 32.7615 7.0041
16 30.8006 33.1458 6.2780
17 30.2723 33.4973 7.0760
18 29.7227 33.8145 4.2492
19 29.1542 34.0963 6.5825
20 28.5689 34.3415 8.3004
21 27.9692 34.5490 1.1733
22 27.3576 34.7181 1.7549
23 26.7365 34.8481 9.7732
24 26.1084 34.9384 6.8621
25 25.4758 34.9887 3.0811
26 24.8413 34.9987 4.6314
27 24.2075 34.9685 2.0982
28 23.5769 34.8982 3.4159
29 22.9519 34.7880 3.3206
30 22.3353 34.6384 3.9850
31 21.7293 34.4500 2.3701
32 21.1365 34.2235 4.1321
Continued on next page
243
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 20.5593 33.9599 2.0949
34 20.0000 33.6603 8.9574
35 19.4608 33.3257 1.8485
36 18.9439 32.9576 9.3704
37 18.4514 32.5575 4.5912
38 17.9853 32.1269 1.4266
39 17.5474 31.6677 4.0814
40 17.1395 31.1816 7.6237
41 16.7632 30.6706 8.1521
42 16.4202 30.1368 5.9042
43 16.1116 29.5823 7.1760
44 15.8389 29.0093 9.0427
45 15.6031 28.4202 1.4931
46 15.4051 27.8173 3.7330
47 15.2457 27.2031 1.4157
48 15.1256 26.5800 2.7593
49 15.0453 25.9506 7.4815
50 15.0050 25.3173 7.4958
51 15.0050 24.6827 8.9002
52 15.0453 24.0494 6.2419
53 15.1256 23.4200 1.6362
54 15.2457 22.7969 9.3047
55 15.4051 22.1827 8.2033
56 15.6031 21.5798 3.5735
57 15.8389 20.9907 5.8930
58 16.1116 20.4177 9.8630
59 16.4202 19.8632 7.4411
60 16.7632 19.3294 8.5507
61 17.1395 18.8184 4.8993
62 17.5474 18.3323 5.2356
63 17.9853 17.8731 6.0464
64 18.4514 17.4425 3.4218
65 18.9439 17.0424 7.7412
66 19.4608 16.6743 5.5350
67 20.0000 16.3397 6.8213
68 20.5593 16.0401 3.7697
69 21.1365 15.7765 2.2485
70 21.7293 15.5500 5.2802
71 22.3353 15.3616 4.2621
72 22.9519 15.2120 8.0930
73 23.5769 15.1018 8.0227
Continued on next page
244
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 24.2075 15.0315 7.0166
75 24.8413 15.0013 2.2015
76 25.4758 15.0113 1.1940
77 26.1084 15.0616 6.0386
78 26.7365 15.1519 3.7074
79 27.3576 15.2819 9.4547
80 27.9692 15.4510 9.8281
81 28.5689 15.6585 3.5796
82 29.1542 15.9037 8.2074
83 29.7227 16.1855 9.0650
84 30.2723 16.5027 6.3777
85 30.8006 16.8542 8.9562
86 31.3055 17.2385 9.4936
87 31.7851 17.6541 5.9424
88 32.2373 18.0992 7.5555
89 32.6604 18.5721 6.1908
90 33.0527 19.0709 1.2327
91 33.4125 19.5936 5.0188
92 33.7385 20.1380 6.8167
93 34.0293 20.7021 5.6908
94 34.2837 21.2834 4.3508
95 34.5007 21.8797 9.4342
96 34.6795 22.4885 8.4658
97 34.8193 23.1075 8.6418
98 34.9195 23.7341 4.3528
99 34.9799 24.3658 6.3387
100 35.0000 25.0000 8.8530
101 85.0000 25.0000 9.4015
102 84.9799 25.6342 7.0162
103 84.9195 26.2659 2.8610
104 84.8193 26.8925 6.8847
105 84.6795 27.5115 1.6485
106 84.5007 28.1203 4.6605
107 84.2837 28.7166 7.0024
108 84.0293 29.2979 9.4035
109 83.7385 29.8620 8.2986
110 83.4125 30.4064 5.3609
111 83.0527 30.9291 7.8107
112 82.6604 31.4279 4.7534
113 82.2373 31.9008 9.7461
114 81.7851 32.3459 9.8918
Continued on next page
245
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 81.3055 32.7615 8.7773
116 80.8006 33.1458 4.5000
117 80.2723 33.4973 5.0927
118 79.7227 33.8145 3.2202
119 79.1542 34.0963 8.0598
120 78.5689 34.3415 8.9455
121 77.9692 34.5490 9.2234
122 77.3576 34.7181 6.0246
123 76.7365 34.8481 6.3898
124 76.1084 34.9384 2.3399
125 75.4758 34.9887 9.0974
126 74.8413 34.9987 5.0535
127 74.2075 34.9685 2.8511
128 73.5769 34.8982 9.0969
129 72.9519 34.7880 7.8633
130 72.3353 34.6384 8.9424
131 71.7293 34.4500 3.5646
132 71.1365 34.2235 7.0590
133 70.5593 33.9599 6.9785
134 70.0000 33.6603 2.1053
135 69.4608 33.3257 4.6659
136 68.9439 32.9576 3.4776
137 68.4514 32.5575 7.4500
138 67.9853 32.1269 3.5505
139 67.5474 31.6677 9.0658
140 67.1395 31.1816 8.4392
141 66.7632 30.6706 4.5102
142 66.4202 30.1368 5.4811
143 66.1116 29.5823 7.2532
144 65.8389 29.0093 8.5093
145 65.6031 28.4202 6.4867
146 65.4051 27.8173 6.1726
147 65.2457 27.2031 3.9344
148 65.1256 26.5800 5.1078
149 65.0453 25.9506 7.4242
150 65.0050 25.3173 8.9596
151 65.0050 24.6827 7.4877
152 65.0453 24.0494 1.1675
153 65.1256 23.4200 7.0730
154 65.2457 22.7969 4.9466
155 65.4051 22.1827 4.9404
Continued on next page
246
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 65.6031 21.5798 2.0533
157 65.8389 20.9907 8.3321
158 66.1116 20.4177 3.9237
159 66.4202 19.8632 3.2161
160 66.7632 19.3294 4.0844
161 67.1395 18.8184 4.3812
162 67.5474 18.3323 5.9190
163 67.9853 17.8731 6.0573
164 68.4514 17.4425 4.5624
165 68.9439 17.0424 4.5832
166 69.4608 16.6743 5.6383
167 70.0000 16.3397 6.9178
168 70.5593 16.0401 9.5582
169 71.1365 15.7765 7.5011
170 71.7293 15.5500 4.6007
171 72.3353 15.3616 8.4868
172 72.9519 15.2120 2.2090
173 73.5769 15.1018 1.5442
174 74.2075 15.0315 1.7582
175 74.8413 15.0013 2.4751
176 75.4758 15.0113 3.9180
177 76.1084 15.0616 3.7155
178 76.7365 15.1519 1.1051
179 77.3576 15.2819 5.8591
180 77.9692 15.4510 1.8584
181 78.5689 15.6585 2.3186
182 79.1542 15.9037 6.6803
183 79.7227 16.1855 8.7339
184 80.2723 16.5027 9.7680
185 80.8006 16.8542 6.1375
186 81.3055 17.2385 9.9717
187 81.7851 17.6541 5.9819
188 82.2373 18.0992 5.6391
189 82.6604 18.5721 3.9761
190 83.0527 19.0709 4.8700
191 83.4125 19.5936 5.4263
192 83.7385 20.1380 1.6393
193 84.0293 20.7021 8.9897
194 84.2837 21.2834 1.5817
195 84.5007 21.8797 4.9257
196 84.6795 22.4885 8.4397
Continued on next page
247
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 84.8193 23.1075 4.5508
198 84.9195 23.7341 6.5213
199 84.9799 24.3658 8.3678
200 85.0000 25.0000 8.9761
201 85.0000 75.0000 9.3800
202 84.9799 75.6342 2.7171
203 84.9195 76.2659 3.3272
204 84.8193 76.8925 9.0808
205 84.6795 77.5115 6.3403
206 84.5007 78.1203 5.5346
207 84.2837 78.7166 6.5153
208 84.0293 79.2979 8.3748
209 83.7385 79.8620 5.7870
210 83.4125 80.4064 2.8187
211 83.0527 80.9291 5.0850
212 82.6604 81.4279 4.8512
213 82.2373 81.9008 9.6945
214 81.7851 82.3459 6.5805
215 81.3055 82.7615 7.2585
216 80.8006 83.1458 7.4815
217 80.2723 83.4973 4.1221
218 79.7227 83.8145 5.6529
219 79.1542 84.0963 6.0103
220 78.5689 84.3415 2.4085
221 77.9692 84.5490 6.0585
222 77.3576 84.7181 7.2532
223 76.7365 84.8481 4.8381
224 76.1084 84.9384 8.5264
225 75.4758 84.9887 7.5825
226 74.8413 84.9987 4.2403
227 74.2075 84.9685 5.0879
228 73.5769 84.8982 4.4775
229 72.9519 84.7880 7.9800
230 72.3353 84.6384 7.6084
231 71.7293 84.4500 4.8725
232 71.1365 84.2235 7.2438
233 70.5593 83.9599 9.5069
234 70.0000 83.6603 8.0581
235 69.4608 83.3257 7.3501
236 68.9439 82.9576 1.9840
237 68.4514 82.5575 4.5094
Continued on next page
248
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 67.9853 82.1269 6.3181
239 67.5474 81.6677 5.1344
240 67.1395 81.1816 1.4531
241 66.7632 80.6706 3.0582
242 66.4202 80.1368 8.5077
243 66.1116 79.5823 1.1408
244 65.8389 79.0093 8.7734
245 65.6031 78.4202 1.7026
246 65.4051 77.8173 7.0214
247 65.2457 77.2031 5.5019
248 65.1256 76.5800 2.9619
249 65.0453 75.9506 6.1445
250 65.0050 75.3173 2.0997
251 65.0050 74.6827 7.0405
252 65.0453 74.0494 6.3963
253 65.1256 73.4200 1.5038
254 65.2457 72.7969 1.5071
255 65.4051 72.1827 2.3725
256 65.6031 71.5798 1.1766
257 65.8389 70.9907 4.9166
258 66.1116 70.4177 8.4900
259 66.4202 69.8632 6.5565
260 66.7632 69.3294 5.6812
261 67.1395 68.8184 8.7748
262 67.5474 68.3323 1.8793
263 67.9853 67.8731 9.1725
264 68.4514 67.4425 1.9722
265 68.9439 67.0424 5.6530
266 69.4608 66.6743 2.2884
267 70.0000 66.3397 6.0343
268 70.5593 66.0401 1.0412
269 71.1365 65.7765 7.9001
270 71.7293 65.5500 8.6384
271 72.3353 65.3616 9.2514
272 72.9519 65.2120 9.8827
273 73.5769 65.1018 5.5462
274 74.2075 65.0315 3.4428
275 74.8413 65.0013 1.9068
276 75.4758 65.0113 5.5706
277 76.1084 65.0616 6.2705
278 76.7365 65.1519 7.8660
Continued on next page
249
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 77.3576 65.2819 1.7467
280 77.9692 65.4510 6.9544
281 78.5689 65.6585 5.6528
282 79.1542 65.9037 2.5394
283 79.7227 66.1855 9.4470
284 80.2723 66.5027 6.3143
285 80.8006 66.8542 4.9657
286 81.3055 67.2385 9.4773
287 81.7851 67.6541 6.9032
288 82.2373 68.0992 5.0675
289 82.6604 68.5721 8.5573
290 83.0527 69.0709 5.7936
291 83.4125 69.5936 5.9850
292 83.7385 70.1380 7.1206
293 84.0293 70.7021 4.3047
294 84.2837 71.2834 3.1536
295 84.5007 71.8797 6.2103
296 84.6795 72.4885 8.8020
297 84.8193 73.1075 4.6610
298 84.9195 73.7341 2.0135
299 84.9799 74.3658 4.9946
300 85.0000 75.0000 3.7017
301 35.0000 75.0000 4.6125
302 34.9799 75.6342 8.5003
303 34.9195 76.2659 4.6327
304 34.8193 76.8925 4.5116
305 34.6795 77.5115 4.2440
306 34.5007 78.1203 2.2623
307 34.2837 78.7166 3.3412
308 34.0293 79.2979 1.7813
309 33.7385 79.8620 4.8646
310 33.4125 80.4064 3.3155
311 33.0527 80.9291 3.6780
312 32.6604 81.4279 4.8237
313 32.2373 81.9008 2.0729
314 31.7851 82.3459 5.4556
315 31.3055 82.7615 7.3577
316 30.8006 83.1458 3.1922
317 30.2723 83.4973 8.0656
318 29.7227 83.8145 1.6668
319 29.1542 84.0963 4.5450
Continued on next page
250
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 28.5689 84.3415 1.0305
321 27.9692 84.5490 2.9861
322 27.3576 84.7181 1.0117
323 26.7365 84.8481 2.7026
324 26.1084 84.9384 2.2824
325 25.4758 84.9887 3.4127
326 24.8413 84.9987 2.5740
327 24.2075 84.9685 2.2478
328 23.5769 84.8982 6.3900
329 22.9519 84.7880 9.1095
330 22.3353 84.6384 9.4544
331 21.7293 84.4500 2.9907
332 21.1365 84.2235 5.3440
333 20.5593 83.9599 4.3841
334 20.0000 83.6603 5.7140
335 19.4608 83.3257 3.3839
336 18.9439 82.9576 1.6152
337 18.4514 82.5575 4.9269
338 17.9853 82.1269 2.5647
339 17.5474 81.6677 1.2350
340 17.1395 81.1816 9.5921
341 16.7632 80.6706 4.8754
342 16.4202 80.1368 9.6540
343 16.1116 79.5823 7.8617
344 15.8389 79.0093 1.0661
345 15.6031 78.4202 7.1203
346 15.4051 77.8173 7.3536
347 15.2457 77.2031 6.8062
348 15.1256 76.5800 5.9708
349 15.0453 75.9506 2.9630
350 15.0050 75.3173 7.9513
351 15.0050 74.6827 3.0523
352 15.0453 74.0494 4.3378
353 15.1256 73.4200 9.0184
354 15.2457 72.7969 8.7074
355 15.4051 72.1827 4.6219
356 15.6031 71.5798 3.8622
357 15.8389 70.9907 6.4777
358 16.1116 70.4177 9.1918
359 16.4202 69.8632 9.1819
360 16.7632 69.3294 6.3243
Continued on next page
251
Table B.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 17.1395 68.8184 3.9931
362 17.5474 68.3323 8.6776
363 17.9853 67.8731 4.9816
364 18.4514 67.4425 9.1392
365 18.9439 67.0424 1.2986
366 19.4608 66.6743 5.7918
367 20.0000 66.3397 7.4485
368 20.5593 66.0401 2.6137
369 21.1365 65.7765 4.0288
370 21.7293 65.5500 2.6894
371 22.3353 65.3616 3.8973
372 22.9519 65.2120 4.6347
373 23.5769 65.1018 5.9371
374 24.2075 65.0315 1.4386
375 24.8413 65.0013 5.9746
376 25.4758 65.0113 3.4733
377 26.1084 65.0616 3.1735
378 26.7365 65.1519 3.1883
379 27.3576 65.2819 2.3874
380 27.9692 65.4510 9.6077
381 28.5689 65.6585 9.4210
382 29.1542 65.9037 8.3684
383 29.7227 66.1855 7.5544
384 30.2723 66.5027 2.5823
385 30.8006 66.8542 4.2433
386 31.3055 67.2385 2.6991
387 31.7851 67.6541 1.0108
388 32.2373 68.0992 3.8478
389 32.6604 68.5721 7.2966
390 33.0527 69.0709 6.6273
391 33.4125 69.5936 5.8876
392 33.7385 70.1380 4.9513
393 34.0293 70.7021 3.5868
394 34.2837 71.2834 5.5149
395 34.5007 71.8797 7.8539
396 34.6795 72.4885 7.8617
397 34.8193 73.1075 6.1845
398 34.9195 73.7341 7.7290
399 34.9799 74.3658 6.8098
400 35.0000 75.0000 2.1090
252
Table B.13: Depot locations and number of vehicles for MS7
Depot index x-coordinate y-coordinate Number of vehicles
1 37.0000 64.0000 3
Table B.14: Customer locations and service time for MS7
Customer index x-coordinate y-coordinate Service time (short)
1 65.5741 48.9764 5.5396
2 3.5712 44.5586 4.1254
3 84.9129 64.6313 1.8293
4 93.3993 70.9365 2.3306
5 67.8735 75.4687 2.7835
6 75.7740 27.6025 7.0504
7 74.3132 67.9703 4.8836
8 39.2227 65.5098 7.2496
9 65.5478 16.2612 3.3111
10 17.1187 11.8998 1.0878
11 70.6046 49.8364 5.7905
12 3.1833 95.9744 3.5145
13 27.6923 34.0386 9.5161
14 4.6171 58.5268 9.1580
15 9.7132 22.3812 4.5342
16 82.3458 75.1267 1.2237
17 69.4829 25.5095 7.0429
18 31.7099 50.5957 8.5345
19 95.0222 69.9077 9.7435
20 3.4446 89.0903 1.5124
21 43.8744 95.9291 5.0529
22 38.1558 54.7216 6.2422
23 76.5517 13.8624 7.1797
24 79.5200 14.9294 7.4749
25 18.6873 25.7508 6.8504
253
Table B.15: Depot locations and number of vehicles for MS8
Depot index x-coordinate y-coordinate Number of vehicles
1 26.9062 28.7498 2
2 76.5500 9.1113 2
3 18.8662 57.6209 2
Table B.16: Customer locations and service time for MS8
Customer index x-coordinate y-coordinate Service time (short)
1 84.0717 10.6762 7.5422
2 25.4282 65.3757 4.3646
3 81.4285 49.4174 6.2342
4 24.3525 77.9052 2.0451
5 92.9264 71.5037 1.5189
6 34.9984 90.3721 9.8179
7 19.6595 89.0923 3.5634
8 25.1084 33.4163 6.3548
9 61.6045 69.8746 9.6594
10 47.3289 19.7810 2.6720
11 35.1660 3.0541 2.7374
12 83.0829 74.4074 4.0748
13 58.5264 50.0022 9.3961
14 54.9724 47.9922 4.5160
15 91.7194 90.4722 3.4590
16 28.5839 60.9867 2.3675
17 75.7200 61.7666 4.5740
18 75.3729 85.9442 4.3725
19 38.0446 80.5489 2.1800
20 56.7822 57.6722 4.9154
21 7.5854 18.2922 1.8236
22 5.3950 23.9932 6.5316
23 53.0798 88.6512 1.0988
24 77.9167 2.8674 6.1593
25 93.4011 48.9901 8.1076
26 12.9906 16.7927 3.1183
27 56.8824 97.8681 5.0322
28 46.9391 71.2694 6.1242
29 1.1902 50.0472 1.5526
30 33.7123 47.1088 5.4666
31 16.2182 5.9619 6.7808
32 79.4285 68.1972 2.9914
33 31.1215 4.2431 8.5335
Continued on next page
254
Table B.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 52.8533 7.1445 9.7397
35 16.5649 52.1650 8.6174
36 60.1982 9.6730 5.5540
37 26.2971 81.8149 3.5099
38 65.4079 81.7547 7.7196
39 68.9215 72.2440 3.1324
40 74.8152 14.9865 9.6161
41 45.0542 65.9605 6.5823
42 8.3821 51.8595 6.4024
43 22.8977 97.2975 2.5534
44 91.3337 64.8991 1.8131
45 15.2378 80.0331 3.2974
46 82.5817 45.3798 8.7271
47 53.8342 43.2392 9.1996
48 99.6135 82.5314 7.2967
49 7.8176 8.3470 7.5266
50 44.2678 13.3171 3.0690
51 10.6653 17.3389 6.1845
52 96.1898 39.0938 8.2957
53 0.4634 83.1380 4.6346
54 77.4910 80.3364 9.8960
55 81.7303 6.0471 1.8100
56 86.8695 39.9258 3.8885
57 8.4436 52.6876 5.6027
58 39.9783 41.6799 1.5455
59 25.9870 65.6860 7.5312
60 80.0068 62.7973 6.0090
61 43.1414 29.1984 5.7642
62 91.0648 43.1651 8.4698
63 18.1847 1.5487 8.7288
64 26.3803 98.4064 8.1013
65 14.5539 16.7168 3.8605
66 13.6069 10.6216 5.0699
67 86.9292 37.2410 7.7701
68 57.9705 19.8118 1.9888
69 54.9860 48.9688 1.9877
70 14.4955 33.9493 3.4290
71 85.3031 95.1630 5.7217
72 62.2055 92.0332 9.7539
73 35.0952 5.2677 7.3937
74 51.3250 73.7858 3.8067
Continued on next page
255
Table B.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 40.1808 26.9119 3.6231
76 7.5967 42.2836 8.6532
77 23.9916 54.7871 9.2048
78 12.3319 94.2737 6.7535
79 18.3908 41.7744 3.2983
80 23.9953 98.3052 1.7980
81 41.7267 30.1455 8.5443
82 4.9654 70.1099 6.2625
83 90.2716 66.6339 9.5330
84 94.4787 53.9126 1.5493
85 49.0864 69.8106 6.2618
86 48.9253 66.6528 3.5660
87 33.7719 17.8132 8.4496
88 90.0054 12.8014 2.7189
89 36.9247 99.9080 4.9828
90 11.1203 17.1121 4.5407
91 78.0252 3.2601 8.4392
92 38.9739 56.1200 7.0918
93 24.1691 88.1867 2.8684
94 40.3912 66.9175 3.8629
95 9.6455 19.0433 2.2043
96 13.1973 36.8917 7.0432
97 94.2051 46.0726 6.1389
98 95.6135 98.1638 2.5279
99 57.5209 15.6405 2.3289
100 5.9780 85.5523 5.2847
101 23.4780 64.4765 9.1729
102 35.3159 37.6272 5.9696
103 82.1194 19.0924 1.2965
104 1.5403 42.8253 1.4848
105 4.3024 48.2022 8.2456
106 16.8990 12.0612 5.0624
107 64.9115 58.9507 4.4438
108 73.1722 22.6188 8.1068
109 64.7746 38.4619 4.2786
110 45.0924 58.2986 5.7911
111 54.7009 25.1806 7.4049
112 29.6321 29.0441 8.8433
113 74.4693 61.7091 3.9582
114 18.8955 26.5281 6.8511
115 68.6775 82.4376 9.7735
Continued on next page
256
Table B.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 18.3511 98.2663 1.6837
117 36.8485 73.0249 6.2832
118 62.5619 34.3877 4.7250
119 78.0227 58.4069 3.7822
120 8.1126 10.7769 3.3745
121 92.9386 90.6308 7.8289
122 77.5713 87.9654 9.9569
123 48.6792 81.7761 2.6791
124 43.5859 26.0728 8.0303
125 44.6784 59.4356 2.7622
126 30.6349 2.2513 9.9312
127 50.8509 42.5259 8.2204
128 51.0772 31.2719 4.8180
129 81.7628 16.1485 7.5598
130 79.4831 17.8766 5.4852
131 64.4318 42.2886 8.2809
132 37.8609 9.4229 4.2086
133 81.1580 59.8524 1.6592
134 53.2826 47.0924 6.3189
135 35.0727 69.5949 9.1917
136 93.9002 69.9888 2.7439
137 87.5943 63.8531 4.8913
138 55.0156 3.3604 7.7424
139 62.2475 6.8806 1.3527
140 58.7045 31.9600 9.5169
141 20.7742 53.0864 7.8731
142 30.1246 65.4446 6.0294
143 47.0923 40.7619 2.6546
144 23.0488 81.9981 5.4815
145 84.4309 71.8359 5.6606
146 19.4764 96.8649 9.9482
147 22.5922 53.1334 8.6937
148 17.0708 32.5146 9.6616
149 22.7664 10.5629 7.1105
150 43.5699 61.0959 4.6315
151 31.1102 77.8802 9.4148
152 92.3380 42.3453 5.3154
153 43.0207 9.0823 3.0861
154 18.4816 26.6471 4.5666
155 90.4881 15.3657 7.3457
156 97.9748 28.1005 6.0270
Continued on next page
257
Table B.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 43.8870 44.0085 7.8097
158 11.1119 52.7143 9.9593
159 25.8065 45.7424 9.6619
160 40.8720 87.5372 5.8156
161 59.4896 51.8052 9.6748
162 26.2212 94.3623 2.0406
163 60.2843 63.7709 1.4630
164 71.1216 95.7694 3.7391
165 22.1747 24.0707 6.2217
166 11.7418 67.6122 5.7787
167 29.6676 28.9065 9.1109
168 31.8778 67.1808 5.8650
169 42.4167 69.5140 4.8878
170 50.7858 6.7993 5.8840
171 8.5516 25.4790 7.4117
172 26.2482 22.4040 1.1501
173 80.1015 66.7833 8.2083
174 2.9220 84.4392 2.2826
175 92.8854 34.4462 5.3063
176 73.0331 78.0520 3.3115
177 48.8609 67.5332 4.3218
178 57.8525 0.6715 6.9559
179 23.7284 60.2170 2.5265
180 45.8849 38.6771 3.5091
181 96.3089 91.5991 2.7840
182 54.6806 0.1151 2.7556
183 52.1136 46.2449 3.9416
184 23.1594 42.4349 8.9230
185 48.8898 46.0916 5.2399
186 62.4060 77.0160 4.6357
187 67.9136 32.2472 2.6131
188 39.5515 78.4739 9.7203
189 36.7437 47.1357 4.6671
190 98.7982 3.5763 8.6004
191 3.7739 17.5874 6.5379
192 88.5168 72.1758 4.3895
193 91.3287 47.3486 8.8946
194 79.6184 15.2721 8.0637
195 9.8712 34.1125 5.1846
196 26.1871 60.7389 8.3258
197 33.5357 19.1745 9.0860
Continued on next page
258
Table B.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 67.9728 73.8427 4.8631
199 13.6553 24.2850 4.0090
200 72.1227 91.7424 6.3698
259
Table B.17: Depot locations and number of vehicles for MS9
Depot index x-coordinate y-coordinate Number of vehicles
1 60.3296 84.8597 3
2 78.3266 5.0646 2
3 11.3931 46.6202 2
4 97.8564 32.5653 1
Table B.18: Customer locations and service time for MS9
Customer index x-coordinate y-coordinate Service time (short)
1 56.0562 26.1645 9.1179
2 38.2674 49.4950 7.3186
3 52.3018 58.7149 4.3971
4 70.2185 52.1100 7.6146
5 45.0966 30.7025 9.5869
6 38.5638 30.6025 5.8853
7 35.7138 60.8385 5.8610
8 53.0924 48.1828 3.8000
9 61.9613 45.1720 1.6411
10 73.2240 66.4526 2.6378
11 43.6292 40.0442 1.8369
12 45.1862 51.6930 5.1714
13 33.8185 55.2226 1.0840
14 65.8856 60.2485 9.2352
15 41.7793 39.3206 6.7847
16 36.0966 54.4665 1.0128
17 74.0606 84.3558 1.2735
18 54.4269 31.0878 2.8762
19 53.0906 55.4247 5.0947
20 28.4918 47.1279 2.1454
21 49.0570 39.6614 1.0778
22 50.2878 39.6002 7.5437
23 27.2536 56.2237 4.1870
24 39.6315 78.9453 8.0240
25 37.0725 40.0772 4.9299
26 50.3980 56.7620 4.9290
27 28.4720 43.0117 1.4429
28 58.4147 74.7071 1.4467
29 68.3554 56.8083 1.8199
30 38.5178 48.2762 6.3463
31 42.7329 57.7484 3.1698
32 50.0948 49.9302 8.5723
Continued on next page
260
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 60.0465 63.8400 8.7149
34 50.3145 47.6801 9.6725
35 48.5292 35.9823 5.4001
36 35.9598 53.0806 2.9828
37 39.5500 69.5130 3.0359
38 51.6198 35.0422 5.8311
39 66.8979 46.9707 7.8590
40 50.9771 62.5604 4.1281
41 25.6282 25.9984 5.1511
42 49.0437 57.8181 6.7539
43 41.5411 59.4120 9.2560
44 39.3706 52.6685 2.4542
45 39.7259 40.3721 7.4407
46 30.2890 49.9108 6.1996
47 38.2742 51.1648 4.8997
48 31.6512 61.6906 8.9582
49 37.6434 58.2940 4.5375
50 44.5324 45.6221 2.6108
51 45.3477 70.2485 6.7000
52 39.7763 49.3646 6.6160
53 40.6770 39.8413 3.9515
54 43.3384 44.5198 8.2267
55 49.4040 60.7326 9.9953
56 61.1662 52.4402 9.8288
57 51.7156 61.1108 2.1433
58 38.7618 50.8653 3.0902
59 51.4002 81.0853 1.2127
60 39.3495 29.1795 6.4669
61 17.4180 44.8009 1.9973
62 9.3252 48.9472 4.6671
63 18.3772 51.1156 8.9567
64 39.4696 68.2018 5.9332
65 34.0053 52.7432 4.3210
66 32.5691 48.5640 2.8751
67 43.4380 50.8575 4.9685
68 33.4431 59.3937 9.6058
69 33.8498 41.3822 2.1162
70 51.5661 55.6352 5.2369
71 54.0334 30.4372 8.7121
72 77.6655 49.0151 1.3905
73 47.1772 38.2276 7.2246
Continued on next page
261
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 43.6903 41.8392 9.8109
75 34.6552 53.5316 3.5494
76 40.0684 35.9365 2.2040
77 42.1353 37.6378 7.1675
78 17.7746 31.0518 9.1851
79 39.1806 22.1436 6.4978
80 53.5649 48.1060 9.0998
81 34.7034 64.5343 2.7409
82 49.9176 47.7258 7.7898
83 57.0206 47.0756 4.1163
84 58.2449 36.9158 4.7676
85 53.9549 69.7915 2.4015
86 10.5737 46.8823 8.3710
87 34.7946 66.1752 6.6243
88 55.7356 54.5248 7.6470
89 48.4954 46.7118 8.2460
90 42.9265 63.5268 1.6050
91 49.0988 62.2804 9.5571
92 59.0010 48.6070 5.4782
93 45.0539 66.1994 7.7963
94 32.0196 72.2662 7.6816
95 40.2834 49.1798 8.4802
96 39.8887 46.8040 2.4085
97 55.6678 55.0580 5.1158
98 48.7473 54.3970 6.5629
99 50.6789 60.0939 9.3897
100 44.9691 46.8051 8.5158
101 37.6819 58.9389 9.0588
102 43.7306 63.1075 6.2427
103 45.9529 52.2194 6.2447
104 22.8840 51.9162 8.6943
105 45.4124 34.3209 1.3138
106 56.1083 35.3400 8.9688
107 41.2832 31.7320 4.6696
108 65.3200 34.4464 1.3274
109 50.8642 48.0613 7.7153
110 36.8522 29.8136 2.3935
111 40.6579 78.0758 2.2952
112 38.9257 59.2410 6.4536
113 46.3017 24.1544 3.2903
114 53.6384 35.5681 3.9174
Continued on next page
262
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 38.6870 48.6601 4.6161
116 49.4064 28.5890 4.6574
117 67.9327 44.2513 4.4757
118 56.1642 63.6375 6.4882
119 54.6466 47.9515 2.5020
120 31.2170 49.1595 2.6928
121 35.2257 37.4801 1.8517
122 46.3222 43.0542 3.9087
123 41.4193 33.1055 7.9264
124 19.6422 54.5526 3.1071
125 21.2225 44.3474 7.6633
126 57.5170 59.7921 7.2354
127 32.0268 65.4655 8.4167
128 72.5478 63.4650 8.4518
129 11.1145 49.5645 3.6403
130 49.2681 43.7002 3.7843
131 42.8661 34.6998 5.7073
132 32.0537 51.4814 3.9277
133 48.6332 61.9934 8.4866
134 31.5164 45.7384 8.2927
135 55.1398 47.8335 6.0130
136 43.8124 57.7038 3.3667
137 19.4373 60.7990 7.1251
138 8.2179 32.2886 3.1029
139 38.8024 52.4994 5.1078
140 59.2258 52.4478 4.4611
141 45.4453 48.1108 5.8474
142 43.6321 61.1598 9.9253
143 52.6822 45.4476 7.7970
144 22.9513 39.6726 9.8241
145 63.2195 53.4501 3.1130
146 30.0878 55.7475 5.7570
147 43.3966 47.2812 1.4629
148 37.6633 59.9515 7.8119
149 44.9937 31.0247 6.4178
150 15.0783 36.5635 8.7145
151 64.6271 11.5979 9.8945
152 50.6544 56.5176 9.3654
153 71.5704 37.6122 4.6856
154 63.0953 46.8359 1.0031
155 43.0212 62.6158 5.8679
Continued on next page
263
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 29.4422 50.6377 2.8696
157 18.0156 44.4946 2.9736
158 43.0996 39.3941 3.9323
159 45.9880 46.9954 1.8635
160 57.7974 57.5366 7.7278
161 29.2717 31.0468 7.7366
162 54.2114 49.1456 5.8897
163 43.8776 59.7799 4.0432
164 31.8045 32.2409 8.4910
165 53.9166 58.3671 5.9731
166 46.6522 58.5405 9.6179
167 39.4985 38.9733 9.0355
168 69.6756 31.1936 4.2085
169 51.5606 55.4142 5.9176
170 41.2818 60.1032 4.1201
171 46.8208 57.2367 6.6052
172 44.1007 59.5356 8.1696
173 45.3370 35.2234 7.7129
174 49.3370 57.2981 2.1298
175 34.2355 42.7499 8.4015
176 31.4711 42.9829 1.2264
177 48.0093 30.5513 4.7299
178 69.7870 63.7526 7.5827
179 38.4740 52.1882 8.0324
180 28.3897 62.5451 4.3056
181 39.4493 68.8876 7.7038
182 35.9426 35.7845 9.0304
183 38.1808 58.0377 3.1834
184 49.6503 49.8405 2.1664
185 40.9999 61.4282 3.0256
186 34.3664 63.8462 4.1501
187 36.5176 60.2559 3.5838
188 23.9639 39.7799 9.3474
189 30.5783 48.4189 1.4618
190 22.6714 53.3018 6.3340
191 35.4859 89.4816 2.4661
192 27.3557 65.3327 8.5457
193 32.7549 79.0079 2.5080
194 38.5478 55.1812 5.5198
195 25.7080 52.6479 9.9940
196 42.5805 57.6646 4.1987
Continued on next page
264
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 47.7196 43.4028 1.4237
198 29.0967 65.5200 2.9229
199 58.7703 48.0296 4.5806
200 20.1985 32.8300 4.0030
201 37.2601 60.8855 3.0664
202 21.6473 30.3933 9.4251
203 37.9339 26.9468 7.1487
204 23.9441 53.6051 9.6590
205 34.6452 38.1136 4.9418
206 32.2756 38.6158 9.4630
207 25.9285 47.9756 1.0525
208 13.3591 43.8887 6.4928
209 50.9294 47.2152 8.2097
210 71.4306 53.4008 3.0968
211 74.6190 35.3934 9.3922
212 35.8260 34.6971 7.8694
213 42.2000 23.7565 8.4380
214 36.2036 45.1220 6.1612
215 43.9421 58.3035 8.1332
216 29.7319 41.2217 3.9614
217 15.4362 56.2666 3.0112
218 42.3365 56.7539 3.8115
219 25.3553 62.3844 6.2607
220 15.6795 62.3672 8.4692
221 76.7750 41.3895 3.6142
222 39.5236 39.2895 4.6230
223 48.6269 50.6049 8.7585
224 59.8924 41.6893 6.5327
225 18.7892 68.1593 9.9207
226 48.7593 67.2481 2.8333
227 50.0249 51.1892 8.4449
228 44.0438 44.6609 7.0828
229 45.1114 56.3851 3.2405
230 35.3151 41.7966 5.2821
231 53.1866 48.4373 4.5917
232 30.7151 43.3692 6.3949
233 31.4802 51.3198 8.2047
234 53.2191 64.1044 1.9456
235 66.9506 59.2810 8.3930
236 37.3372 64.2950 8.5698
237 35.6417 38.5661 4.1906
Continued on next page
265
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 48.6868 52.2475 4.8706
239 58.1765 37.7082 6.1502
240 56.6855 54.8104 7.3074
241 46.7164 54.0712 7.6822
242 33.7942 66.2039 7.8210
243 51.8538 63.7404 4.5022
244 41.7252 58.1653 4.8637
245 62.5278 43.6866 9.6071
246 22.7398 44.0501 6.1567
247 44.8747 24.3555 8.6475
248 61.2817 44.3962 3.4871
249 35.7866 30.6100 6.6009
250 33.9311 61.6228 6.2953
251 29.5195 61.2742 9.6712
252 38.8754 51.7286 1.7731
253 39.9925 45.2699 5.5045
254 44.8106 51.7883 5.6943
255 30.2379 70.0630 1.8115
256 44.0363 66.8640 9.1420
257 34.2304 44.3945 8.9595
258 37.5896 52.1051 4.9509
259 30.8833 35.9938 8.0355
260 38.8218 55.0091 2.3362
261 93.8553 59.2383 6.5783
262 91.5362 61.2506 3.3456
263 59.2417 30.8598 5.0109
264 54.1037 56.3078 8.5960
265 24.5980 39.1973 2.7658
266 34.5058 45.2931 3.7347
267 34.0085 59.8501 5.3497
268 50.5043 53.7276 4.0403
269 49.7570 47.9532 8.1864
270 44.4068 57.5842 9.8874
271 37.9959 70.4312 2.4314
272 29.6307 42.2063 3.1319
273 42.9332 33.1237 7.3201
274 59.1307 35.4720 4.3792
275 48.9623 38.1965 9.7633
276 45.4433 41.6099 9.7508
277 52.2497 57.2085 6.7933
278 51.2035 23.9279 8.7409
Continued on next page
266
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 19.7650 52.9495 4.6170
280 43.1253 40.2697 6.6874
281 36.7720 63.7445 9.8671
282 13.7996 39.3054 6.0353
283 23.8778 50.0945 9.4023
284 38.2873 38.2802 7.4831
285 54.6490 41.4805 5.3563
286 39.5815 46.7483 6.7513
287 46.6036 47.1401 8.9887
288 30.0289 43.4398 2.7886
289 12.0385 64.1040 4.5583
290 44.1988 56.8767 9.9296
291 29.2688 73.1893 4.6212
292 59.6084 46.5338 6.9297
293 67.6442 63.3329 9.1121
294 37.5472 23.7595 9.9584
295 59.8981 57.9810 6.8785
296 56.4807 54.6433 1.9759
297 22.6422 45.3228 1.3250
298 42.3806 58.6919 6.5628
299 46.5874 60.9704 6.1043
300 50.3285 62.9201 9.6577
301 52.5255 55.2474 7.7149
302 52.4914 57.5134 6.9626
303 52.5486 41.5748 5.7098
304 38.3917 36.3103 3.3390
305 48.2749 46.6548 9.6579
306 10.6729 52.3319 5.8618
307 26.1664 61.8868 1.2724
308 60.0281 40.1185 7.2668
309 33.4180 43.8815 5.6774
310 47.5366 87.1809 1.5313
311 64.4018 42.2177 9.0103
312 30.1584 74.0038 3.9718
313 29.1531 62.0144 3.0673
314 35.8183 43.0275 2.0255
315 49.1580 48.6681 3.7983
316 39.9319 47.3105 3.0559
317 28.8885 55.9186 6.8680
318 20.3865 67.0705 1.5954
319 37.5677 29.5275 3.4789
Continued on next page
267
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 39.6979 75.2966 3.5364
321 35.2112 59.7224 8.9206
322 39.1147 43.1387 4.9990
323 27.2084 48.4249 7.8032
324 50.7033 53.7448 6.4297
325 11.7911 53.7021 8.0494
326 44.9231 65.0098 2.0254
327 52.4148 63.6272 9.8071
328 30.7310 45.5162 8.6374
329 42.0416 48.3759 1.4558
330 47.0255 59.1717 5.1958
331 34.0769 51.5041 3.9309
332 42.6622 64.2041 6.6718
333 48.7445 41.4153 3.0727
334 29.4693 55.8960 6.2190
335 54.7880 53.6043 6.4284
336 58.4934 67.3982 6.3989
337 47.4454 33.1812 5.0359
338 43.0730 50.0093 1.3188
339 26.2215 50.6687 5.6243
340 49.9263 20.7262 4.6696
341 25.4879 65.6012 1.9724
342 65.5827 85.1154 5.1389
343 50.3782 47.0977 5.0579
344 46.6403 53.5879 5.9603
345 37.2343 44.1924 8.2486
346 11.7670 54.8040 7.3077
347 25.7764 45.2522 8.8501
348 48.0761 48.7278 1.4697
349 77.3206 70.2269 2.9771
350 53.4321 39.4096 5.1368
351 47.2821 42.8015 9.6268
352 35.1145 49.0511 8.1104
353 44.6040 48.3441 5.0669
354 56.6040 67.9914 4.0009
355 39.2289 75.3908 1.5319
356 69.8822 37.7725 7.6681
357 25.4249 41.9872 5.5612
358 37.4823 56.5059 2.7993
359 43.6061 45.2413 4.8447
360 14.9438 74.9106 2.5182
Continued on next page
268
Table B.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 50.9346 70.4484 7.7653
362 43.9685 56.9877 4.3152
363 44.0100 57.0455 9.4764
364 54.2101 45.7700 1.1546
365 57.7670 59.5456 8.4615
366 54.3169 64.0930 6.6393
367 36.1597 51.7696 5.8487
368 42.1915 74.1017 6.8546
369 47.9065 58.3830 7.5397
370 24.9028 48.6236 1.8504
371 28.0567 54.6370 8.8982
372 36.7577 63.7074 1.1293
373 43.9667 45.0230 3.6487
374 68.4419 48.9317 2.6192
375 54.2466 79.6661 9.3366
376 36.5357 44.0760 1.6136
377 33.8701 61.8293 6.2298
378 64.7685 60.2270 6.7344
379 81.9077 69.8621 6.8614
380 45.2491 56.5751 8.7816
381 36.0162 19.1850 1.5036
382 22.6764 39.3434 8.3517
383 56.7855 56.3967 5.7603
384 46.9960 53.2222 7.2492
385 59.5058 74.5306 2.9116
386 29.8756 67.5789 5.8895
387 46.2939 56.2104 7.3227
388 33.5136 51.0354 9.6079
389 61.0708 30.6440 5.0009
390 34.9830 73.2895 1.7686
391 41.6084 51.6753 1.5161
392 37.8883 30.6750 6.6651
393 57.0566 55.4160 8.1656
394 48.9777 51.2869 7.2207
395 28.5116 42.8707 4.1078
396 33.8187 56.1633 9.5214
397 27.9184 41.1561 5.6817
398 50.0815 33.1497 9.5843
399 47.5993 28.0712 1.6624
400 19.4941 45.4524 2.8633
269
Table B.19: Depot locations and number of vehicles for MS10
Depot index x-coordinate y-coordinate Number of vehicles
1 57.7414 97.9788 1
2 58.8255 81.6171 1
3 15.1868 80.7170 1
4 67.7835 79.3016 1
5 9.3111 83.4786 1
Table B.20: Customer locations and service time for
MS10
Customer index x-coordinate y-coordinate Service time (short)
1 13.9101 73.3572 7.9753
2 80.1760 11.0916 9.2277
3 25.1768 43.4769 8.0430
4 75.2904 55.9157 3.6598
5 14.9107 27.7160 2.3666
6 13.9866 57.7608 8.6312
7 66.8281 78.6792 8.0637
8 72.8494 26.6905 3.4375
9 52.0159 8.0015 3.0503
10 37.8769 66.7042 3.8892
11 35.0886 65.4607 8.4661
12 33.8570 7.0006 8.3996
13 8.6564 8.8704 6.1361
14 13.4911 22.1040 6.1465
15 94.2045 16.9353 3.5742
16 98.0828 99.7183 7.2922
17 36.3779 50.3678 8.1663
18 4.7367 83.0884 4.9743
19 90.9440 8.7179 5.0159
20 10.0580 91.2066 5.1910
21 5.1369 74.8024 3.5114
22 61.8200 11.2874 7.0784
23 76.2004 29.4551 9.1330
24 86.1616 39.0946 9.1767
25 37.6759 81.9315 7.7248
26 68.4753 39.7109 3.3446
27 1.0803 97.7365 7.2067
28 57.8439 75.4148 2.1865
29 51.6434 44.3531 2.1115
30 25.3183 36.4009 2.7181
Continued on next page
270
Table B.20 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 71.2754 86.6030 2.3116
32 71.9774 61.1971 6.2654
33 86.9030 28.6301 1.6603
34 51.6930 44.2035 8.4009
35 84.0120 40.2920 7.5061
36 12.7584 93.3000 9.3327
37 48.8197 12.1854 5.4337
38 33.3632 88.6730 6.8939
39 2.0502 6.8694 9.0111
40 56.5288 26.7518 5.8467
41 62.6645 63.2938 3.5398
42 97.4316 3.1550 9.7836
43 34.8002 87.5025 1.3278
44 82.5828 62.3307 3.9362
45 30.5917 9.0164 9.7571
46 95.6239 15.3623 4.2853
47 19.6524 7.1491 3.7823
48 39.7401 33.8837 2.0882
49 40.6499 27.3435 9.2419
50 33.0560 92.3707 2.2193
271
Table B.21: Depot locations and number of vehicles for MS11
Depot index x-coordinate y-coordinate Number of vehicles
1 5.1399 99.2428 1
2 40.9326 95.2956 1
3 94.5372 31.1508 1
4 59.1796 77.8629 1
5 12.2829 47.9044 1
6 15.4306 42.8746 1
7 22.3423 39.6704 1
8 90.7130 67.6403 1
9 82.5080 71.2048 1
10 94.8137 99.3811 1
Table B.22: Customer locations and service time for
MS11
Customer index x-coordinate y-coordinate Service time (short)
1 2.6674 57.5368 3.9891
2 3.5652 9.7947 9.0773
3 64.3782 86.9809 5.4968
4 81.2668 30.1085 6.5376
5 38.8833 66.9797 6.2482
6 8.4198 99.1974 7.2843
7 35.5116 70.2578 1.2640
8 1.4450 21.0481 5.7509
9 46.7375 95.4999 1.2887
10 72.8599 69.7781 8.4443
11 72.3784 60.0850 4.0599
12 57.5165 57.6609 8.6204
13 44.2243 42.6026 3.2146
14 32.4027 81.6076 6.2334
15 3.6741 58.1288 9.4391
16 82.4656 77.2154 1.4301
17 48.4269 5.7463 1.4858
18 46.2789 53.8695 1.1856
19 35.9623 88.0525 7.1333
20 70.9636 89.8417 6.3877
21 94.2521 67.7323 2.0263
22 37.9749 51.0343 8.1662
23 43.8165 87.8222 6.5607
24 84.3402 88.0361 1.6319
25 27.9308 41.6597 1.6235
Continued on next page
272
Table B.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
26 24.1490 75.0759 2.2241
27 7.9304 98.9051 8.1000
28 7.9270 47.9617 1.8316
29 82.8677 62.3566 3.1408
30 11.9271 16.8022 3.1928
31 5.3021 88.9436 1.9434
32 62.8386 12.0909 8.7252
33 71.8067 60.0299 7.2838
34 47.3595 69.9011 7.6037
35 96.8337 35.9944 6.8548
36 77.2015 56.4388 5.6464
37 30.7836 57.0001 3.9375
38 57.5944 66.9409 6.9560
39 85.2369 7.7982 2.0581
40 59.5812 51.4278 2.3304
41 82.9913 42.8144 1.1779
42 81.7100 29.3103 9.6786
43 46.3333 14.9322 9.7334
44 88.9017 84.1730 2.1147
45 44.6931 86.9811 5.2067
46 99.2755 97.7289 6.9102
47 59.5808 71.0659 3.6117
48 81.4165 69.7454 7.7908
49 88.7809 8.3062 6.0231
50 40.0024 3.1112 4.8501
51 97.1473 77.9183 3.4047
52 86.8116 41.3687 7.7836
53 8.7943 88.9695 9.0854
54 24.7970 27.9276 7.5560
55 84.7975 95.6279 4.6615
56 26.8378 60.2501 9.4448
57 0.6183 77.2996 3.2988
58 31.4865 79.5838 5.7985
59 81.0160 74.7446 9.5928
60 12.6118 14.5703 3.4097
61 67.3843 59.7275 3.2508
62 29.6429 24.8321 9.3491
63 68.1019 0.2224 1.6172
64 42.6812 18.6048 3.6946
65 11.8274 43.8759 6.3243
66 76.8099 80.7740 2.8297
Continued on next page
273
Table B.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
67 58.5799 46.5256 6.7229
68 76.1654 74.0685 8.1853
69 62.8008 96.0086 5.5153
70 27.8368 6.6571 6.8573
71 17.1257 49.7518 8.1636
72 16.0127 62.3515 3.1004
73 80.3727 76.5584 6.4076
74 61.4369 55.4403 2.0122
75 11.3839 46.1961 5.6419
76 18.7029 94.9898 8.5406
77 60.6554 47.3963 9.2871
78 44.6592 75.2075 5.4841
79 22.1432 93.8007 3.4985
80 27.9252 59.8272 6.8727
81 35.5684 47.4444 9.2557
82 27.5665 35.0596 5.5886
83 73.4136 41.8614 9.7677
84 10.7109 40.7034 2.7755
85 51.8309 45.5369 2.0007
86 75.8132 67.8294 3.6762
87 19.0193 82.6729 4.5678
88 90.9900 63.7608 4.7868
89 66.1143 18.9957 3.8033
90 56.6582 91.9704 7.2446
91 54.3360 34.2368 1.8268
92 21.5530 69.9487 4.6188
93 50.6242 71.2903 3.6566
94 90.8622 16.4965 3.7585
95 52.8936 90.2401 1.9501
96 49.4804 15.4084 6.3444
97 97.4544 22.3874 3.5445
98 71.4946 46.4983 2.3970
99 33.2944 21.7388 1.0059
100 93.8843 51.0154 3.5524
274
Table B.23: Depot locations and number of vehicles for MS12
Depot index x-coordinate y-coordinate Number of vehicles
1 79.2328 89.5452 1
2 65.4914 31.7236 1
3 39.5365 95.5817 1
4 34.0986 8.7049 1
5 19.3701 56.3395 1
6 17.7701 86.8037 1
7 33.4280 12.8627 1
8 96.7222 91.5623 1
9 15.8952 51.3489 1
10 12.1682 11.7241 1
11 87.2591 8.6689 1
12 9.7448 94.3246 1
13 40.1110 54.9028 1
14 77.7212 51.7343 1
15 30.5305 18.7454 1
Table B.24: Customer locations and service time for
MS12
Customer index x-coordinate y-coordinate Service time (short)
1 84.8838 76.7164 5.9573
2 7.4965 61.4920 8.8381
3 34.6679 15.1291 1.3803
4 54.1668 83.9111 9.1425
5 71.9803 17.3691 2.1788
6 88.1973 83.3605 8.5036
7 80.4918 78.1370 8.2042
8 39.8681 71.7369 9.2609
9 71.6123 47.2104 2.2357
10 59.3099 30.8544 5.5426
11 91.9977 67.7132 4.6446
12 36.0995 60.8741 2.5621
13 87.6580 29.3219 6.1767
14 79.0508 83.5840 6.4560
15 39.9935 26.8413 2.9300
16 97.4063 29.6483 5.6794
17 47.3952 38.0316 9.9027
18 62.8858 68.1348 5.4092
19 63.9848 50.3475 7.2539
20 92.4296 49.5073 4.7028
Continued on next page
275
Table B.24 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
21 51.4633 5.7136 1.3130
22 35.9821 47.3741 3.6355
23 98.6112 45.6489 8.2130
24 37.2214 44.0584 4.1185
25 24.1912 83.8965 1.7498
26 98.4222 23.6235 5.6000
27 88.9401 19.1235 4.3015
28 51.6035 71.6161 7.6553
29 21.6915 32.4501 5.7227
30 84.4665 10.0158 8.2407
31 20.4530 54.6944 8.3522
32 71.8650 39.1058 2.7052
33 37.9119 46.0879 2.1132
34 31.6365 76.0468 8.3890
35 80.3795 95.7029 6.7411
36 13.7151 83.3024 1.1451
37 28.2269 93.9429 9.0636
38 93.5620 65.4148 5.6384
39 73.3356 91.8315 5.9007
40 25.2357 27.8333 6.4580
41 70.8616 45.0372 7.8439
42 44.2847 33.8453 8.6981
43 12.6414 40.0331 4.4458
44 56.6498 38.4749 1.7618
45 13.7892 62.2959 7.6049
46 99.4235 90.3701 3.9879
47 20.5406 13.3576 8.5577
48 16.1358 31.9299 4.3455
49 11.2159 17.2428 8.4539
50 89.8153 72.3215 2.5887
51 29.9263 96.9070 2.1657
52 2.4689 54.0433 8.9190
53 78.0181 63.7164 1.3967
54 70.2509 98.4452 7.1805
55 90.3480 65.8928 7.6040
56 93.4307 31.6856 4.9346
57 50.4669 29.9761 4.4186
58 25.4714 58.0236 9.8169
59 9.3391 48.1903 4.5909
60 90.5070 91.6805 4.9617
61 92.4821 12.5090 2.4113
Continued on next page
276
Table B.24 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
62 43.9733 5.2424 3.9343
63 63.9823 65.2836 3.8266
64 47.6791 63.2134 9.0505
65 21.8455 38.0676 3.2232
66 33.3453 89.7187 3.7961
67 18.7407 5.8015 4.6798
68 33.8638 21.3627 7.3721
69 53.9213 20.3135 2.2927
70 95.9540 38.5715 8.8419
71 33.0622 34.3493 1.7484
72 87.7187 2.9828 5.1556
73 74.5795 78.0242 1.2735
74 36.9616 4.4396 7.7788
75 2.9581 15.7177 7.3004
76 57.3854 90.3904 2.9306
77 93.4200 75.2448 7.1191
78 91.8947 52.9195 6.0156
79 30.2341 54.4974 8.6561
80 4.5993 90.5775 6.0271
81 57.2539 0.2591 9.1160
82 89.6137 71.4522 4.7757
83 39.3908 16.0302 4.2232
84 14.3409 36.0827 5.4009
85 6.5196 73.9671 3.3037
86 27.2358 39.8498 9.3625
87 66.3161 94.2627 5.2008
88 53.2208 44.8656 3.2861
89 18.6890 96.5921 4.8810
90 51.5501 19.5253 7.3228
91 7.8789 77.3108 4.6210
92 57.3898 82.2491 2.6366
93 52.5279 4.5997 8.7063
94 32.9479 13.4850 6.2578
95 46.0387 92.3910 4.3622
96 92.3387 68.6517 2.9953
97 26.0633 85.1518 2.9709
98 89.3198 81.0635 5.7001
99 93.9919 67.4228 4.9008
100 23.2644 8.2232 7.6717
277
Table B.25: Depot locations and number of vehicles for MS13
Depot index x-coordinate y-coordinate Number of vehicles
1 75.3025 45.3429 1
2 48.1377 48.4770 1
3 95.4844 48.4203 1
4 16.0127 28.1074 1
5 53.3086 76.7624 1
6 79.4255 68.3671 1
7 42.6890 44.5856 1
8 31.4857 55.3484 1
9 61.2524 61.1174 1
10 1.7678 6.4381 1
Table B.26: Customer locations and service time for
MS13
Customer index x-coordinate y-coordinate Service time (short)
1 38.4046 81.9824 1.6340
2 15.7315 88.0233 8.6260
3 71.6633 59.7598 7.1189
4 82.8184 92.5286 2.2299
5 51.2924 86.5152 8.7256
6 5.6883 79.3977 2.7985
7 73.0230 93.2013 6.4661
8 29.1937 56.7226 5.8874
9 88.8814 27.3759 2.4609
10 44.7806 3.2031 1.0509
11 65.1449 21.8420 7.9434
12 19.7955 12.8206 7.8831
13 34.9659 23.1896 4.7896
14 30.1467 75.1538 1.5113
15 34.9174 11.4795 6.2717
16 89.6056 41.6898 2.5674
17 64.2363 48.0861 7.5575
18 86.0558 76.5752 5.8086
19 13.3779 9.2853 3.2776
20 47.8741 11.2863 9.2535
21 27.3411 20.1287 7.8238
22 58.1609 83.2626 8.9833
23 15.1083 48.2931 1.6192
24 1.0940 58.2560 2.6518
25 43.7077 46.5662 7.6337
Continued on next page
278
Table B.26 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
26 81.8049 64.1693 7.2704
27 38.6612 1.7803 7.9929
28 81.1967 69.0865 5.5171
29 78.5434 7.6852 4.8295
30 14.1194 47.7202 6.5011
31 6.9957 13.2942 8.7019
32 23.6076 90.4177 7.0372
33 13.5709 5.0989 5.7123
34 51.3808 86.1329 3.6893
35 81.0218 0.1233 7.3357
36 41.6035 50.9610 4.4345
37 42.0985 84.3904 6.1092
38 95.0245 26.8292 8.9907
39 82.9276 94.7960 8.5865
40 61.1001 63.8211 9.0892
41 64.0161 93.5116 9.4510
42 86.8000 90.4675 8.3389
43 74.8358 73.4878 1.0122
44 7.2096 38.8988 1.0278
45 28.3765 93.6475 1.7872
46 67.9808 49.8622 3.3465
47 52.7609 34.8022 1.2052
48 19.3448 66.0084 4.8168
49 13.7742 57.1662 4.0696
50 19.8092 39.2005 5.8722
51 92.3349 83.4178 9.3355
52 75.0160 36.0487 3.6865
53 93.9900 0.8925 4.0428
54 11.3533 12.8318 8.7353
55 86.9494 98.7228 4.0643
56 40.6627 53.1273 2.2431
57 70.5614 82.2435 5.5702
58 15.5556 89.2311 8.7099
59 30.2592 53.8919 4.4588
60 95.4580 82.7336 7.2612
61 78.0448 77.2385 6.6511
62 12.5153 81.1148 5.0535
63 60.5574 87.3184 5.2626
64 19.2593 28.2841 9.5474
65 60.1699 31.0673 1.7515
66 92.3424 70.8875 3.5185
Continued on next page
279
Table B.26 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
67 65.8284 83.0132 5.0231
68 49.1116 64.1517 6.2881
69 26.7149 87.6817 8.8987
70 0.5501 86.8896 5.2219
71 40.7605 78.5222 4.9368
72 5.9845 45.5789 7.7157
73 9.1087 9.0935 5.2112
74 26.1522 26.4278 8.7474
75 92.9512 87.7384 5.1986
76 16.2000 44.5277 5.4829
77 86.8666 55.6758 5.3869
78 65.9508 23.9985 3.0652
79 33.4629 2.8775 1.7700
80 6.8542 39.1089 1.6064
81 15.4129 93.6924 8.9955
82 36.2408 96.4002 3.0985
83 83.7933 46.4083 8.7544
84 78.4464 53.0032 7.4056
85 32.7664 75.1074 8.8553
86 28.1587 45.0526 9.4420
87 33.4650 19.5776 2.2572
88 81.6511 37.1952 4.5451
89 79.2793 87.1983 9.8251
90 20.9674 24.6748 6.8031
91 34.5006 25.7683 9.0677
92 61.0463 56.4980 5.3401
93 80.8030 23.8069 1.1268
94 21.5873 20.6731 6.6059
95 6.0116 80.9983 3.0799
96 56.5336 91.7677 5.7469
97 14.7862 33.8864 7.5249
98 85.4760 18.2345 6.4667
99 28.7712 32.9070 6.2953
100 31.8631 75.5483 4.9009
101 5.2765 98.1078 3.1976
102 11.3527 84.5170 4.8606
103 49.0543 58.0095 1.0916
104 49.2519 14.8817 6.4794
105 0.7589 93.8698 9.6218
106 32.3446 70.8335 1.8590
107 10.4311 27.1163 1.3203
Continued on next page
280
Table B.26 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
108 71.6200 53.8359 8.9761
109 56.8327 56.5314 3.2225
110 70.3127 46.6551 1.0802
111 76.2664 6.3306 8.3343
112 95.1919 17.9179 2.2645
113 69.4616 17.7301 8.9188
114 56.9940 45.0039 1.8584
115 43.5692 34.3838 4.1730
116 34.5676 56.3986 6.3408
117 21.1172 32.2013 6.2666
118 56.1776 41.2997 7.0091
119 21.4503 45.3095 6.8322
120 63.8317 2.9586 4.9003
121 52.2746 19.0441 2.2578
122 29.4720 70.5819 7.7674
123 11.2972 24.6521 3.1761
124 73.7633 18.8298 6.8541
125 94.1852 78.3202 8.7164
126 94.5175 23.2220 1.7593
127 75.5635 29.6525 9.7488
128 55.5291 4.6170 1.2831
129 87.5019 70.9775 8.5186
130 32.5093 84.9996 8.5214
131 75.1625 44.7553 1.4487
132 45.3528 88.4267 5.9130
133 22.2157 68.2814 9.4885
134 42.8586 83.8519 3.8933
135 8.0592 26.3103 8.2582
136 43.7028 32.1639 6.4126
137 86.9149 73.9457 8.1066
138 6.8397 72.7802 8.1927
139 97.0996 62.3384 1.4461
140 33.7546 0.3840 3.5488
141 72.8519 88.4373 6.8811
142 84.5155 88.0378 5.4069
143 84.2709 49.3070 9.7557
144 93.1851 27.5528 7.7364
145 43.3289 45.8167 6.1106
146 5.4162 45.0135 3.6907
147 36.1782 26.8808 3.3050
148 85.6894 60.2161 8.9791
Continued on next page
281
Table B.26 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
149 90.7921 45.7708 5.0212
150 94.3764 79.9694 8.3439
282
Table B.27: Depot locations and number of vehicles for MS14
Depot index x-coordinate y-coordinate Number of vehicles
1 50.9477 11.0443 1
2 52.9504 34.4700 1
3 37.2480 20.3357 1
4 13.5668 46.6052 1
5 55.9797 89.9157 1
6 5.2539 42.6109 1
7 8.3353 4.2426 1
8 97.9748 7.9603 1
9 45.6481 42.1063 1
10 36.1703 62.9647 1
Table B.28: Customer locations and service time for
MS14
Customer index x-coordinate y-coordinate Service time (short)
1 34.0682 47.7248 1.8850
2 73.1047 91.1516 8.7363
3 58.9121 0.0285 1.2487
4 87.3705 21.1197 9.0924
5 22.4711 54.2240 9.0994
6 94.9757 60.5166 5.7170
7 50.5346 35.6386 2.0818
8 58.6995 12.2596 2.6001
9 78.7107 92.4724 7.3550
10 60.6314 45.0438 8.4822
11 27.5973 16.4567 1.3135
12 20.9587 93.3727 7.8205
13 63.8576 33.9486 9.6140
14 5.0658 54.9143 4.0858
15 23.5190 62.7872 6.7442
16 50.9214 61.4709 4.0871
17 71.8875 51.9026 2.9482
18 23.5131 14.4930 8.0758
19 68.9906 57.1562 7.5078
20 39.5743 57.3022 3.5096
21 45.4098 14.0397 6.2419
22 34.9428 13.4217 4.7891
23 8.8914 72.1064 1.8286
24 64.3515 66.8602 1.2162
25 63.9235 48.7290 5.4203
Continued on next page
283
Table B.28 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
26 89.0775 64.9199 3.5044
27 83.5526 6.9878 4.0578
28 19.8948 94.3572 3.5861
29 48.2615 47.9180 2.5381
30 74.6043 37.9257 4.5934
31 51.0344 56.2950 7.2788
32 16.1966 11.0337 2.8331
33 96.9306 73.7059 6.9969
34 22.9774 73.0330 4.9876
35 24.1708 18.4982 4.8997
36 50.0251 20.2014 2.5772
37 85.0863 98.6389 2.7388
38 85.7453 7.2576 6.5478
39 63.0492 38.3593 3.4211
40 59.3343 46.0343 6.0371
41 43.8832 27.7129 9.5031
42 8.9289 9.2281 7.4302
43 31.1514 8.5463 7.1130
44 82.0607 49.9539 9.6344
45 20.3401 44.0501 7.9780
46 41.6228 92.5386 6.4695
47 59.4766 94.2454 9.5320
48 12.1474 24.4952 1.5368
49 14.3340 28.2829 3.4184
50 82.5198 3.0400 9.8801
51 55.9053 86.0957 7.9499
52 19.6033 67.9961 5.2782
53 26.0766 31.8231 7.1281
54 46.7499 96.5846 4.7524
55 71.6791 57.1251 4.4213
56 54.7767 67.0669 2.9194
57 79.5080 7.2774 4.4464
58 94.2238 5.3281 1.2670
59 33.5589 31.9823 5.2509
60 73.8772 65.4969 4.0004
61 66.3296 41.5111 9.7826
62 8.2097 24.3938 5.9990
63 84.7047 44.3410 8.6167
64 5.5759 0.9972 4.6726
65 10.8237 47.9729 5.1582
66 1.3048 64.3192 8.4368
Continued on next page
284
Table B.28 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
67 3.4662 92.4457 9.9208
68 26.5897 45.6692 5.7155
69 3.9818 14.8053 9.3289
70 7.2103 49.2107 7.6512
71 44.4772 22.8131 6.1069
72 12.1012 4.0364 9.7190
73 62.9775 37.6335 8.4205
74 78.9437 90.2753 9.6365
75 32.4933 15.4110 6.8171
76 6.0002 34.8458 4.4162
77 74.2784 47.0526 5.2892
78 21.4135 50.6707 9.2070
79 9.6196 54.2071 1.1337
80 35.6511 60.1855 2.4102
81 69.8125 10.7143 5.2441
82 13.7772 75.1515 5.8869
83 3.4487 4.7172 1.5372
84 86.5825 87.6240 6.9223
85 96.8178 25.7666 9.0067
86 73.2148 93.3628 1.9867
87 6.0559 26.6090 4.9400
88 84.3849 32.2155 3.5221
89 61.3738 44.6251 9.8672
90 36.2290 34.6663 6.4788
91 86.6690 71.7504 3.2837
92 85.8173 58.2244 2.1935
93 44.4085 90.2696 5.9050
94 26.5976 79.4241 8.4502
95 5.2205 48.9509 8.5331
96 71.1852 93.6590 8.5001
97 65.1925 64.1101 2.8334
98 2.4963 16.9525 5.8998
99 54.5672 78.4591 8.8745
100 22.8351 76.6663 2.0890
101 14.9282 55.5932 8.7072
102 11.8268 90.2985 9.0980
103 18.4141 0.8639 2.9608
104 24.9133 16.0063 1.6928
105 35.3673 46.4992 5.2679
106 26.3691 61.7522 8.5152
107 44.5311 67.5322 5.2245
Continued on next page
285
Table B.28 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
108 46.7969 0.7669 4.7239
109 51.1808 94.4520 5.5247
110 42.0698 27.5375 2.1290
111 16.9687 57.7956 2.1906
112 0.0295 1.9687 8.8343
113 68.5550 23.7139 6.4266
114 77.6316 3.1725 3.3877
115 59.3658 4.7617 8.7832
116 39.3476 63.0482 1.5230
117 4.7282 92.8014 5.1198
118 64.4047 25.3419 7.4999
119 67.8625 43.8807 4.0510
120 8.8041 38.5523 4.6110
121 42.2692 10.5689 5.7428
122 34.2623 53.7708 9.0481
123 21.0132 59.1484 8.0052
124 70.4211 95.1834 1.6243
125 35.1593 16.0609 3.5091
126 67.8446 64.9370 4.4143
127 77.7020 82.5812 8.7821
128 76.7738 3.5974 4.7796
129 72.4167 97.0257 3.1589
130 49.9858 39.2246 6.3789
131 33.9372 80.6794 5.3146
132 73.7536 47.9707 9.0869
133 40.6698 57.4196 9.4124
134 5.0236 40.8764 8.3610
135 50.1057 93.7172 7.3802
136 49.5534 33.2394 7.6890
137 72.8798 17.3133 9.0974
138 68.7816 5.0080 1.5872
139 27.0168 88.3460 4.0232
140 70.9288 51.9753 1.0390
141 30.5717 94.9801 8.4529
142 20.1278 76.7067 5.5669
143 33.4082 2.7198 4.2955
144 54.6521 8.8647 3.0398
145 96.2750 8.0197 5.8135
146 51.5600 79.1613 3.6054
147 73.3446 24.5464 1.6153
148 70.6524 62.0514 1.7647
Continued on next page
286
Table B.28 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
149 89.0745 40.7637 1.6151
150 23.4481 43.8167 4.6883
151 52.9067 3.3222 2.1104
152 79.3450 56.2426 4.9871
153 2.5190 90.6573 9.0905
154 14.9375 71.2760 4.1828
155 97.3608 32.5911 2.0816
156 9.5061 68.6444 6.1220
157 75.4307 60.8648 8.8753
158 72.2382 84.5703 4.1372
159 81.5137 51.5252 1.3773
160 97.3707 22.7095 2.2811
161 16.4119 0.7236 1.6893
162 21.7680 34.6486 7.6647
163 15.1729 16.5658 5.1087
164 4.1410 8.0079 7.0142
165 88.2381 83.2683 7.2932
166 15.4246 97.3957 6.1422
167 51.8210 67.8655 6.6582
168 97.9325 31.5769 8.8999
169 17.1000 52.7683 6.9612
170 17.3423 33.9339 8.8787
171 23.0803 40.6514 5.2077
172 71.5006 53.6792 2.2720
173 17.2084 75.7755 1.6132
174 79.3838 96.0459 7.4282
175 39.3794 22.1355 3.7719
176 98.9994 63.0437 7.0405
177 34.5886 84.4377 6.8718
178 57.5531 2.8326 5.7794
179 41.4077 71.4274 7.4360
180 86.0199 4.3968 5.5433
181 75.2088 85.0030 5.3920
182 55.3456 62.0369 5.4805
183 83.0181 25.5402 9.4238
184 2.2514 44.7884 4.5035
185 51.6314 17.9253 2.0543
186 54.2119 35.2360 3.1638
187 86.1579 7.8450 7.1642
188 77.9652 11.2370 8.5533
189 86.4454 21.9861 9.7313
Continued on next page
287
Table B.28 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
190 29.6715 81.9656 2.9365
191 91.4258 5.3710 7.8431
192 7.3030 28.2665 6.2569
193 36.0603 33.5689 4.6266
194 83.5813 72.9290 5.5904
195 39.3918 69.7007 5.4608
196 31.1664 40.7809 6.8623
197 51.4351 60.1450 7.6934
198 10.8848 31.1384 3.7176
199 60.4039 63.8843 1.8065
200 61.7219 62.2465 8.4337
288
Table B.29: Depot locations and number of vehicles for MS15
Depot index x-coordinate y-coordinate Number of vehicles
1 82.7138 46.0477 1
2 62.3415 2.4759 1
3 69.7335 36.2333 1
4 85.4939 74.6624 1
5 67.5608 20.6114 1
6 72.2931 92.8864 1
7 92.9658 37.0591 1
8 1.6773 90.2385 1
9 60.9782 1.0761 1
10 40.5933 66.9059 1
11 1.3957 22.3919 1
12 12.5167 40.1077 1
13 4.4000 16.5540 1
14 90.8243 26.1612 1
15 4.9054 22.6277 1
Table B.30: Customer locations and service time for
MS15
Customer index x-coordinate y-coordinate Service time (short)
1 52.6191 41.9685 4.5063
2 45.4754 94.4392 7.9777
3 74.5108 21.1852 2.6143
4 43.7398 97.2133 1.9843
5 54.8130 23.5469 9.1464
6 9.3981 93.4518 8.8872
7 30.4627 88.1543 9.9981
8 21.3497 90.3259 8.7783
9 50.6712 70.8485 1.3319
10 20.4348 62.6591 5.9021
11 72.6632 27.3688 9.9785
12 29.3073 59.1189 5.5991
13 35.1586 16.9864 8.8616
14 79.7836 71.3801 1.6320
15 17.5590 51.5580 9.8878
16 73.1566 63.5009 9.3044
17 24.2365 83.7488 6.0783
18 35.9603 41.9824 4.8832
19 80.6551 63.5321 4.0406
20 3.8360 57.0699 7.4865
Continued on next page
289
Table B.30 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
21 70.6084 51.0100 1.1229
22 92.5684 32.9466 4.3665
23 95.7143 52.3347 9.3042
24 85.5912 53.1489 5.9183
25 79.8043 93.4029 5.2650
26 16.4660 5.4815 5.4688
27 0.9393 70.1807 3.7807
28 8.6167 50.2172 9.5575
29 33.4376 55.2349 9.8379
30 95.1178 24.3973 5.6221
31 2.2754 5.1771 9.9333
32 77.4854 10.6673 5.1026
33 39.1151 11.4094 4.8344
34 73.3815 53.9032 2.9189
35 48.6522 13.1238 2.7392
36 10.1803 67.6535 8.4948
37 24.9967 65.3466 7.5397
38 35.8891 71.8359 5.7677
39 88.7415 91.6172 8.4617
40 39.2293 23.4555 5.6069
41 67.4695 50.8875 5.9677
42 27.7345 40.0228 2.9196
43 84.3636 54.1670 6.2904
44 47.7457 82.3342 2.2849
45 89.7487 52.6801 1.4700
46 46.6371 17.2711 7.1498
47 11.2998 55.9483 6.4770
48 91.1164 70.0526 2.9769
49 76.6736 15.8703 4.6565
50 13.2314 43.3857 6.6692
51 85.0772 83.2705 5.9978
52 72.2032 56.0467 2.1482
53 50.6660 61.4987 2.5228
54 65.5667 46.0642 1.0090
55 89.1753 45.4488 4.7635
56 88.8252 22.9161 5.3964
57 77.7470 17.9931 2.4388
58 41.9711 7.3758 7.0015
59 56.0199 2.2425 1.1613
60 70.0990 13.2425 2.0771
61 14.0448 72.7218 9.5691
Continued on next page
290
Table B.30 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
62 76.5040 43.2792 9.7827
63 44.8577 71.0036 1.2782
64 63.4764 1.6535 5.4449
65 39.8621 64.9684 8.7645
66 70.0038 57.5809 3.1859
67 78.3498 13.9306 8.5084
68 49.6652 63.9250 8.3223
69 79.8168 40.5893 6.6608
70 14.6513 7.3171 1.0201
71 97.2576 89.6088 4.4175
72 21.6487 43.0584 9.1397
73 50.5662 94.3031 7.1232
74 31.1862 30.3139 4.4094
75 40.2148 72.4127 6.6876
76 7.8520 82.4206 3.1894
77 28.1037 54.1722 6.1427
78 84.8573 67.3412 9.8356
79 83.2829 46.1439 8.6471
80 21.3707 9.4002 3.5510
81 30.5034 51.4731 7.1421
82 5.9127 52.5096 4.2231
83 49.6670 61.6561 9.8823
84 9.4147 50.8664 1.7559
85 28.8266 62.6359 3.2528
86 52.0959 24.2776 8.3021
87 24.6714 21.3666 1.7598
88 52.4989 93.2445 5.7813
89 0.0216 71.4865 8.2056
90 60.6740 87.9242 7.6494
91 42.6572 5.5312 2.2750
92 32.6130 45.9128 4.9410
93 45.8415 68.8961 4.1534
94 89.0975 8.0184 5.3065
95 14.0619 23.7447 6.2866
96 5.5848 7.3990 2.3123
97 89.4689 2.4026 9.1480
98 83.0803 19.4479 6.7617
99 12.9668 61.3517 2.4665
100 30.3434 50.0500 6.0932
101 95.7392 36.2198 9.3845
102 5.1894 34.9276 8.0479
Continued on next page
291
Table B.30 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
103 77.4386 93.1591 7.1712
104 50.3188 87.5076 5.1960
105 22.9283 65.3519 3.3429
106 0.8506 88.7309 6.1234
107 74.6547 27.5570 3.2389
108 69.7549 81.2539 3.8737
109 0.3831 92.7308 9.1972
110 66.0206 46.8375 8.9670
111 3.1405 85.0647 8.1513
112 39.8171 97.8265 9.3323
113 21.8759 53.7081 2.6096
114 82.1511 21.8348 5.6579
115 86.4652 26.7599 6.6430
116 66.0394 90.0181 9.2186
117 9.9822 10.9677 6.9757
118 88.3171 71.0194 4.5027
119 85.9947 76.5775 7.6601
120 8.7871 0.6287 8.3587
121 3.8823 84.5070 6.4031
122 29.0958 0.2111 1.7650
123 94.3212 66.1206 9.3012
124 40.6678 60.7921 1.4824
125 37.3480 22.3083 5.7432
126 68.9022 33.5125 2.0697
127 39.7022 18.4480 4.4213
128 32.3493 36.0395 8.3155
129 73.0854 48.2812 3.1969
130 23.1858 67.5851 8.9598
131 26.8343 75.5826 7.4138
132 82.3748 37.4737 4.4033
133 28.9639 91.2783 3.2403
134 78.6753 23.1210 3.2757
135 60.5930 3.5129 7.9052
136 72.4255 19.1041 1.4488
137 49.9148 10.6091 7.1676
138 17.8161 33.5842 6.5825
139 80.7403 76.5902 7.7202
140 4.0684 83.4964 9.7953
141 29.9519 71.3710 4.4552
142 71.8089 74.4422 3.3419
143 64.8999 13.8708 8.8972
Continued on next page
292
Table B.30 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
144 59.5550 40.8846 8.2549
145 93.6151 88.7777 5.1501
146 56.4706 15.4694 1.8187
147 48.5860 54.5062 6.0784
148 60.0572 60.8617 2.6864
149 77.1968 46.1180 5.7852
150 15.6894 8.6627 4.1953
151 73.6769 54.0661 3.8331
152 85.0173 6.5706 7.5407
153 94.4269 50.7296 5.6420
154 99.0855 95.8065 8.1158
155 39.0393 91.1629 2.8404
156 41.9616 27.5429 7.1030
157 75.9690 12.0248 1.4724
158 67.0435 11.7439 8.2106
159 40.4143 40.4541 7.1071
160 88.6360 99.7240 9.5141
161 6.1133 22.7405 1.8240
162 1.8487 29.7179 9.1759
163 47.5989 24.5366 5.5896
164 39.2928 99.8526 6.5341
165 62.6853 19.6622 3.8446
166 47.1226 62.8252 1.6974
167 22.1875 72.8184 8.6555
168 77.1351 34.9442 2.3007
169 73.3761 62.7602 4.3344
170 82.0011 5.3531 6.6015
171 29.0746 78.0673 9.9780
172 21.2930 23.3376 5.6561
173 33.7055 32.4291 9.9146
174 51.0144 42.2676 3.0388
175 20.0273 42.8808 4.5820
176 35.0940 16.7854 7.2691
177 41.7122 96.6105 1.5818
178 21.2701 73.7416 7.7290
179 96.0120 15.8647 4.7836
180 25.3234 75.2734 8.3019
181 60.2012 9.2748 4.4164
182 5.8580 64.8614 3.8716
183 49.4950 22.7149 9.8745
184 80.6352 43.6651 7.4636
Continued on next page
293
Table B.30 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
185 38.8180 39.5433 4.7187
186 60.6827 6.6797 1.8877
187 79.1451 50.8395 7.6110
188 74.9905 72.0357 6.7358
189 56.8547 92.9759 1.6646
190 49.4238 63.7829 2.0846
191 51.7639 11.2372 9.8344
192 87.3649 93.6142 5.4712
193 92.5130 62.0842 1.2017
194 29.1919 79.4782 1.4845
195 71.6016 94.5143 2.2679
196 70.4746 43.4996 9.0413
197 32.0214 20.2160 5.1924
198 31.8399 94.8296 6.0477
199 35.9972 25.2442 5.4501
200 54.1179 0.1149 1.6101
294
Table B.31: Depot locations and number of vehicles for MS16
Depot index x-coordinate y-coordinate Number of vehicles
1 30.5941 53.0751 1
2 71.2459 75.9094 1
3 49.7526 30.0855 1
4 6.4983 56.9495 1
5 8.5534 0.6741 1
6 23.0418 72.7248 1
7 86.8254 98.0680 1
8 15.3820 92.0042 1
9 92.9129 43.1917 1
10 33.9653 46.9081 1
11 4.1665 31.9300 1
12 5.1632 3.3848 1
13 68.2048 78.9141 1
14 89.3803 93.3408 1
15 90.3510 8.5425 1
16 6.9326 91.7872 1
17 78.5355 47.5713 1
18 23.3435 77.3246 1
19 33.8876 78.3497 1
20 77.7837 3.7876 1
Table B.32: Customer locations and service time for
MS16
Customer index x-coordinate y-coordinate Service time (short)
1 83.6273 13.4138 9.0788
2 25.3914 32.1400 3.5971
3 78.0193 64.2589 3.4214
4 81.2506 67.3135 6.3477
5 98.5365 65.5603 5.2829
6 72.4040 24.7084 4.3148
7 22.9113 12.4256 6.9005
8 15.9973 93.2218 9.4438
9 63.3852 69.6086 6.5838
10 82.0131 95.3983 3.5456
11 82.0259 61.3463 2.8466
12 71.9662 72.6297 4.9522
13 77.2423 47.2813 1.2453
14 6.8482 81.6732 8.8857
15 69.1949 72.7783 6.4908
Continued on next page
295
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
16 88.8836 27.0925 2.8323
17 75.9363 35.2158 5.6793
18 97.2073 13.9324 1.4844
19 37.1875 63.0829 8.7597
20 5.8579 56.7421 4.9864
21 72.1451 7.6372 5.9321
22 46.3058 87.1420 6.1017
23 11.0376 27.4157 7.1236
24 28.6049 59.1674 4.3424
25 47.4359 22.9871 1.7041
26 50.6120 15.0409 5.1072
27 52.4789 20.9920 1.4306
28 64.2384 56.4531 7.6443
29 58.3572 11.1331 1.3420
30 85.0996 44.6561 9.5882
31 85.4822 17.7285 7.6814
32 61.7680 70.5119 9.4370
33 68.3814 35.3039 5.6203
34 52.4318 89.1144 3.1681
35 49.6775 51.9680 3.3397
36 35.8253 60.1015 7.8308
37 28.5674 87.8569 9.9401
38 78.8281 24.4384 4.2104
39 27.8982 1.2551 7.7757
40 3.3948 96.1300 1.9904
41 15.1250 36.3034 6.3734
42 5.9394 55.7092 4.8754
43 88.4695 67.5221 7.5765
44 65.2163 4.9816 3.3506
45 30.4307 21.6877 1.8533
46 12.3870 67.7737 5.0587
47 93.8755 59.6624 6.7607
48 99.2395 14.8774 2.1883
49 20.1747 55.9261 5.0754
50 57.6672 73.0361 6.8698
51 74.8502 36.1978 8.4430
52 52.7801 93.4878 3.7727
53 75.2836 99.0340 4.6213
54 78.4849 71.9893 8.9581
55 17.9508 65.4987 7.3052
56 43.6256 56.2842 3.1769
Continued on next page
296
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
57 33.1336 67.6886 7.8385
58 67.9275 48.8686 3.6183
59 82.0844 27.7066 3.4969
60 81.1331 69.2565 1.0550
61 54.1045 65.8366 4.3724
62 68.4049 69.5436 4.9324
63 41.0557 5.3107 3.7387
64 35.5577 69.0316 3.6177
65 85.6898 71.4025 3.1826
66 4.0079 25.6822 9.4302
67 54.7535 47.2767 8.7417
68 26.2973 81.3231 4.5751
69 85.8985 75.3718 5.3148
70 14.5887 90.9521 6.0850
71 23.0548 78.2805 5.4066
72 92.3024 9.0596 3.4283
73 55.2752 73.1954 9.9077
74 76.9321 3.4239 2.6531
75 72.6873 76.9977 8.7549
76 43.7713 10.6540 1.2937
77 21.0285 24.1021 3.9876
78 52.1351 56.2473 7.7387
79 9.0336 91.5313 6.7993
80 88.9070 3.4448 2.5231
81 66.7487 19.5637 9.5698
82 66.6791 31.1933 5.8894
83 3.7761 89.2717 3.2627
84 71.9952 90.4974 6.2072
85 81.1435 76.9257 9.2393
86 72.4261 70.2054 9.0604
87 21.5199 37.9402 5.3426
88 78.0268 49.6084 4.9847
89 45.1968 74.0316 3.8058
90 90.1915 28.1185 1.4978
91 41.8902 2.7138 7.7841
92 38.2491 96.4877 2.1875
93 7.2397 60.4587 4.2033
94 33.4091 56.1719 4.5628
95 68.7402 49.8904 8.9697
96 85.2551 18.7859 1.1912
97 50.7309 48.6177 8.5967
Continued on next page
297
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
98 42.3945 6.5442 3.5926
99 62.9568 34.1208 3.2531
100 28.9318 60.7920 5.3954
101 33.6669 27.5734 7.5613
102 51.6900 90.0075 2.8235
103 70.5938 22.0113 2.9465
104 28.9810 62.9220 9.7870
105 16.4195 71.4924 6.3391
106 35.5511 62.0014 3.7396
107 10.1090 0.0441 9.7093
108 47.1034 18.1602 9.0637
109 28.4684 64.2044 2.7102
110 76.8534 84.3855 1.0162
111 3.5429 12.4015 7.4059
112 52.3437 64.7618 8.8095
113 6.4394 13.0585 2.0648
114 38.7566 30.1491 1.3512
115 37.6659 82.6570 6.3838
116 52.3649 98.6209 6.4388
117 74.8536 47.7087 5.6479
118 30.4541 79.6311 1.0676
119 62.2527 62.8181 7.2004
120 78.3454 91.7540 9.5142
121 51.0584 36.4480 8.8618
122 23.8503 67.0573 2.0195
123 96.8738 44.6289 4.1911
124 5.3979 77.7150 3.1774
125 77.1972 40.4756 6.0430
126 95.4528 31.1688 6.5145
127 56.2504 17.1436 3.7073
128 70.2530 66.6227 8.1833
129 59.0035 72.9626 8.1608
130 32.9469 48.8609 8.0298
131 58.0126 39.7254 4.1599
132 45.6109 69.8326 1.4887
133 26.6090 52.0006 7.3783
134 88.2168 61.8112 9.9364
135 46.5590 34.4391 2.4623
136 34.1952 51.6429 2.0221
137 86.3692 17.1102 9.2159
138 68.4147 49.7452 5.3349
Continued on next page
298
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
139 32.1115 87.2089 8.6663
140 4.1623 84.9397 8.2892
141 9.4374 68.3027 2.6808
142 14.2798 76.9184 3.2248
143 7.6083 24.9397 1.4877
144 99.6860 27.9478 6.4807
145 99.8070 89.5055 7.9951
146 9.7580 74.9350 5.5996
147 29.5423 94.3449 1.2498
148 7.4823 37.6382 9.9135
149 72.2519 82.7073 5.5085
150 84.5874 19.5925 3.9880
151 41.8889 65.3375 2.5649
152 42.0836 21.0795 6.6307
153 96.1056 74.9380 6.1762
154 4.7442 76.3263 7.7589
155 86.3227 73.6764 2.3817
156 30.4649 22.8298 4.2111
157 13.1091 47.4383 2.2956
158 34.5838 61.8314 8.6555
159 28.9813 23.2079 4.0408
160 99.1615 22.3869 3.4768
161 40.5411 98.9728 1.0541
162 82.7164 32.3630 8.2172
163 55.5244 7.9538 5.4767
164 72.1747 2.7638 5.8406
165 21.7502 42.7484 8.8382
166 67.1286 7.3023 7.5056
167 9.5841 78.9739 7.0128
168 14.2781 41.3731 2.6095
169 46.8255 17.1118 5.9545
170 12.9453 35.6296 9.6389
171 66.5920 54.0189 6.3642
172 24.1543 34.9451 8.2771
173 78.6979 57.4980 9.8608
174 66.0186 23.5142 8.9733
175 84.0606 51.0532 2.9245
176 89.0851 93.3506 1.3117
177 43.5979 42.3752 5.0601
178 79.8357 18.5118 1.1242
179 35.8177 32.5795 5.2634
Continued on next page
299
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
180 29.0567 54.0114 9.5608
181 13.2049 55.6515 3.2406
182 29.6228 60.0637 4.4778
183 13.4185 5.0335 4.8829
184 66.3954 92.7492 8.4780
185 64.8759 52.1568 8.4218
186 38.1936 59.3168 5.0770
187 82.4117 4.8602 4.4250
188 40.7519 31.8646 9.3328
189 40.7603 31.2755 7.6676
190 84.3031 48.8249 7.6387
191 67.6528 40.6287 9.5222
192 23.7067 15.3257 5.5909
193 13.6666 87.4145 8.1269
194 36.9112 89.0138 5.0696
195 61.2510 46.4154 8.6428
196 46.5676 55.5598 4.5139
197 10.4211 68.6089 7.6454
198 55.3354 81.3035 9.7879
199 75.1216 87.6230 5.7097
200 20.9624 54.6080 4.8692
201 72.5237 23.4034 2.8644
202 88.7311 43.9713 3.9106
203 31.7848 21.1602 1.9978
204 23.8851 31.7062 4.3769
205 5.3005 69.8511 3.9691
206 28.3050 0.4145 4.0789
207 96.1946 11.1278 8.3541
208 59.5213 25.6654 5.7852
209 12.5944 50.5640 5.6901
210 33.7481 35.2143 7.9688
211 43.6707 82.0170 2.0824
212 46.4840 3.5376 6.6291
213 19.8928 55.2643 4.1198
214 31.2437 99.6854 4.0116
215 61.4243 28.6419 6.1715
216 84.2377 34.3819 8.7754
217 34.4674 24.5274 2.7871
218 65.0229 22.1678 7.0521
219 82.6152 58.6575 9.1165
220 63.9230 60.2019 2.7924
Continued on next page
300
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
221 27.9889 28.4304 3.6846
222 68.1264 96.4126 5.4687
223 67.0078 58.8176 9.0091
224 64.5547 43.1629 5.5127
225 80.6805 25.8366 3.4930
226 7.1452 54.1601 5.8056
227 60.5724 82.1745 6.1682
228 30.7538 1.8671 4.7152
229 69.9887 0.0693 1.1329
230 21.0559 95.1881 7.3249
231 17.1636 78.8707 5.5607
232 4.1477 6.7218 4.4314
233 23.4573 58.9159 1.5844
234 62.1966 93.4178 4.2272
235 99.4877 72.9679 3.1083
236 47.7832 11.3415 2.8315
237 94.5501 54.7822 8.3240
238 29.8136 37.1847 4.5409
239 37.3291 0.6609 1.4822
240 28.0092 65.8637 4.3755
241 22.6651 72.8266 7.9749
242 10.9719 82.9271 2.4877
243 52.6815 5.5271 9.2100
244 68.5546 12.3668 3.8729
245 86.3801 42.7940 3.9680
246 3.2580 48.3365 2.8381
247 32.0232 68.9513 7.9049
248 15.2189 43.8155 1.6298
249 36.2978 16.3159 9.5503
250 30.8702 13.2865 2.4239
251 13.8538 0.2071 3.5780
252 51.8378 71.9086 7.1842
253 70.3343 36.6122 2.2703
254 40.9914 14.5009 5.6088
255 97.6691 67.1912 7.4919
256 72.3245 7.9443 9.3596
257 59.3197 89.3727 7.5889
258 36.1890 42.7059 7.7486
259 41.4369 57.9219 4.6659
260 80.3465 80.6668 3.1554
261 70.7753 55.5773 5.6877
Continued on next page
301
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
262 21.9454 14.3563 2.9717
263 99.6323 15.9648 8.5815
264 82.4775 64.9636 6.9664
265 92.9664 76.1384 8.3461
266 50.8914 89.1876 8.1449
267 53.7478 90.2929 5.2219
268 47.9874 74.5592 3.7857
269 31.7078 4.7780 7.1882
270 99.3214 19.0511 9.8817
271 96.8150 84.6854 7.9294
272 81.4333 26.5603 8.4662
273 38.2692 44.4779 7.3548
274 9.0227 18.4100 6.3580
275 13.5141 74.8350 7.7759
276 45.5964 26.1417 5.4705
277 49.9855 3.0949 8.7862
278 35.6861 25.8744 1.6122
279 82.7003 97.4909 9.7169
280 56.9921 62.2335 1.8888
281 58.5904 11.4813 5.9228
282 35.3933 68.1641 4.6267
283 69.6625 4.8603 1.9634
284 15.5309 57.5336 7.5175
285 96.1699 68.6401 6.5231
286 19.8193 83.7089 8.0467
287 79.0636 60.1657 6.0996
288 87.9582 71.5423 8.3019
289 53.4913 33.5876 6.1910
290 28.1810 24.3498 9.4963
291 7.8989 4.8129 8.8431
292 99.0843 92.7817 5.5684
293 30.5336 14.6126 8.0994
294 20.0885 23.9020 5.2573
295 28.8278 27.6707 8.4592
296 28.2919 91.4633 3.9023
297 37.8837 87.0358 9.7853
298 27.5112 24.9717 3.5039
299 52.4671 58.5451 1.6555
300 78.9537 68.9615 7.7610
301 59.2400 14.2448 8.4807
302 46.1638 9.4883 9.3010
Continued on next page
302
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
303 3.9206 21.5729 3.9432
304 48.2431 87.4577 8.2366
305 51.1400 49.8845 5.8443
306 48.5021 13.4619 5.1697
307 60.1092 58.3302 8.3868
308 30.3268 59.5625 9.5672
309 70.6812 21.8147 1.6865
310 40.6076 52.0709 7.3780
311 2.5503 35.0184 3.1143
312 82.4370 36.1829 4.5901
313 75.6241 20.0929 3.4131
314 87.8341 49.8174 8.4926
315 22.2303 78.5249 9.9584
316 17.3134 37.9571 6.8478
317 21.5612 93.2677 7.3356
318 89.0336 57.2262 9.3907
319 80.7219 64.1863 7.1889
320 32.2264 37.8729 6.1152
321 70.8655 93.2131 4.4276
322 48.7394 62.2542 6.7112
323 9.9905 44.9324 4.2691
324 64.4508 71.9840 4.6686
325 91.2805 86.6334 4.3183
326 22.9310 63.7123 5.2156
327 59.9455 20.4294 5.5307
328 5.6518 46.7243 9.1948
329 1.8068 95.7587 2.8579
330 55.4073 36.8310 4.0474
331 60.2711 28.2750 6.1671
332 58.3277 26.7562 5.3824
333 85.7517 6.3572 3.3600
334 71.8649 38.9343 6.2163
335 86.4947 10.9066 8.9049
336 0.4961 75.3147 1.5486
337 67.2604 50.5242 4.9679
338 77.2338 91.9815 1.7583
339 68.7893 17.2141 6.0691
340 41.1953 88.1958 5.8538
341 5.3899 0.7962 7.9125
342 37.7046 26.7336 3.0978
343 22.3171 46.2730 6.2863
Continued on next page
303
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
344 10.3852 16.0249 5.1308
345 44.5516 71.1385 8.7488
346 73.6901 65.3564 6.9475
347 65.3271 76.6332 4.1849
348 70.3674 54.9928 4.1247
349 87.2967 68.1229 3.2835
350 36.9236 22.7567 9.5728
351 19.3340 62.8886 3.6838
352 50.5989 94.3380 2.4257
353 53.2623 47.0560 4.2517
354 73.1320 49.4925 7.6747
355 34.8167 86.6775 7.3531
356 72.5305 0.5953 7.3080
357 81.0881 60.0507 1.0560
358 27.5374 27.3986 4.3691
359 27.0413 16.1304 9.1135
360 33.1666 59.8931 3.8651
361 9.9130 71.5914 6.3737
362 50.2947 83.0994 3.6802
363 75.7520 96.5808 2.1251
364 14.5749 95.9650 4.4952
365 65.9084 6.4964 8.3592
366 90.6467 33.8136 9.8306
367 59.7386 60.9382 8.7579
368 23.3337 19.1122 1.7544
369 73.0851 25.7067 4.0394
370 85.0063 92.5547 3.1252
371 36.6237 84.3547 3.8602
372 21.9630 74.4138 9.8600
373 11.6501 57.5202 5.9343
374 55.4393 68.7866 7.7433
375 42.4683 91.1837 8.5767
376 44.5172 92.9185 2.5020
377 33.0563 4.4128 9.1279
378 23.7857 81.5201 1.9461
379 85.6897 40.5950 7.7058
380 35.8244 90.0965 7.5643
381 9.0875 96.2033 7.4572
382 88.8327 60.0698 2.2009
383 26.2022 60.5780 5.0121
384 66.0621 31.5406 5.5791
Continued on next page
304
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
385 47.3200 89.2316 5.7744
386 37.1157 36.0147 8.7375
387 63.1419 86.2332 7.0995
388 70.8833 44.7124 8.2525
389 84.4786 20.0179 5.7812
390 2.9731 30.7646 9.6031
391 83.5732 0.0635 1.6001
392 11.0115 57.8047 5.8737
393 25.0147 10.5918 3.5349
394 90.1421 94.5503 5.3281
395 42.2903 94.1672 7.1638
396 46.6450 83.4614 2.8743
397 2.7744 83.9566 6.4734
398 99.9635 66.3509 3.9356
399 87.1309 14.3425 8.9276
400 12.4625 81.2300 2.2006
401 69.6480 68.0498 1.9217
402 85.6216 60.1203 9.6321
403 94.8601 2.4498 2.3761
404 13.8291 36.1770 2.3728
405 75.8103 82.6972 2.4000
406 73.3446 39.8728 1.8061
407 22.2534 76.2698 5.0898
408 27.2640 9.4955 7.0201
409 90.0841 48.2271 8.4817
410 4.9400 30.0808 8.1121
411 46.7135 84.1755 7.4144
412 72.6552 94.8797 5.2534
413 72.5001 25.6608 7.3773
414 70.0004 5.6050 9.6225
415 27.4118 20.4262 5.5520
416 99.8883 18.4695 3.7455
417 41.8041 27.5795 8.1083
418 7.6958 58.5219 3.1275
419 50.9499 70.5852 3.1087
420 79.2801 22.9321 5.1823
421 87.1855 44.5900 6.5745
422 31.5241 72.3181 6.5380
423 38.4946 52.4527 2.1036
424 93.1367 39.9355 2.1141
425 6.4939 66.9043 3.5601
Continued on next page
305
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
426 58.6540 41.0171 7.6216
427 85.7887 56.2696 4.7018
428 48.5789 42.5327 8.4608
429 87.3613 58.1622 9.4160
430 5.9912 38.0970 4.5916
431 28.0485 97.4925 1.4699
432 11.0064 8.1281 6.1407
433 14.5471 71.3322 7.7290
434 60.9363 18.2524 3.8822
435 47.8568 51.2964 5.4364
436 86.3848 63.8632 2.9949
437 34.0932 32.1014 9.4535
438 79.8495 15.0627 5.3407
439 77.4927 85.5940 5.8600
440 46.0189 85.4591 2.9895
441 36.8783 70.8467 1.8635
442 30.4860 37.8482 1.5415
443 85.0130 9.8284 8.3756
444 4.0364 38.3813 7.9433
445 30.1841 12.5245 2.7613
446 83.1498 22.1172 9.0561
447 2.7342 65.1652 7.1587
448 2.7634 28.4505 6.9116
449 1.5746 49.0644 9.9134
450 23.0410 44.3664 1.3032
451 12.6614 81.9575 4.8183
452 7.2701 19.8952 5.4099
453 48.7939 5.4821 6.2515
454 13.6214 32.0200 1.7494
455 28.1430 54.5708 6.9414
456 55.2356 19.4002 1.4707
457 12.1351 2.7756 6.0115
458 21.1733 40.9677 7.4082
459 24.7317 1.8912 5.3912
460 91.3518 53.6560 6.5584
461 65.1253 7.1775 2.9240
462 87.0338 54.6654 6.8109
463 93.8043 14.6098 4.4258
464 8.8729 24.6039 1.9334
465 32.5083 19.5743 4.3976
466 90.9627 98.7790 3.3657
Continued on next page
306
Table B.32 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
467 45.4574 21.4868 3.1716
468 2.1161 36.8042 6.6063
469 98.7262 96.0385 5.7063
470 11.0076 17.6528 4.7191
471 47.4674 23.5248 2.9601
472 62.0475 85.0245 8.7270
473 40.1033 76.5287 8.7491
474 60.9001 36.6935 3.5555
475 95.1030 86.8446 6.5385
476 3.8282 89.5959 8.0154
477 42.4845 82.9588 9.5936
478 19.5832 75.1997 9.2764
479 33.2656 71.5682 4.4633
480 54.1069 19.3536 2.4638
481 52.3277 59.1760 8.1708
482 85.8211 38.8465 2.0244
483 83.7580 4.6413 2.4294
484 58.4855 39.4074 4.2025
485 41.6375 76.9052 8.6298
486 42.4323 17.3147 6.2450
487 7.1230 71.3003 6.2756
488 89.0572 56.6626 9.3325
489 69.3810 66.0685 6.1757
490 6.5244 63.3813 1.0898
491 97.5718 3.4284 8.2844
492 87.2843 84.4262 6.4793
493 4.6176 85.6129 5.3192
494 43.5048 2.5544 3.4160
495 90.3892 30.2877 3.3229
496 8.5737 60.6761 5.3291
497 79.5302 89.2820 3.0461
498 45.9480 42.2346 1.4374
499 77.6448 15.9174 2.5232
500 84.5341 42.0531 3.3260
307
Table B.33: Depot locations and number of vehicles for MS17
Depot index x-coordinate y-coordinate Number of vehicles
1 40.0000 50.0000 2
2 60.0000 50.0000 2
Table B.34: Customer locations and service time for
MS17
Customer index x-coordinate y-coordinate Service time (short)
1 73.8564 69.4413 2.7812
2 51.5279 70.2137 6.4512
3 63.0879 58.0923 8.4133
4 47.1635 67.1003 8.2955
5 47.9687 64.5121 8.2201
6 58.6256 43.6374 7.3730
7 56.9470 57.1482 8.7344
8 35.9968 45.0145 8.0298
9 30.8413 35.0022 2.8342
10 36.2767 60.5791 9.9401
11 32.3028 51.1242 1.8426
12 50.7446 46.8813 6.8556
13 44.8594 54.8621 2.9366
14 45.3999 66.4616 3.1949
15 32.9880 56.5489 4.0572
16 59.7446 53.2425 2.7808
17 55.4926 54.6631 5.5615
18 48.8797 50.8537 9.5568
19 62.7648 37.0922 4.5515
20 39.0753 63.1130 6.2602
21 55.1838 73.4818 6.4588
22 54.3555 41.0984 7.4318
23 54.3657 82.1293 4.6138
24 40.8844 47.0625 8.7282
25 54.0855 45.9375 9.2844
26 43.5640 35.0400 7.7576
27 38.7944 36.7944 3.5703
28 34.9591 34.1171 8.1713
29 62.9727 55.8984 2.2849
30 39.4257 76.6171 5.5410
31 47.8386 58.7912 6.4962
32 34.8918 64.2367 7.3342
33 46.2859 72.3641 4.4501
Continued on next page
308
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 9.5995 8.3411 7.5582
35 36.4130 47.2073 8.9856
36 32.1695 55.8836 1.5026
37 37.3194 61.9542 2.2439
38 47.3342 28.2525 8.7676
39 45.9332 33.2355 4.7957
40 74.3050 63.1781 4.7018
41 42.8528 48.0571 9.6323
42 46.8746 59.2182 7.7522
43 30.3836 33.9893 9.8290
44 44.0327 22.7700 3.1016
45 33.2753 62.6867 1.8660
46 50.3787 69.8885 4.4612
47 60.6636 77.2010 5.5025
48 55.0532 24.4635 6.1323
49 41.2422 27.7191 9.7897
50 29.6182 25.4359 5.4357
51 68.2502 49.3056 4.6079
52 75.6255 39.7415 9.9549
53 51.5063 71.9026 3.3490
54 37.6262 25.7489 6.9879
55 64.9721 20.9608 9.6783
56 42.5918 53.4217 7.0404
57 44.1274 69.8822 3.6926
58 61.0797 36.6196 5.7801
59 32.6848 28.9061 1.0132
60 25.5406 47.5111 8.9541
61 55.2585 22.7259 4.6395
62 55.0092 50.2891 3.7109
63 51.1893 63.8065 9.5552
64 56.2086 53.6290 5.1458
65 63.5280 18.1793 3.5888
66 62.1306 41.0530 1.7616
67 42.8929 44.9661 6.2396
68 60.1247 80.2264 2.3776
69 52.1656 65.2475 1.6578
70 43.6807 49.0487 6.2251
71 35.0837 71.8227 3.5831
72 58.0871 32.5877 4.2573
73 45.5797 44.1956 7.5234
74 50.5804 73.5427 8.7248
Continued on next page
309
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 40.0882 75.0397 4.1312
76 30.6186 62.1729 9.6557
77 52.1448 58.1792 9.5821
78 49.2233 40.2312 2.8543
79 64.9878 62.4150 7.9142
80 60.0213 36.1974 6.5398
81 63.1663 59.5753 9.2703
82 40.6390 54.6974 6.4228
83 38.2959 68.9884 7.3192
84 34.1364 42.9022 7.6931
85 56.2248 60.6023 4.4659
86 84.8635 63.2196 3.2635
87 59.0947 35.0270 1.3308
88 40.3367 52.6041 5.2491
89 60.4579 76.6209 6.8057
90 35.8959 51.8740 3.5107
91 32.1941 44.8563 5.6607
92 58.9680 57.6110 3.2110
93 40.2762 45.4150 3.6776
94 53.9498 57.3857 6.8543
95 67.5817 47.7539 9.0225
96 55.0141 49.6945 8.7500
97 61.6208 57.6798 2.8892
98 29.9275 72.7053 4.5918
99 58.2692 57.5312 8.9909
100 76.7313 77.4731 3.3088
101 56.7642 16.1940 9.7012
102 30.7390 42.5124 6.5724
103 47.4607 53.9332 2.4881
104 43.7504 36.0805 8.4358
105 54.7878 28.7341 6.9012
106 55.1504 60.2839 5.9181
107 55.0687 60.2117 3.2620
108 45.4527 54.8230 1.3614
109 42.5091 56.5886 3.1004
110 42.6301 35.4906 4.2500
111 60.6693 41.7052 6.7011
112 26.8374 48.2221 9.8749
113 47.4087 38.5362 2.8644
114 53.3797 55.5313 7.8138
115 41.8404 89.4204 8.9770
Continued on next page
310
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 55.9653 41.9628 5.2501
117 49.1085 60.7908 2.4302
118 38.2712 32.7596 8.2983
119 52.0170 72.3259 5.2886
120 46.6477 33.8477 2.0466
121 44.8766 53.4786 8.8815
122 41.1085 39.6901 6.7167
123 50.7681 58.5336 1.8755
124 26.9234 50.1892 9.1760
125 45.0208 49.2669 1.3151
126 43.2056 99.1515 1.3577
127 38.6013 39.4992 9.8971
128 58.1587 49.2187 7.1756
129 40.8216 94.7171 4.3902
130 56.7579 30.8885 5.5389
131 62.1980 59.2166 7.8715
132 48.0391 32.0590 1.4399
133 53.4725 67.1773 7.5333
134 57.9940 55.4588 7.3120
135 48.9878 60.8687 5.1300
136 56.7609 45.3523 6.2407
137 34.2179 54.0865 4.0518
138 63.8803 74.5419 2.5356
139 37.6305 12.0816 4.5927
140 27.1396 22.7785 9.2780
141 67.3062 56.9245 3.0344
142 49.2159 39.0872 4.2491
143 55.6115 45.0609 3.9211
144 45.4593 25.0514 1.7522
145 37.2427 34.9194 5.6140
146 11.5876 43.2636 8.4958
147 57.8285 37.9034 9.1415
148 46.4164 35.5586 7.5124
149 47.5332 42.9692 4.4470
150 55.0701 34.2889 3.6822
151 32.2581 72.3647 7.2254
152 40.8819 33.5261 8.9241
153 64.3416 80.2990 9.3209
154 57.4733 43.7594 1.7313
155 33.9840 25.8043 5.3441
156 22.4592 39.6886 2.1544
Continued on next page
311
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 42.8594 65.5750 3.2762
158 52.6750 67.5988 8.9557
159 61.7797 52.6705 2.7665
160 51.1716 54.7900 2.0922
161 35.9711 60.5484 5.8933
162 53.8270 25.6826 3.8316
163 35.3458 40.3048 4.4384
164 37.9879 19.4975 8.1239
165 41.8283 42.5149 8.5526
166 34.6326 65.8212 7.1221
167 46.6129 61.9574 4.7523
168 38.7506 88.1305 6.7860
169 46.4289 52.7788 2.9267
170 44.2197 14.0585 6.5554
171 44.8777 78.1567 7.0767
172 43.7058 71.3713 6.4092
173 65.4162 40.2895 4.1168
174 57.6288 53.7102 4.2796
175 50.7384 62.9909 2.5433
176 31.6632 56.4118 8.1583
177 29.6775 61.6061 5.4340
178 25.4406 48.1214 4.1916
179 82.5649 49.3529 7.9756
180 62.1547 51.4681 3.1312
181 53.2123 36.8391 8.6035
182 37.8220 73.7160 8.3487
183 35.6704 50.1055 8.6161
184 56.8455 61.4413 4.3317
185 69.5635 35.7511 4.4491
186 28.8332 32.0794 8.7520
187 44.3825 48.4839 5.1752
188 48.9463 45.7871 6.1349
189 25.1000 69.9137 7.2578
190 60.5156 60.1011 9.6483
191 44.8168 59.0086 5.9168
192 73.9023 25.9177 6.7292
193 45.1138 33.8718 6.1380
194 55.1148 53.3675 9.3440
195 35.7196 44.2020 8.7739
196 42.1892 71.5015 2.5286
197 35.3910 72.3526 2.6083
Continued on next page
312
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 54.9072 40.3200 3.1915
199 66.2730 64.5856 7.7660
200 42.5795 73.2575 2.7922
201 55.4547 55.3498 9.8465
202 43.6955 77.0564 7.3867
203 51.2763 67.7072 2.5789
204 64.9531 53.5684 8.7247
205 51.5035 64.6134 9.1847
206 37.0395 53.2401 9.6550
207 39.2862 43.0851 6.1354
208 47.8766 55.9743 6.0659
209 47.6041 50.6037 2.5900
210 39.1773 43.9228 5.6231
211 52.2583 79.5170 5.9362
212 65.8316 53.6879 2.4875
213 46.8604 95.5063 5.4450
214 47.4429 45.0639 5.8161
215 22.4810 59.4049 2.7893
216 40.3186 76.3770 6.6085
217 32.5841 95.4872 1.2368
218 45.1721 55.0594 3.8691
219 56.5698 36.8290 5.7970
220 69.0409 63.3897 3.9410
221 72.4812 28.0016 6.4197
222 48.5389 45.4359 4.2574
223 45.9975 54.5311 2.2143
224 60.2190 74.8259 9.2243
225 56.1270 73.9524 6.7650
226 59.5656 49.5406 6.9290
227 59.7285 65.3989 7.0780
228 31.4962 44.6453 7.7010
229 56.7545 61.0187 8.5796
230 48.8558 81.9216 5.6499
231 40.4968 52.6127 2.3668
232 41.3301 44.9911 4.4260
233 66.0182 41.6661 8.3892
234 39.8783 61.9412 2.5423
235 34.5398 72.2881 3.9698
236 52.6836 85.4280 9.6982
237 75.1346 50.9008 8.2566
238 50.3194 52.7173 2.9997
Continued on next page
313
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 53.8537 39.4549 9.9980
240 38.2719 76.8665 1.5736
241 70.9277 48.7425 4.8293
242 51.5624 42.1127 4.6390
243 56.6263 86.4040 4.6026
244 38.0991 63.4980 2.0073
245 60.6755 61.9390 4.8188
246 54.8643 33.2405 6.5219
247 35.5500 57.2331 9.8926
248 50.4968 58.6691 2.9791
249 44.3675 31.7959 4.1867
250 51.3656 46.2368 3.3962
251 46.8681 43.2513 3.6235
252 47.6262 58.7977 2.6955
253 37.0886 33.2173 1.2057
254 45.9589 68.1504 5.0446
255 59.5816 79.7479 3.1928
256 71.8084 44.9374 8.8185
257 35.4935 49.8551 5.7575
258 79.7176 58.4439 9.2272
259 69.0760 70.0542 9.7654
260 52.1063 58.7003 6.2688
261 46.2349 56.6174 2.0708
262 41.2668 41.9532 9.3388
263 60.4096 46.1417 6.3420
264 41.3174 60.2231 8.9525
265 44.2265 78.0475 4.8203
266 61.0452 59.4732 6.4653
267 55.4493 29.8995 1.6369
268 61.2093 57.2177 9.3230
269 56.3092 48.4647 6.7787
270 44.9888 45.9324 1.9405
271 43.5769 46.3469 7.3020
272 59.9546 35.3372 4.5622
273 41.6101 44.6533 1.7641
274 64.8332 36.9264 2.9303
275 59.8838 43.9173 3.2392
276 53.5965 51.9545 3.0399
277 50.0403 52.9057 7.3270
278 54.5702 46.4057 7.7874
279 94.0835 47.4565 5.9256
Continued on next page
314
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 48.5945 50.5615 5.9814
281 30.5426 57.6380 6.6752
282 73.9388 71.3605 9.8691
283 57.6231 60.3348 6.7085
284 41.9011 45.2221 6.4041
285 82.7167 59.9669 9.1827
286 56.8869 45.9078 6.1375
287 53.6775 20.3210 4.0188
288 40.2770 10.8793 9.6143
289 36.6884 21.4401 4.9593
290 27.8948 46.0479 6.4139
291 44.7135 39.6729 7.4824
292 36.8362 37.9973 7.1090
293 58.0969 50.6776 2.9148
294 46.0296 39.0170 1.7346
295 72.1124 39.4914 3.4703
296 68.8823 60.1604 8.8077
297 52.0501 63.0389 6.0342
298 46.4655 90.6097 5.1816
299 64.4021 55.0401 4.8727
300 35.6687 50.9720 7.9659
301 58.4212 40.4311 6.8853
302 41.6361 46.7465 6.9196
303 44.9960 49.1578 2.4492
304 41.6025 20.7371 4.8914
305 57.1954 45.7107 5.5458
306 40.2738 62.4924 4.3780
307 36.7055 40.4873 5.3234
308 56.9122 58.2372 4.0818
309 44.7071 66.5240 7.9943
310 54.5198 67.9523 4.4555
311 45.6014 62.9474 7.4040
312 53.3693 12.3360 5.3284
313 17.9444 40.5937 7.5626
314 55.8233 65.0249 9.4380
315 73.1695 56.5779 5.6553
316 62.9911 50.0809 9.1276
317 61.3862 57.2820 2.9637
318 47.0034 68.8345 8.8590
319 52.2625 52.5628 1.7442
320 53.0531 37.3562 5.1886
Continued on next page
315
Table B.34 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
321 51.2049 46.9973 1.1974
322 39.6191 46.5368 8.2745
323 45.5968 64.9458 2.6129
324 47.8153 56.8718 2.4885
325 43.9918 59.1253 2.6344
326 60.4605 52.4639 7.2229
327 81.7294 43.9622 2.9239
328 33.4583 51.0190 3.6829
329 51.6043 53.6118 7.9150
330 31.9703 26.6980 5.5104
331 66.2814 52.9812 9.1852
332 67.6239 65.4597 1.5207
333 29.2182 48.1637 4.9308
334 74.2961 76.2066 6.1503
335 36.4413 59.3415 6.0856
336 52.8352 42.9943 8.4143
337 63.7366 47.4342 2.1349
338 51.8399 45.4134 3.7011
339 78.6958 54.0187 1.0191
340 84.4070 62.5781 9.5600
341 51.7290 45.1348 7.8967
342 26.1617 57.6408 7.7617
343 45.4376 79.2548 2.2498
344 39.3986 65.5248 4.1439
345 40.4406 63.7544 2.3621
346 35.9038 36.4199 5.4705
347 50.9774 41.0966 8.2779
348 76.3329 54.0425 6.6958
349 41.0519 48.3225 7.1956
350 46.4936 22.9159 6.7561
316
Table B.35: Depot locations and number of vehicles for MS18
Depot index x-coordinate y-coordinate Number of vehicles
1 20.0000 80.0000 1
2 80.0000 20.0000 3
Table B.36: Customer locations and service time for
MS18
Customer index x-coordinate y-coordinate Service time (short)
1 7.8069 12.7266 7.5639
2 66.9043 0.8648 8.7386
3 50.0211 72.7080 6.6426
4 21.7994 35.4116 2.6253
5 57.1616 78.0446 6.1598
6 12.2189 43.6657 2.4721
7 67.1166 43.6555 9.1545
8 59.9586 4.9213 1.6961
9 5.5976 4.9632 4.0468
10 5.6343 9.1100 6.2256
11 15.2501 59.4037 5.2771
12 1.9621 24.1084 8.2479
13 43.5176 84.1369 5.7770
14 83.2221 85.7213 3.0458
15 61.7390 96.3612 7.3854
16 52.0129 48.8900 2.3377
17 86.3868 22.0310 6.9230
18 9.7698 22.6209 6.7058
19 90.8052 53.6788 3.0638
20 10.8017 76.2110 2.6401
21 51.6997 34.7567 2.4972
22 14.3156 46.1232 2.3465
23 55.9371 63.9324 2.8247
24 0.4580 91.7336 9.5946
25 76.6682 16.1573 1.1432
26 84.8709 71.5635 9.6176
27 91.6821 57.7739 1.2312
28 98.6968 43.3299 9.7400
29 50.5133 88.4243 3.6784
30 27.1422 39.3052 5.7257
31 10.0751 17.8975 8.7611
32 50.7849 63.3334 9.0676
33 58.5609 62.4001 2.7011
Continued on next page
317
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 76.2887 32.7942 6.9465
35 8.2963 80.2965 9.4711
36 66.1596 99.9478 9.7814
37 51.6979 98.0978 1.9714
38 17.1048 12.7037 2.6101
39 93.8558 23.2240 7.7190
40 59.0483 2.3632 1.4452
41 44.0635 60.7433 1.6416
42 94.1919 11.0809 5.4021
43 65.5914 40.7460 8.6490
44 45.1946 88.4077 9.9734
45 83.9697 54.8133 1.0395
46 53.2624 36.9003 5.8835
47 55.3887 20.8346 8.7521
48 68.0066 44.0943 9.1823
49 36.7190 95.6196 8.6082
50 23.9291 12.4026 8.9099
51 57.8923 47.0763 7.7156
52 86.6887 85.6896 2.0574
53 40.6777 4.3390 5.5812
54 11.2615 69.1625 2.5195
55 44.3846 97.8985 8.4800
56 30.0184 28.3268 9.3521
57 40.1387 13.3780 2.5254
58 83.3364 68.5280 8.9536
59 40.3629 90.9455 4.4908
60 39.0176 61.0869 4.4431
61 36.0449 89.9983 3.4431
62 14.0255 19.3434 8.8109
63 26.0130 75.4425 7.6735
64 8.6815 34.6261 5.0309
65 42.9397 41.8625 7.3867
66 25.7283 15.5720 9.4990
67 29.7555 81.9001 2.5671
68 42.4858 62.4924 3.2014
69 11.9207 73.8560 6.7684
70 49.5067 80.5112 8.2775
71 70.6407 6.7223 8.6803
72 24.3573 95.0790 4.5831
73 78.5070 49.7577 2.0394
74 7.4090 75.5146 1.7225
Continued on next page
318
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 39.3883 74.2405 4.2442
76 0.3394 83.1130 8.4601
77 22.0677 15.6502 2.9315
78 0.1301 45.7309 8.1194
79 18.9180 61.8100 6.8922
80 14.2484 93.2183 1.2353
81 26.8076 83.5088 8.0720
82 17.4892 89.5424 9.3031
83 13.8649 58.2519 5.4308
84 59.8886 58.2747 8.5061
85 90.1058 85.4926 2.1822
86 93.9380 3.4866 7.8381
87 22.1184 88.5420 9.3316
88 48.2671 40.7731 8.4944
89 37.6011 3.6382 3.3346
90 52.3780 74.6148 2.9172
91 26.4873 15.4829 5.7008
92 6.8357 14.3908 4.5762
93 43.6327 60.5959 5.3120
94 17.3853 25.4481 9.9451
95 2.6107 32.4154 6.4403
96 95.4678 40.1791 9.5042
97 43.0597 40.6373 5.4140
98 96.1559 38.6191 4.9415
99 76.2414 60.9802 7.9539
100 0.7349 16.6891 7.6966
101 68.0039 18.8092 4.9861
102 70.5951 9.4629 1.4770
103 64.5129 32.3186 1.7904
104 55.2310 76.9597 8.1819
105 21.8109 23.4118 6.9002
106 77.2366 74.0365 1.2910
107 22.8028 69.2818 6.0136
108 37.0865 82.4078 7.4782
109 89.0929 82.7978 1.9937
110 85.6377 29.3368 2.9498
111 40.2434 30.9369 8.2992
112 31.8019 52.3030 2.2480
113 60.8635 32.5299 8.9371
114 91.0195 83.1843 9.3120
115 90.9098 81.0295 1.1148
Continued on next page
319
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 59.1594 55.6998 4.3944
117 33.2571 26.2964 2.5103
118 85.3064 68.0566 5.8620
119 44.2398 23.3653 1.9150
120 90.4355 45.6425 1.3534
121 3.3179 38.4567 9.3991
122 53.2426 53.8601 9.7443
123 71.6497 99.1704 4.2484
124 17.9302 75.5220 6.7978
125 33.6533 98.0455 1.6115
126 18.7713 23.4783 2.8712
127 32.1927 52.8559 1.3564
128 40.3857 5.1436 5.2242
129 54.8566 75.6875 2.3509
130 4.8739 60.1980 9.9218
131 55.2732 85.7169 4.8436
132 27.4811 98.8277 9.5983
133 24.1502 92.9484 7.5182
134 24.3145 40.9515 6.2280
135 15.4159 0.0341 5.8623
136 95.6416 54.0878 7.3490
137 93.5661 20.7731 1.0453
138 81.8714 21.9284 8.0426
139 72.8262 32.5806 9.3417
140 17.5812 9.5949 1.0747
141 36.0371 74.7534 8.4217
142 18.8790 74.8509 7.9060
143 0.1198 54.3299 9.9742
144 31.6420 33.8132 3.0489
145 69.9617 83.2334 9.2759
146 62.5255 55.2572 6.7780
147 54.3062 95.7543 1.9479
148 43.9037 89.2833 3.4134
149 28.7427 35.6504 7.8746
150 50.1659 54.6402 8.2496
151 76.1546 34.6682 1.9383
152 76.2408 62.2803 5.2278
153 57.6056 79.6625 2.9716
154 74.7663 74.5875 9.3044
155 64.5535 12.5536 3.8829
156 12.3220 82.2394 8.7179
Continued on next page
320
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 50.4398 2.5151 3.3386
158 34.7261 41.4429 8.9026
159 9.2148 73.1407 2.6944
160 14.7849 78.1374 7.8327
161 19.8170 36.7286 1.2852
162 67.2270 74.4868 6.7811
163 43.1511 89.2267 6.1018
164 69.4404 24.2603 4.3877
165 25.6785 12.9597 2.9129
166 0.9759 22.5068 8.1294
167 53.2283 35.0014 2.3090
168 27.9392 28.7085 5.4023
169 94.6230 92.7488 1.1156
170 90.6443 5.1314 2.6795
171 39.2685 59.2667 5.3671
172 2.4855 16.2899 8.5440
173 67.1437 83.8406 2.2695
174 83.7171 16.7561 7.5900
175 97.1500 50.2201 7.2196
176 5.6933 99.9329 1.3104
177 45.0324 35.5407 5.3997
178 58.2470 4.7078 9.7425
179 68.6638 21.3661 2.0121
180 71.9433 39.7839 7.6889
181 65.0041 33.3668 6.7469
182 72.6915 22.9603 6.3476
183 37.3848 93.6120 5.4876
184 58.1582 68.3189 6.1107
185 11.6119 96.2114 4.8385
186 5.7654 43.7973 1.6862
187 97.9765 94.0337 3.6153
188 28.4824 0.5834 6.0520
189 59.4974 61.0307 6.7000
190 96.2161 80.1076 9.3770
191 18.5778 23.2982 9.7999
192 19.3040 93.2469 1.8424
193 34.1644 76.3263 6.9556
194 93.2898 82.6450 6.4250
195 39.0668 57.3464 5.2644
196 27.3217 79.2582 4.2063
197 15.1947 32.9041 5.2802
Continued on next page
321
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 39.7109 22.3462 7.0392
199 37.4722 31.2386 9.6368
200 13.1115 58.4523 1.8018
201 43.5041 82.9914 8.1797
202 9.1513 29.0462 6.3170
203 61.4627 40.2554 9.2098
204 1.0979 86.2057 1.9102
205 57.3260 61.4740 3.6397
206 78.9730 99.1188 1.4643
207 23.5367 20.3699 5.5372
208 44.8020 82.7209 7.9154
209 56.9358 67.5862 3.5469
210 6.1401 24.8949 3.0282
211 49.6289 47.5786 3.9816
212 64.2315 39.9075 5.0793
213 22.1266 59.9438 7.6365
214 83.7056 80.0523 5.5890
215 97.1075 10.5069 4.4426
216 84.6373 82.1442 9.1493
217 50.5999 84.1086 9.6873
218 27.8876 35.4506 6.6544
219 74.6617 43.0069 2.1883
220 23.6930 57.2239 6.5647
221 95.7345 70.0825 4.4472
222 62.0260 74.2470 9.9207
223 60.0262 75.7884 3.5814
224 17.2605 38.9129 7.3557
225 9.0347 42.9302 5.8169
226 25.5262 95.6345 2.7389
227 85.8571 57.2971 7.2049
228 91.1067 84.9722 1.4541
229 69.9634 27.6345 2.6599
230 72.5182 62.2324 1.4109
231 22.9886 58.8362 8.9654
232 57.6053 96.3468 8.5581
233 81.0628 8.5903 2.0634
234 40.3843 50.0499 4.6937
235 98.8439 52.1590 2.0821
236 8.9999 9.0166 6.1488
237 32.0941 90.4666 9.5445
238 51.1409 88.4389 3.3075
Continued on next page
322
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 6.0606 43.8990 9.9088
240 72.5688 78.1723 4.1483
241 55.6556 14.8465 2.8767
242 52.9360 61.9816 6.9924
243 82.9982 26.0624 9.7601
244 85.8759 44.5656 6.6043
245 78.9029 84.4000 1.5718
246 31.7833 19.6205 4.3616
247 45.2207 30.3852 2.4963
248 75.2228 48.3295 3.0815
249 10.9862 33.7812 1.4699
250 10.9742 79.8486 9.1158
251 26.9884 98.7488 8.1396
252 52.4637 15.9048 4.3571
253 97.2651 23.6880 8.4885
254 71.0409 70.2237 7.7845
255 31.1860 37.5472 6.5968
256 29.1457 97.3705 4.5468
257 85.0357 97.2306 4.2335
258 91.1647 64.3698 1.7997
259 63.9276 86.0099 4.0751
260 25.5370 40.1883 5.9380
261 8.8666 63.1931 5.1449
262 83.8256 98.5237 6.8091
263 58.4719 55.9477 5.6217
264 94.8109 93.3592 8.3298
265 6.1029 72.0343 1.8746
266 58.4641 48.4039 5.1734
267 28.5108 63.9031 6.3084
268 82.7732 88.7637 2.6845
269 19.0986 19.8737 6.5020
270 44.2530 39.5366 1.4675
271 39.3412 99.2175 6.1815
272 82.6574 40.2352 8.5811
273 67.6871 65.8856 5.4975
274 20.7603 90.1348 4.9512
275 31.8105 99.5382 2.3415
276 13.3811 65.3163 1.2545
277 67.1463 10.8436 7.8100
278 57.0991 3.6114 8.1650
279 16.9767 61.8091 3.6420
Continued on next page
323
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 14.7656 56.7144 2.0369
281 47.6080 96.1965 4.3758
282 90.8102 74.6105 8.4600
283 55.2175 66.2516 8.5760
284 3.2940 52.3313 6.9871
285 5.3863 25.9894 9.6413
286 80.5063 96.1994 9.4881
287 45.1375 54.0204 2.0143
288 38.2646 3.0270 6.8346
289 78.9644 69.6314 5.3272
290 36.4287 51.9716 1.5987
291 53.2350 5.9031 9.0799
292 71.1657 89.0036 5.4751
293 87.1477 33.0202 7.9417
294 32.8690 22.9701 1.5433
295 65.0118 11.3949 3.3621
296 97.4836 31.0923 6.8596
297 7.5967 22.8432 2.2024
298 58.7019 65.1997 6.7469
299 41.3886 6.6160 4.4645
300 30.9136 27.5431 7.8913
301 26.3834 28.1820 6.8762
302 75.8766 88.0066 4.4334
303 99.5216 44.4330 3.7002
304 18.6571 75.5914 4.0613
305 78.1145 60.3296 9.2703
306 19.5798 78.3266 5.1064
307 99.2359 11.3931 4.9825
308 80.2262 97.8564 5.0877
309 42.4227 84.8597 9.5075
310 72.8864 5.0646 2.9721
311 49.8354 46.6202 8.9416
312 80.8990 32.5653 1.1789
313 35.6509 63.0205 4.0759
314 7.3243 23.0299 7.8942
315 59.0991 57.9885 4.0852
316 91.0188 60.3156 6.5693
317 19.3766 59.9879 5.0772
318 43.2368 44.8428 1.0915
319 74.9160 3.5423 6.3917
320 3.9184 51.3815 6.4141
Continued on next page
324
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
321 94.6325 40.7730 6.8448
322 76.3673 10.8046 4.0845
323 55.8821 45.9876 5.4397
324 18.3843 45.0883 7.3160
325 49.7949 55.1140 8.9902
326 51.7846 80.5404 1.4955
327 99.4243 70.0850 1.8853
328 85.4852 87.2236 6.8480
329 96.2404 5.2192 7.8766
330 67.8941 21.9681 9.8916
331 40.3501 45.9642 2.1279
332 93.4979 95.8534 4.2803
333 47.9485 79.0045 7.0861
334 23.1792 45.1875 4.3818
335 39.6290 33.3428 8.7711
336 70.5077 5.9095 3.6278
337 55.8559 74.0905 2.2013
338 75.6631 50.6795 7.0539
339 99.5481 19.9925 2.8233
340 96.2431 42.7194 8.8166
341 53.5067 16.8690 7.7604
342 96.3870 75.1695 4.7744
343 11.5626 36.8351 1.0021
344 5.1448 94.1818 2.3452
345 30.4349 1.7173 3.4645
346 58.0192 82.9056 8.8518
347 53.0964 62.6591 6.4113
348 90.1208 53.8747 3.8907
349 54.0550 65.0508 3.5586
350 43.1981 72.6630 4.9178
351 54.2667 9.4489 9.1338
352 71.2415 87.7574 9.3260
353 1.6675 1.4362 5.5476
354 80.0921 29.4303 6.6482
355 14.2509 17.9915 7.4734
356 47.8474 92.6294 1.2152
357 25.6835 6.8180 6.1744
358 36.9092 58.1093 1.4188
359 66.1765 63.7151 4.8028
360 16.9609 65.1269 5.2096
361 27.8784 86.4622 1.2037
Continued on next page
325
Table B.36 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
362 19.8222 5.5953 1.5857
363 19.5072 81.6855 9.3156
364 32.6840 52.8922 5.8073
365 88.0338 69.4351 4.3012
366 47.1102 21.2405 4.2755
367 40.3969 54.3280 2.3624
368 17.9231 70.2520 2.3465
369 96.8925 95.6435 4.1572
370 40.7456 44.4542 4.0237
371 84.4487 8.5398 8.0563
372 61.5325 5.7340 5.3807
373 37.6611 62.9450 5.1832
374 87.7182 79.6179 2.1813
375 78.4852 69.1191 8.9775
376 46.4954 34.5308 7.0710
377 81.3977 94.6817 8.5164
378 89.8444 52.0190 6.9084
379 42.9239 95.3813 9.8553
380 33.4329 7.3596 9.8181
381 59.6647 20.7032 3.2514
382 90.1991 77.5028 6.6211
383 70.2066 91.4188 7.5542
384 37.7455 78.2551 5.4835
385 73.4956 29.5534 8.6485
386 95.4103 15.1846 2.7183
387 54.2813 84.7911 2.1173
388 54.0106 78.4855 1.0251
389 31.1110 27.0832 2.3766
390 7.1235 22.7811 5.8074
391 18.1980 32.1023 5.5957
392 9.2989 82.9562 4.4669
393 46.3489 82.2182 3.7954
394 0.9333 57.0683 1.0320
395 91.5026 57.1830 8.3372
396 64.2742 28.6018 6.7458
397 0.1419 69.9134 5.0351
398 3.0385 79.6258 3.1968
399 20.8470 44.1589 8.2305
400 45.4966 44.6216 8.4157
326
Table B.37: Depot locations and number of vehicles for MS19
Depot index x-coordinate y-coordinate Number of vehicles
1 20.0000 70.0000 1
2 70.0000 20.0000 1
3 10.0000 10.0000 2
Table B.38: Customer locations and service time for
MS19
Customer index x-coordinate y-coordinate Service time (short)
1 12.6820 37.7550 8.6697
2 7.8183 6.0331 5.2053
3 9.5451 30.8690 9.7363
4 69.9089 71.5373 8.5712
5 9.7705 8.9562 1.7069
6 29.5166 11.2224 3.1384
7 26.3677 10.8578 8.3581
8 7.9879 3.1220 4.6525
9 55.8517 45.1865 5.1968
10 34.4087 10.1366 9.5638
11 20.5853 23.9799 9.6850
12 13.3106 9.1599 7.8876
13 29.5222 29.7540 6.1708
14 20.7833 10.7837 9.2433
15 29.2525 25.5736 5.4589
16 2.1943 2.2791 2.4941
17 10.4478 23.6190 3.9340
18 43.3033 9.7144 3.6679
19 10.9586 7.1034 6.0247
20 83.6020 40.3118 1.6073
21 6.1281 9.7035 1.6208
22 100.0000 5.8614 2.5011
23 23.8943 7.9978 9.5269
24 9.9201 43.5462 8.2998
25 80.7923 56.7733 7.3941
26 20.8241 5.0362 9.7322
27 43.6629 0.5026 9.9858
28 13.4801 7.1360 9.8871
29 41.3824 2.3649 2.3508
30 23.9513 12.4183 9.6263
31 3.1340 19.4567 5.7741
32 100.0000 77.0249 1.6668
Continued on next page
327
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 9.6341 12.7845 3.8064
34 31.6006 6.1659 9.0565
35 4.9184 5.0207 8.5129
36 30.5951 37.5054 1.0211
37 23.5338 7.7685 6.7619
38 1.2539 9.7315 8.2286
39 4.5005 0.7075 3.2062
40 2.9073 22.1926 1.5771
41 1.7448 74.2873 3.3683
42 51.1288 28.8581 1.9245
43 26.3683 28.8987 5.3535
44 8.4355 17.6945 4.7700
45 11.7441 72.2255 4.4316
46 4.5495 58.8515 8.9809
47 37.7960 35.7741 4.7850
48 28.5390 6.1336 3.5546
49 37.9231 3.5152 1.4336
50 89.3572 11.7908 2.9725
51 9.6339 27.5261 3.1526
52 31.2811 32.6180 1.2633
53 87.0135 86.0708 7.3208
54 31.4299 3.5007 1.0687
55 54.4664 34.8938 6.4983
56 65.9083 0.3671 4.6728
57 13.5745 51.4740 3.2405
58 100.0000 15.7330 6.8721
59 4.2548 24.2821 3.8825
60 67.9291 6.0909 1.9330
61 18.1367 2.2456 5.8201
62 45.4419 25.4633 2.4838
63 21.5712 2.3291 8.9509
64 3.6818 53.1902 6.9981
65 10.5242 83.9336 8.6297
66 0.9562 2.5091 7.8639
67 23.1737 1.7944 8.2631
68 22.1726 13.1910 6.6966
69 6.2351 71.8609 7.3938
70 2.5771 3.1346 7.1980
71 10.0376 4.0772 3.8885
72 44.0974 14.1083 5.7848
73 28.5029 19.3814 8.8587
Continued on next page
328
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 32.6219 67.3518 1.4909
75 36.6554 23.9791 5.5036
76 8.8280 7.5140 4.8949
77 29.3223 16.2365 9.1385
78 0.6620 17.4912 6.6717
79 3.6999 4.6523 9.8473
80 11.9600 100.0000 6.2668
81 3.2116 33.2896 8.5657
82 29.5134 48.8156 5.2193
83 11.7023 85.3035 5.9070
84 11.3933 31.0061 2.6119
85 29.9997 2.8050 6.7102
86 13.4912 45.3341 9.6666
87 55.7157 0.2771 5.8061
88 5.6284 50.7563 5.3165
89 3.3344 19.0196 8.1430
90 10.8594 24.8455 1.8344
91 72.4791 10.4804 8.9272
92 1.5852 3.3793 1.0349
93 71.1995 30.5300 5.6038
94 34.7430 32.4731 7.1062
95 24.5129 62.8663 6.0917
96 22.0757 42.0038 5.3061
97 45.0173 6.8606 3.8846
98 1.4944 2.3685 6.4142
99 51.3847 10.9772 9.2184
100 7.0131 16.4711 7.1427
101 11.1511 8.8600 9.5206
102 29.5540 77.4861 1.8918
103 53.9148 2.9063 5.5993
104 1.1367 9.9144 1.9912
105 4.8351 45.0645 5.9074
106 47.0644 17.2008 7.1991
107 23.3556 15.7863 2.3268
108 19.2635 11.7900 7.9980
109 7.6014 0.9019 4.5915
110 3.3196 14.0892 9.0847
111 0.6626 13.7187 3.7634
112 8.0783 1.6138 1.5495
113 11.8336 69.6935 2.9752
114 4.2966 10.4259 1.7455
Continued on next page
329
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 24.3187 57.7156 9.5536
116 2.6707 12.4120 1.1473
117 5.9323 5.4429 2.0320
118 2.3908 85.8053 1.1117
119 21.6037 16.2554 2.9460
120 66.2728 30.2961 1.1028
121 2.4259 10.3633 6.7820
122 12.2454 12.8659 5.6529
123 7.1808 69.6981 3.2099
124 13.6008 2.8807 2.7437
125 0.1373 1.1947 1.8178
126 44.9142 42.7486 4.3160
127 8.6037 65.2464 1.0701
128 44.7886 0.3010 6.4243
129 63.3532 21.2213 5.3097
130 11.3896 6.8944 3.7731
131 14.8787 1.9987 7.7000
132 6.4604 3.4208 8.5541
133 72.5640 0.9331 3.3619
134 76.6311 30.3708 5.6281
135 13.5102 8.5609 5.0210
136 6.8036 2.6035 4.0709
137 42.1498 3.3611 8.5523
138 15.5922 4.7004 9.8424
139 13.8914 83.6610 6.6382
140 12.5657 2.4642 2.6315
141 79.9820 11.6331 2.1072
142 32.7220 13.9394 6.2197
143 43.0164 7.5890 3.9568
144 15.9793 16.9209 3.4137
145 7.6946 3.6307 5.9522
146 2.1489 49.1103 2.6247
147 87.1702 10.4966 7.1064
148 4.8330 13.0643 1.5012
149 4.1397 16.6691 1.3065
150 18.8950 35.2012 3.5787
151 24.8348 0.6713 1.6965
152 64.5453 2.1876 9.1052
153 44.3052 10.6924 8.6195
154 9.9387 55.0681 4.5613
155 13.1853 16.6078 2.5229
Continued on next page
330
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 10.0946 18.2945 4.8741
157 19.9483 67.1431 4.7460
158 5.8316 23.6145 7.5589
159 19.6426 5.4165 4.6583
160 2.7882 5.9991 9.5663
161 65.5847 53.0113 9.2079
162 11.3361 22.1697 9.5627
163 5.3106 5.6391 4.1140
164 28.4002 34.3868 3.6122
165 15.5872 13.2979 8.9803
166 3.5945 82.6017 2.8903
167 15.6739 9.5817 2.1779
168 5.7790 4.7542 5.6846
169 13.3509 8.9201 9.1492
170 3.1531 26.1193 4.6228
171 20.3447 17.8773 2.9419
172 59.3349 31.4583 1.7087
173 1.8278 33.1092 9.3975
174 21.7726 6.6994 6.4258
175 16.0280 13.4301 4.3974
176 9.2424 15.4716 6.9844
177 72.6668 0.2342 8.1297
178 26.9401 6.5615 4.0014
179 5.8050 13.3567 7.2339
180 100.0000 5.8661 2.8343
181 72.8760 14.9948 9.6284
182 32.3590 64.2878 7.4065
183 25.7170 18.6470 2.5022
184 6.1777 4.0710 4.9850
185 41.6707 22.7155 6.6969
186 22.5055 36.0137 9.3697
187 9.1337 15.3358 5.7640
188 4.6739 24.9303 6.6383
189 15.1204 6.9096 7.1274
190 2.2936 6.5654 9.3088
191 2.1491 26.5106 2.3755
192 12.0098 0.8272 4.6515
193 2.3448 25.8342 3.8123
194 2.8051 41.1015 7.2451
195 26.5841 59.9070 9.0162
196 0.0905 29.0201 5.4160
Continued on next page
331
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 2.9059 1.0637 8.2524
198 25.2777 11.2172 3.9380
199 6.1189 39.2386 5.9489
200 27.8439 27.4812 4.4991
201 46.3344 26.7495 9.0715
202 7.5451 2.7777 7.0851
203 11.4821 17.1215 8.4556
204 12.7747 14.3964 1.9908
205 35.6194 5.9138 3.5130
206 31.6155 26.1793 7.9087
207 5.6181 37.8327 2.9445
208 13.3206 4.8751 1.3066
209 29.9537 64.4118 4.9290
210 30.4255 62.4694 9.4318
211 37.2686 29.3025 3.3588
212 17.0581 3.9019 6.1277
213 14.2716 18.6480 4.2360
214 66.8790 28.1570 1.2415
215 45.2120 19.4108 5.5038
216 16.8082 9.8567 8.4431
217 15.3335 13.8755 3.3308
218 16.8319 4.2749 1.4130
219 52.6105 64.4843 3.2182
220 46.4877 33.6913 6.9466
221 22.3421 9.3652 3.9647
222 9.1446 20.9544 6.9355
223 6.1868 28.1964 1.1170
224 11.2996 76.9387 7.4626
225 13.5405 29.2511 4.5201
226 0.6398 21.2964 1.3015
227 15.8890 12.1301 4.6541
228 31.0877 35.3658 7.4468
229 40.7144 4.2189 9.2920
230 38.3846 3.1165 9.8561
231 20.6576 1.8612 9.8508
232 14.1871 14.3782 9.0668
233 2.2048 29.8517 8.7913
234 28.7926 6.5294 8.2086
235 31.7330 16.9703 5.9948
236 11.9953 12.2517 4.7698
237 37.8027 9.4009 2.1441
Continued on next page
332
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 44.0040 61.9516 6.8916
239 100.0000 8.4180 8.7757
240 16.5250 30.2348 3.4714
241 100.0000 36.3974 8.5615
242 14.6746 28.6863 1.6368
243 14.6866 31.6446 4.4091
244 65.1829 34.6010 3.4135
245 23.1012 52.2788 2.3763
246 6.4627 10.0813 6.6790
247 13.9420 31.9682 3.8474
248 22.7162 34.9017 9.6320
249 16.1890 14.1071 5.4881
250 23.3814 74.2284 7.6475
251 67.5672 4.8649 1.1148
252 6.2591 82.4578 6.4482
253 6.7195 32.9967 6.1881
254 14.1175 29.9175 8.2664
255 12.1752 10.3007 6.8947
256 13.2387 11.7198 8.9041
257 12.0872 8.4800 9.1214
258 35.7011 32.1988 2.3701
259 5.8588 0.0981 2.7332
260 8.7160 30.0622 8.1188
261 7.5995 17.2655 1.5463
262 49.4370 50.5629 4.5084
263 100.0000 2.7019 3.6997
264 7.5778 35.8933 7.6076
265 5.2438 67.5430 1.9379
266 14.2856 25.1538 8.1332
267 72.2024 0.2764 8.0446
268 28.2451 38.7763 5.7916
269 1.7173 31.1603 3.2802
270 3.9820 17.1003 1.6386
271 9.3938 11.5283 6.6322
272 44.7085 23.3370 1.2221
273 9.6539 9.6430 1.5584
274 63.2783 50.9991 2.1665
275 14.4507 66.3966 5.0555
276 19.4653 77.3151 7.0510
277 10.1967 14.7680 8.7050
278 20.8612 2.8904 5.4860
Continued on next page
333
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 87.0850 13.3697 1.4391
280 20.3880 15.7991 3.8245
281 19.0321 10.9999 6.7747
282 100.0000 22.4424 8.0775
283 13.0408 33.5450 3.6024
284 29.9638 12.3898 5.4808
285 4.7810 11.4406 8.3659
286 2.1957 6.8849 6.3562
287 32.9796 36.3222 5.8278
288 30.4335 31.0570 3.9779
289 59.5208 94.6371 4.7052
290 8.0109 30.8233 8.1461
291 8.3009 25.9556 4.0889
292 11.9159 10.7838 5.1635
293 24.4465 12.4559 4.3104
294 11.5243 6.9873 7.1161
295 16.4789 3.0722 6.1100
296 10.7616 2.7593 6.8660
297 3.4455 63.7518 5.4200
298 27.6395 16.0675 4.5861
299 14.6053 77.4467 5.2974
300 88.8465 5.6847 1.5993
301 31.4831 97.1466 4.6993
302 23.5507 14.2859 9.7218
303 26.7438 85.6912 8.0265
304 14.2384 76.2052 7.5612
305 19.3852 76.0262 7.8909
306 83.3386 45.9418 7.8092
307 74.5104 38.4084 8.5894
308 74.3855 10.7429 7.9314
309 26.5942 45.5472 9.8079
310 11.3418 14.7247 2.0022
311 4.8981 29.3592 4.5647
312 27.6120 38.0417 5.4285
313 65.7360 92.4546 3.3229
314 62.6701 19.3468 1.3327
315 57.4108 65.5051 9.7694
316 20.0358 39.4229 7.5378
317 40.9374 19.3486 2.3317
318 28.4314 3.1735 2.3311
319 83.4083 80.1822 7.3434
Continued on next page
334
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 75.7352 31.3325 4.4289
321 86.5908 74.6942 1.6877
322 41.6935 59.0634 4.6976
323 74.2514 29.6429 2.2869
324 6.9935 81.5503 8.1903
325 95.8454 89.2513 9.3722
326 68.7191 58.9583 1.0425
327 26.0030 81.5188 6.8504
328 73.5626 55.5128 7.1068
329 47.8618 81.4574 3.2826
330 87.1375 3.8354 8.5886
331 32.2553 84.8485 3.6456
332 56.1023 11.4486 1.2417
333 24.5850 15.1174 1.8398
334 13.4488 72.8034 8.1810
335 23.7612 20.1974 7.4026
336 36.3673 73.8008 8.0507
337 68.8089 86.7171 6.6153
338 3.9020 20.9039 8.4287
339 68.8734 72.8760 1.3152
340 26.0818 61.3300 4.6493
341 85.6589 51.2972 3.2470
342 54.6114 95.9335 5.3281
343 46.0499 18.4444 8.9276
344 15.2666 20.0738 3.5262
345 25.5789 65.9121 6.3923
346 39.1646 73.9105 1.2360
347 96.4607 37.4368 2.3968
348 51.9424 97.6080 8.5052
349 12.0884 3.5211 2.7540
350 91.4895 32.8246 8.4681
351 45.6607 65.0959 4.0427
352 90.4683 3.9350 7.0400
353 29.1900 13.5622 1.4713
354 78.2189 23.8739 7.6088
355 5.5907 85.9359 5.4953
356 21.3044 91.4478 9.4897
357 77.6544 0.7608 3.6080
358 69.6810 24.6182 4.3890
359 90.7883 60.9730 2.0238
360 60.8883 98.4514 9.6837
Continued on next page
335
Table B.38 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 54.4557 97.9311 4.8926
362 75.3118 61.9195 1.7611
363 87.7259 94.8318 7.4501
364 89.3774 37.3761 5.5611
365 85.5831 22.7565 3.9528
366 68.3244 56.8183 7.7817
367 40.7614 56.0081 8.5241
368 4.7855 28.1103 3.2834
369 23.8428 87.2199 5.8098
370 1.3959 84.5637 4.9165
371 38.1700 64.7979 2.4193
372 90.7123 72.3669 6.4043
373 30.3596 26.6740 9.4371
374 86.7330 12.1991 1.9698
375 14.7173 15.0853 9.0998
376 30.9913 66.7906 5.9542
377 41.8244 33.6551 4.8462
378 21.0176 61.7685 2.3714
379 76.7455 77.5326 3.2279
380 24.2546 73.2936 5.0263
381 88.6141 73.6284 5.7951
382 29.7543 5.9901 4.1919
383 19.0678 22.7051 7.9580
384 72.4119 46.6279 8.9351
385 95.6810 89.8958 7.6068
386 90.1467 54.4241 4.6579
387 70.0584 5.7137 6.4376
388 81.3472 79.4493 6.7699
389 86.6425 77.4849 2.1472
390 88.8213 50.9021 5.4657
391 23.0451 2.5752 3.7942
392 62.6476 97.5528 6.2072
393 24.3942 24.2368 9.4925
394 44.2680 90.1012 4.8425
395 78.2786 44.8384 1.2982
396 71.5829 6.2794 9.3649
397 24.4633 9.9259 9.3248
398 73.7832 36.8498 4.2248
399 90.7812 51.3531 3.3399
400 84.2232 38.0071 8.0817
336
Table B.39: Depot locations and number of vehicles for MS20
Depot index x-coordinate y-coordinate Number of vehicles
1 25.6060 1.6149 1
2 30.0000 30.0000 2
3 70.0000 70.0000 2
Table B.40: Customer locations and service time for
MS20
Customer index x-coordinate y-coordinate Service time (short)
1 4.2018 36.5997 5.6042
2 17.1602 39.2858 6.0627
3 52.7356 35.3461 7.1631
4 44.0164 41.4880 1.8316
5 14.4179 33.3959 8.8532
6 52.8884 23.8118 9.4864
7 27.2686 45.9001 1.8693
8 30.6371 30.7543 8.6129
9 37.1386 28.7998 9.1846
10 32.5833 12.5864 1.1021
11 64.7317 42.0604 5.7131
12 31.0256 18.5135 6.8531
13 32.0664 42.9399 4.4663
14 25.6741 10.7300 6.8437
15 8.4971 33.4598 7.8657
16 35.8140 23.9867 6.1812
17 38.3398 28.6541 6.6873
18 38.2171 9.0215 3.5038
19 39.3133 21.6025 8.5585
20 45.0584 44.3805 4.8415
21 18.3947 64.5842 6.6846
22 38.3871 40.4169 8.5012
23 39.0688 2.2105 3.4317
24 23.3464 22.9831 4.6072
25 29.5895 36.2596 5.9883
26 17.7956 19.6608 4.9948
27 35.8404 60.9155 1.8135
28 24.8826 29.0918 7.6994
29 58.7577 49.2761 1.2935
30 36.9916 34.2850 4.8677
31 25.4193 31.0962 1.3354
32 19.1042 57.5082 9.7822
Continued on next page
337
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 1.0000 11.9495 5.7011
34 33.3619 22.5401 9.1867
35 18.2371 6.4420 4.4492
36 33.4853 34.1546 8.9601
37 7.4295 36.4559 3.2952
38 41.7407 38.0011 9.1814
39 19.9933 45.9441 9.0510
40 36.0906 10.6709 4.5867
41 18.5207 51.4470 6.6252
42 28.9498 2.2946 6.1084
43 48.1555 38.1287 9.0506
44 31.0259 0.9940 2.9275
45 34.8522 42.1337 1.0347
46 48.7670 33.6994 8.9252
47 23.3411 48.0565 3.1161
48 36.8956 40.1752 3.2038
49 45.9998 49.3303 6.7683
50 47.1081 21.0803 3.7407
51 39.5031 6.1646 8.4306
52 70.1808 1.0000 8.9532
53 10.9101 60.4333 9.5084
54 17.3579 47.0016 4.5172
55 34.4009 41.4462 8.2119
56 23.1983 37.8937 2.4140
57 37.3757 15.3048 6.6265
58 9.3782 32.0551 7.2909
59 31.1935 26.0003 1.7728
60 42.8258 36.8273 5.7806
61 14.8478 21.5168 8.9971
62 24.8780 67.0746 3.3730
63 1.0000 11.3143 3.1131
64 17.4946 41.7573 8.5569
65 34.5788 39.8622 5.4599
66 49.3897 25.7832 2.3713
67 48.8168 75.9203 3.0769
68 33.8530 23.4514 6.9216
69 20.9420 28.0715 6.0665
70 8.5099 62.7814 3.6265
71 41.8643 55.4148 6.6007
72 35.6718 7.6526 7.4431
73 21.5751 46.7418 3.5266
Continued on next page
338
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 26.3221 36.3800 4.7105
75 31.0761 38.1466 4.2599
76 18.5178 21.6122 8.0325
77 19.7962 10.2288 2.2194
78 25.7427 9.4795 9.1186
79 21.4979 12.3690 3.6067
80 50.8109 20.8986 5.4960
81 33.5060 12.3039 8.0523
82 38.6620 45.1187 7.0936
83 62.3390 33.7020 2.3483
84 24.4542 33.3709 7.2696
85 25.5830 11.7220 2.1611
86 10.2557 40.9440 9.5135
87 37.0405 1.0000 8.9777
88 22.7030 20.3513 5.6350
89 18.7156 38.9326 7.1147
90 39.7972 60.0346 9.7911
91 9.3039 23.7804 2.1291
92 1.0000 43.0286 7.7702
93 55.1485 63.6988 8.4435
94 50.0119 20.6197 8.0329
95 40.0966 19.4731 2.7179
96 2.3984 64.7104 4.8578
97 23.9212 31.7682 1.1301
98 64.3039 47.1101 3.9276
99 42.2801 34.6173 2.2123
100 19.1989 41.2427 5.0547
101 21.6111 39.8648 6.1505
102 24.5733 36.5552 8.1282
103 25.4264 1.0000 4.7776
104 15.2472 22.0241 5.7928
105 59.9856 23.1952 9.3313
106 44.6384 16.7735 9.0917
107 35.7488 18.3101 5.9035
108 52.9662 22.3562 9.1101
109 15.8206 11.9255 1.4664
110 30.7198 30.6669 8.2774
111 31.5311 18.1156 4.0141
112 12.4404 18.5735 3.0581
113 40.1094 5.5040 8.4016
114 27.0358 43.1720 4.1341
Continued on next page
339
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 49.0969 2.2846 2.4892
116 40.4510 41.9489 1.2532
117 21.3891 29.9530 9.5983
118 51.4771 39.5188 7.1226
119 47.4047 20.2256 8.7451
120 43.5502 38.0543 9.4518
121 43.1607 44.0961 7.1217
122 24.2446 33.3733 9.2568
123 7.9602 32.4499 3.3102
124 39.9992 30.4458 8.9706
125 43.2080 28.0023 9.2804
126 45.1519 32.4457 3.7006
127 14.2751 24.6127 1.6605
128 21.2377 4.0227 7.9066
129 42.0759 45.9993 1.7646
130 41.0076 20.3847 7.5589
131 42.8157 28.5139 5.0310
132 16.9129 27.5304 6.8612
133 42.4870 39.5396 2.5255
134 35.9210 52.5352 5.7830
135 40.8582 1.0000 6.7042
136 1.0000 34.3270 1.1269
137 16.3878 23.9099 5.2333
138 53.1124 9.4374 8.9769
139 46.7406 24.6117 2.0263
140 4.7476 27.5846 4.9829
141 18.9248 63.4662 6.9359
142 1.0000 8.0265 3.6530
143 32.9027 58.9804 9.5533
144 28.2052 30.4159 7.2486
145 19.5624 42.4775 2.8613
146 16.6948 23.5501 5.9929
147 17.0824 14.1971 8.9135
148 3.4815 39.8755 6.0207
149 8.6735 41.7757 7.7710
150 37.2506 43.7922 9.0541
151 33.2950 26.4283 8.5766
152 46.7121 44.8726 2.1777
153 37.8318 27.0132 2.7024
154 27.9967 49.7689 2.3828
155 25.1698 32.1721 1.2601
Continued on next page
340
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 9.5501 26.2656 1.0818
157 20.4951 4.6282 6.3681
158 27.3950 64.4344 6.4814
159 24.6110 40.7937 9.2703
160 2.6859 23.7797 7.6022
161 17.3167 33.0521 3.7103
162 13.5573 25.2406 5.4602
163 35.0304 20.5987 3.3235
164 28.8342 17.6789 7.5957
165 21.7567 6.6307 2.0508
166 14.2944 50.6012 7.7144
167 14.7638 43.0021 8.2881
168 1.0000 27.0720 7.7071
169 50.4943 24.2461 4.0343
170 15.3748 45.0745 6.2589
171 1.0000 2.2791 5.2206
172 24.2523 1.0000 1.7854
173 38.5077 17.1122 8.4585
174 16.7739 15.5612 7.1735
175 25.8551 51.0725 3.4059
176 31.4219 17.1986 9.7254
177 31.2302 4.2888 2.6540
178 46.9592 7.0799 3.6995
179 7.4688 22.5956 4.7007
180 48.6560 40.4680 3.1284
181 51.8310 1.0000 2.7555
182 38.1713 22.1435 7.3484
183 16.2131 18.4730 2.6249
184 11.7700 47.4833 5.7010
185 22.7331 61.0565 3.6655
186 23.5389 38.1246 5.1650
187 34.3477 41.0800 9.3271
188 44.0151 20.4182 2.9430
189 44.4083 14.5860 1.0091
190 45.2059 28.6909 9.1595
191 29.2864 41.3054 7.1204
192 27.7754 63.2071 5.6346
193 32.3259 34.0267 5.6986
194 36.7458 15.3110 1.9263
195 14.9369 15.3833 9.9719
196 40.1105 13.1520 4.2307
Continued on next page
341
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 29.2047 39.6502 6.6272
198 3.3481 35.7266 4.5403
199 20.8271 32.2175 1.0690
200 31.1438 37.2201 5.9076
201 69.0646 77.3671 5.5820
202 64.6178 62.1799 3.2210
203 74.3829 73.4577 1.4086
204 75.8705 64.2169 8.5756
205 59.7133 76.0858 1.4342
206 46.7299 75.6822 3.8469
207 63.4393 71.9451 8.0508
208 58.4249 89.2167 9.7516
209 60.9937 59.3636 6.2782
210 79.7658 67.8599 8.0024
211 62.4135 70.0642 7.5493
212 68.8915 71.8740 6.8589
213 98.7211 77.4477 6.9815
214 70.2304 84.3332 9.4490
215 60.0511 63.3360 5.8157
216 72.1888 71.6392 4.5860
217 55.5788 49.8524 7.0341
218 62.3851 53.4991 4.9648
219 64.5391 71.3395 2.1959
220 70.1182 69.7806 4.9528
221 82.0717 63.7263 5.9288
222 71.5687 54.2798 4.5562
223 68.0493 66.1970 4.5844
224 72.2814 80.9690 7.7621
225 57.9911 73.5898 5.7012
226 74.1075 61.6411 5.4139
227 63.7151 69.5902 1.7981
228 74.9104 80.8101 3.2577
229 66.4415 76.8658 5.0280
230 60.9176 47.1491 6.7416
231 52.7684 72.3562 7.3850
232 71.6035 77.9266 9.9336
233 74.6412 68.3896 9.3898
234 64.1983 58.5480 1.8301
235 56.3478 71.5552 9.5819
236 58.3293 74.4006 2.4652
237 80.3066 65.2813 9.7341
Continued on next page
342
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 62.6042 66.8331 6.3731
239 72.8318 69.8920 3.1620
240 69.8404 74.4226 1.6327
241 79.9664 73.5631 3.7004
242 64.4832 76.3750 8.3219
243 70.1972 67.0347 1.6904
244 87.3394 61.3254 4.1903
245 77.3827 78.0772 2.1881
246 91.9065 76.6529 2.4236
247 72.3452 60.9747 1.5593
248 76.9114 74.8788 7.3166
249 81.0845 76.3785 1.7783
250 79.7799 63.4651 6.5511
251 60.6619 83.9109 2.5639
252 49.4378 71.5197 6.8626
253 75.8314 56.0465 5.4883
254 61.4918 73.1223 3.5606
255 91.3132 81.4637 8.4750
256 75.4400 62.7372 8.3652
257 77.0508 67.5041 9.4435
258 77.2800 83.6568 1.0029
259 81.5499 77.8549 6.7635
260 66.9946 67.5229 1.0662
261 69.3418 65.8327 1.9578
262 72.2263 74.3643 1.9611
263 80.5934 74.8185 4.3040
264 74.9325 73.1404 3.1565
265 64.7851 62.8782 4.1153
266 79.5491 70.7952 3.2466
267 72.7897 75.0733 4.4836
268 59.9754 84.6433 4.7893
269 70.3129 83.5507 6.7607
270 58.6779 68.5668 8.0880
271 62.5699 67.2485 3.4299
272 75.9571 66.8209 8.5958
273 50.9208 89.2139 7.6642
274 55.7005 80.9352 8.4349
275 84.0168 88.1517 2.6397
276 74.2375 71.4266 1.5889
277 76.4629 77.6405 6.4932
278 80.4672 53.1342 7.3140
Continued on next page
343
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 82.5482 57.1889 2.0046
280 73.0182 71.3759 1.8624
281 78.4825 60.7319 6.3805
282 62.4617 54.2955 8.3101
283 67.0331 67.8406 8.3312
284 66.7126 80.2867 1.8049
285 63.1727 64.5674 7.5815
286 64.7526 67.4787 9.1347
287 74.4957 92.7338 5.0701
288 67.6919 87.2376 1.6362
289 71.5461 62.2728 3.1715
290 66.0447 70.1393 7.5868
291 70.6290 47.6220 1.3644
292 79.5832 75.0717 4.8207
293 52.7862 70.9491 5.8619
294 83.6369 73.7984 9.5845
295 75.7169 83.4493 2.8802
296 84.2463 75.7281 2.0470
297 80.6037 55.8990 6.8160
298 57.5233 53.8101 1.9757
299 68.7099 71.8455 9.8515
300 65.3068 63.7068 3.2351
301 55.6229 60.5623 6.4572
302 85.9657 47.5305 8.3503
303 66.5013 62.6333 8.4705
304 67.6009 78.5235 5.4014
305 79.2554 63.4522 7.8466
306 68.6543 69.9450 9.2360
307 68.7316 63.6160 9.1088
308 74.6082 72.2593 2.9281
309 76.6058 68.6349 5.9235
310 78.1571 82.2732 8.0624
311 75.8990 59.1924 2.7500
312 78.3570 73.6465 7.7220
313 66.0095 71.5120 5.2800
314 52.4256 52.5016 6.2493
315 89.7248 73.1456 3.3449
316 64.0644 59.4687 1.7634
317 85.7873 56.5607 3.6832
318 85.4575 69.1952 9.2542
319 79.0443 81.7565 5.2347
Continued on next page
344
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 76.8254 74.9941 3.4252
321 72.0040 85.0558 7.8667
322 68.1962 65.8366 7.9495
323 65.6697 70.0684 1.1917
324 63.6405 75.1080 8.9199
325 64.1417 78.8193 8.1835
326 86.9992 63.1922 3.9175
327 49.4217 65.8585 7.0214
328 67.9391 68.9786 3.6666
329 66.0160 69.3440 9.3696
330 79.1480 73.1007 3.5376
331 72.6254 74.0130 2.5199
332 60.3701 66.2622 7.7065
333 82.9260 72.1275 5.2942
334 85.8779 78.7332 6.8810
335 72.8560 58.0064 9.6992
336 71.1839 64.7918 3.8172
337 73.7968 46.2830 1.6880
338 65.4757 82.7432 8.1227
339 83.9179 80.0402 4.2885
340 51.4345 65.0645 6.2659
341 84.7788 65.0988 2.6500
342 62.2280 91.6454 1.6923
343 61.7832 71.9983 2.3830
344 71.6156 54.0917 8.4419
345 73.4156 82.3353 3.7086
346 75.4898 74.2629 4.4550
347 76.0660 82.3057 6.8567
348 56.5785 83.1113 8.3563
349 77.0262 46.4632 7.8964
350 76.8379 67.4667 4.3676
351 77.0586 93.9092 2.7088
352 71.7876 70.2714 6.8185
353 72.9868 64.4372 1.0324
354 61.5485 70.7602 3.5460
355 69.8888 83.0682 6.7474
356 78.0033 69.1621 6.3287
357 55.0570 85.6977 3.9276
358 66.0657 61.9614 9.9006
359 56.7374 56.9189 2.1091
360 83.3812 62.6098 7.6229
Continued on next page
345
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 74.5669 64.3533 2.4096
362 82.9788 72.0780 4.9118
363 66.2818 89.3002 8.4902
364 75.5776 56.7485 4.2392
365 76.0320 51.6192 1.6861
366 80.2913 61.9231 6.0123
367 72.4720 53.4272 3.4654
368 75.2854 71.6889 2.1885
369 53.6417 69.0762 7.2969
370 82.2771 60.9105 5.3731
371 65.0517 75.6712 2.6444
372 63.1854 55.7114 1.9109
373 53.3516 67.4709 2.8143
374 70.9840 72.6539 2.2127
375 70.7802 67.8396 3.9141
376 73.5082 70.8230 9.5549
377 76.4065 65.6242 5.7892
378 66.9837 64.1214 3.2292
379 80.7399 67.2449 4.9355
380 65.4695 70.1555 7.0218
381 57.9031 64.3663 5.9293
382 65.8768 70.7586 6.4815
383 63.0643 78.5991 8.7682
384 71.5935 48.2003 4.4263
385 74.2891 65.1540 7.7406
386 58.7196 70.8577 2.4103
387 72.9441 69.2767 1.5231
388 64.8784 88.5989 4.0574
389 79.0633 78.9579 8.3546
390 62.6882 75.6286 4.3979
391 69.1334 77.3270 9.7534
392 64.9247 59.6753 6.4479
393 67.4154 76.5832 4.0441
394 75.2514 66.9008 9.3519
395 62.6349 50.3805 9.0858
396 56.1678 48.4706 8.6564
397 60.1792 77.4615 3.3111
398 56.5232 63.5025 3.5695
399 74.7486 69.7633 8.0195
400 72.0386 66.6399 7.3126
401 26.3626 89.0660 5.4326
Continued on next page
346
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
402 26.3116 89.5253 9.7090
403 69.9527 79.4324 5.2855
404 5.6731 53.5218 9.9541
405 78.8717 34.2401 5.4152
406 29.2302 28.0784 5.5311
407 83.9438 47.4461 7.9190
408 48.4634 0.8580 4.4928
409 23.3479 42.4800 5.0793
410 22.0535 71.7987 2.1957
411 31.4285 41.0536 7.8266
412 99.5427 60.4571 6.0871
413 18.9132 59.0882 6.8377
414 85.0491 97.8606 8.1825
415 84.3905 27.5977 2.9840
416 52.8317 4.2786 8.7210
417 66.4871 87.0653 9.1426
418 36.9616 88.7844 3.6282
419 31.7438 37.1951 7.5328
420 81.0324 14.8874 4.0550
421 10.2623 16.9315 3.4541
422 21.2763 16.2823 2.5325
423 44.6422 59.5221 6.9762
424 38.6551 85.1466 5.8227
425 77.4648 4.4113 8.4620
426 47.4231 59.0111 3.4063
427 79.6791 24.7793 2.5854
428 2.4859 21.8489 4.8807
429 99.9140 72.8445 5.2809
430 28.3053 18.3082 8.0670
431 76.7825 10.6938 2.1759
432 3.5064 45.3108 1.4622
433 87.0359 19.3715 6.6476
434 74.2945 37.1959 1.2618
435 10.9293 18.3761 2.2258
436 86.6617 88.6769 7.2510
437 82.1526 21.3487 5.6411
438 0.3792 54.2775 5.8832
439 66.0263 16.5275 8.2764
440 63.2365 44.8273 8.1432
441 21.0481 82.2608 5.5168
442 43.4947 47.2541 3.4897
Continued on next page
347
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
443 93.3109 87.9506 2.0770
444 45.7283 65.6411 8.9794
445 11.0029 54.7909 9.7326
446 67.9891 51.8561 9.4827
447 97.1732 42.5358 6.7432
448 43.5377 81.2119 1.8153
449 23.7959 64.2030 1.6724
450 88.7421 18.4273 2.6421
451 95.2771 99.7704 1.2852
452 39.1655 48.8388 7.5244
453 76.3328 50.9235 2.2974
454 10.0053 76.4176 6.7233
455 22.3862 67.4589 8.1086
456 10.2477 72.5292 6.0963
457 2.1421 22.2260 4.3967
458 51.6928 38.3085 8.3943
459 25.8686 34.6163 3.7439
460 3.3903 84.1848 3.8744
461 74.9682 97.5266 8.0648
462 54.1712 28.2174 5.5336
463 88.1948 97.5571 3.3490
464 56.1391 60.2170 7.5923
465 96.8690 18.6945 2.4665
466 75.2475 46.3329 9.2897
467 94.9283 12.4167 3.0000
468 73.8814 69.9965 1.7525
469 26.3525 75.8415 1.6633
470 8.7485 47.9748 7.9260
471 68.5885 68.3121 8.3591
472 81.0465 71.8050 7.6638
473 15.0807 21.2783 7.8242
474 31.3814 14.0420 9.6508
475 48.7028 48.0692 5.1978
476 70.3631 99.9407 8.0830
477 59.6085 88.0798 4.8031
478 5.4351 3.8926 9.4936
479 97.1161 94.8633 1.0118
480 57.4372 89.2860 9.8314
481 57.4443 21.2325 6.1317
482 57.7154 98.1949 4.1182
483 60.0920 25.4547 6.0175
Continued on next page
348
Table B.40 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
484 13.6016 62.6856 3.6981
485 3.4933 51.8767 2.4317
486 41.3837 49.4841 6.9873
487 27.2949 24.6604 7.1578
488 68.9648 6.3756 8.1317
489 98.5591 16.8444 4.1376
490 24.6915 66.4876 3.2507
491 76.6348 70.6078 4.1050
492 66.6660 85.8070 3.9577
493 53.6316 26.9826 9.3474
494 90.0525 2.2469 7.8047
495 66.6921 55.8130 3.5941
496 54.3385 19.8975 6.4556
497 8.9272 92.0241 7.8943
498 2.7788 27.5098 8.6154
499 95.9793 22.8960 9.1178
500 73.2243 51.8150 6.3614
349
Table B.41: Depot locations and number of vehicles for MS21
Depot index x-coordinate y-coordinate Number of vehicles
1 58.2249 11.9215 1
2 54.0739 93.9829 1
3 86.9941 64.5552 1
4 26.4779 47.9463 1
5 31.8074 63.9317 1
Table B.42: Customer locations and service time for
MS21
Customer index x-coordinate y-coordinate Service time (short)
1 81.4724 96.3089 1.6168
2 90.5792 54.6806 2.9624
3 12.6987 52.1136 8.8247
4 91.3376 23.1594 4.7280
5 63.2359 48.8898 6.9509
6 9.7540 62.4060 8.0514
7 27.8498 67.9136 3.2310
8 54.6882 39.5515 5.9898
9 95.7507 36.7437 3.0663
10 96.4889 98.7982 1.0622
11 15.7613 3.7739 7.8998
12 97.0593 88.5168 1.1965
13 95.7167 91.3287 4.5379
14 48.5376 79.6184 3.2729
15 80.0280 9.8712 2.8380
16 14.1886 26.1871 6.9605
17 42.1761 33.5357 9.2327
18 91.5736 67.9728 1.0621
19 79.2207 13.6553 7.7178
20 95.9492 72.1227 8.1970
21 65.5741 10.6762 9.1702
22 3.5712 65.3757 9.7712
23 84.9129 49.4174 2.0788
24 93.3993 77.9052 5.6707
25 67.8735 71.5037 8.3978
26 75.7740 90.3721 6.7332
27 74.3132 89.0923 9.5852
28 39.2227 33.4163 9.5223
29 65.5478 69.8746 9.6994
30 17.1187 19.7810 1.6061
Continued on next page
350
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 70.6046 3.0541 4.9378
32 3.1833 74.4074 3.8876
33 27.6923 50.0022 2.2065
34 4.6171 47.9922 2.2113
35 9.7132 90.4722 8.2535
36 82.3458 60.9867 5.7229
37 69.4829 61.7666 9.4983
38 31.7099 85.9442 9.8951
39 95.0222 80.5489 4.6890
40 3.4446 57.6722 4.3407
41 43.8744 18.2922 3.0417
42 38.1558 23.9932 5.0143
43 76.5517 88.6512 3.3960
44 79.5200 2.8674 5.1319
45 18.6873 48.9901 4.8961
46 48.9764 16.7927 3.3366
47 44.5586 97.8681 2.2034
48 64.6313 71.2694 4.7731
49 70.9365 50.0472 5.5617
50 75.4687 47.1088 3.9189
51 27.6025 5.9619 7.1622
52 67.9703 68.1972 4.9878
53 65.5098 4.2431 4.9210
54 16.2612 7.1445 8.1372
55 11.8998 52.1650 8.3400
56 49.8364 9.6730 7.7690
57 95.9744 81.8149 8.1033
58 34.0386 81.7547 5.5114
59 58.5268 72.2440 5.9966
60 22.3812 14.9865 6.6767
61 75.1267 65.9605 1.8819
62 25.5095 51.8595 3.2111
63 50.5957 97.2975 6.5415
64 69.9077 64.8991 3.7446
65 89.0903 80.0331 7.9027
66 95.9291 45.3798 3.4051
67 54.7216 43.2392 1.3556
68 13.8624 82.5314 3.6691
69 14.9294 8.3470 6.0073
70 25.7508 13.3171 9.7217
71 84.0717 17.3389 7.2021
Continued on next page
351
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
72 25.4282 39.0938 7.4609
73 81.4285 83.1380 6.0313
74 24.3525 80.3364 5.8002
75 92.9264 6.0471 8.8815
76 34.9984 39.9258 4.5379
77 19.6595 52.6876 5.1226
78 25.1084 41.6799 2.8742
79 61.6045 65.6860 7.8155
80 47.3289 62.7973 5.9202
81 35.1660 29.1984 4.2165
82 83.0829 43.1651 7.3090
83 58.5264 1.5487 1.9830
84 54.9724 98.4064 1.0595
85 91.7194 16.7168 6.3757
86 28.5839 10.6216 6.9326
87 75.7200 37.2410 6.2201
88 75.3729 19.8118 9.1896
89 38.0446 48.9688 6.7241
90 56.7822 33.9493 5.7301
91 7.5854 95.1630 3.3366
92 5.3950 92.0332 1.4605
93 53.0798 5.2677 7.5876
94 77.9167 73.7858 2.4786
95 93.4011 26.9119 3.5236
96 12.9906 42.2836 3.3348
97 56.8824 54.7871 5.9239
98 46.9391 94.2737 5.8714
99 1.1902 41.7744 8.0930
100 33.7123 98.3052 8.8264
101 16.2182 30.1455 8.0879
102 79.4285 70.1099 9.7249
103 31.1215 66.6339 2.6242
104 52.8533 53.9126 9.3754
105 16.5649 69.8106 1.4064
106 60.1982 66.6528 3.1658
107 26.2971 17.8132 1.0797
108 65.4079 12.8014 7.0443
109 68.9215 99.9080 9.1433
110 74.8152 17.1121 6.1517
111 45.0542 3.2601 2.3992
112 8.3821 56.1200 5.5213
Continued on next page
352
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
113 22.8977 88.1867 6.1096
114 91.3337 66.9175 2.6944
115 15.2378 19.0433 3.9178
116 82.5817 36.8917 7.4443
117 53.8342 46.0726 5.9764
118 99.6135 98.1638 2.2805
119 7.8176 15.6405 4.4233
120 44.2678 85.5523 4.5691
121 10.6653 64.4765 6.1907
122 96.1898 37.6272 1.1746
123 0.4634 19.0924 6.1982
124 77.4910 42.8253 9.3898
125 81.7303 48.2022 1.9619
126 86.8695 12.0612 7.5893
127 8.4436 58.9507 9.7347
128 39.9783 22.6188 6.4800
129 25.9870 38.4619 7.4770
130 80.0068 58.2986 3.7248
131 43.1414 25.1806 5.1312
132 91.0648 29.0441 1.4323
133 18.1847 61.7091 4.4682
134 26.3803 26.5281 4.2554
135 14.5539 82.4376 3.5883
136 13.6069 98.2663 8.3504
137 86.9292 73.0249 5.0548
138 57.9705 34.3877 8.2597
139 54.9860 58.4069 8.1116
140 14.4955 10.7769 3.5466
141 85.3031 90.6308 1.6148
142 62.2055 87.9654 1.4944
143 35.0952 81.7761 6.7377
144 51.3250 26.0728 4.8186
145 40.1808 59.4356 9.1498
146 7.5967 2.2513 4.7559
147 23.9916 42.5259 2.3865
148 12.3319 31.2719 5.8600
149 18.3908 16.1485 9.4338
150 23.9953 17.8766 6.9486
151 41.7267 42.2886 4.5519
152 4.9654 9.4229 3.3309
153 90.2716 59.8524 8.6312
Continued on next page
353
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
154 94.4787 47.0924 9.5055
155 49.0864 69.5949 4.3930
156 48.9253 69.9888 1.6055
157 33.7719 63.8531 2.6342
158 90.0054 3.3604 6.1817
159 36.9247 6.8806 2.6730
160 11.1203 31.9600 3.6230
161 78.0252 53.0864 5.1550
162 38.9739 65.4446 4.1228
163 24.1691 40.7619 3.8635
164 40.3912 81.9981 5.1392
165 9.6455 71.8359 3.1231
166 13.1973 96.8649 1.2498
167 94.2051 53.1334 6.9261
168 95.6135 32.5146 2.4292
169 57.5209 10.5629 8.2240
170 5.9780 61.0959 4.6772
171 23.4780 77.8802 3.9465
172 35.3159 42.3453 7.7141
173 82.1194 9.0823 7.7172
174 1.5403 26.6471 2.5656
175 4.3024 15.3657 2.0579
176 16.8990 28.1005 2.5663
177 64.9115 44.0085 6.6467
178 73.1722 52.7143 8.5770
179 64.7746 45.7424 5.5907
180 45.0924 87.5372 2.4919
181 54.7009 51.8052 7.4287
182 29.6321 94.3623 9.1633
183 74.4693 63.7709 2.9668
184 18.8955 95.7694 8.8387
185 68.6775 24.0707 2.9065
186 18.3511 67.6122 8.5300
187 36.8485 28.9065 8.7337
188 62.5619 67.1808 5.7104
189 78.0227 69.5140 5.2963
190 8.1126 6.7993 9.0089
191 92.9386 25.4790 1.5857
192 77.5713 22.4040 5.5851
193 48.6792 66.7833 6.5872
194 43.5859 84.4392 7.6021
Continued on next page
354
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
195 44.6784 34.4462 3.0700
196 30.6349 78.0520 1.1968
197 50.8509 67.5332 2.2509
198 51.0772 0.6715 7.9256
199 81.7628 60.2170 9.7279
200 79.4831 38.6771 4.4811
201 64.4318 91.5991 9.9409
202 37.8609 0.1151 3.9375
203 81.1580 46.2449 2.2344
204 53.2826 42.4349 4.4628
205 35.0727 46.0916 6.0637
206 93.9002 77.0160 6.7045
207 87.5943 32.2472 5.8745
208 55.0156 78.4739 3.8349
209 62.2475 47.1357 2.4339
210 58.7045 3.5763 2.3735
211 20.7742 17.5874 2.2326
212 30.1246 72.1758 7.3882
213 47.0923 47.3486 5.1838
214 23.0488 15.2721 2.0194
215 84.4309 34.1125 7.3079
216 19.4764 60.7389 2.6199
217 22.5922 19.1745 8.2330
218 17.0708 73.8427 5.6256
219 22.7664 24.2850 5.9359
220 43.5699 91.7424 2.8706
221 31.1102 26.9062 8.0613
222 92.3380 76.5500 5.7384
223 43.0207 18.8662 6.1392
224 18.4816 28.7498 4.7984
225 90.4881 9.1113 7.4904
226 97.9748 57.6209 1.6582
227 43.8870 68.3363 6.3538
228 11.1119 54.6593 8.7578
229 25.8065 42.5729 5.0392
230 40.8720 64.4443 6.8732
231 59.4896 64.7618 3.7313
232 26.2212 67.9017 6.4670
233 60.2843 63.5787 3.5101
234 71.1216 94.5174 8.1961
235 22.1747 20.8935 8.1655
Continued on next page
355
Table B.42 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
236 11.7418 70.9282 9.5868
237 29.6676 23.6231 4.9990
238 31.8778 11.9396 5.1119
239 42.4167 60.7304 6.3984
240 50.7858 45.0138 8.5836
241 8.5516 45.8725 1.2808
242 26.2482 66.1945 2.6854
243 80.1015 77.0286 9.4923
244 2.9220 35.0218 9.5313
245 92.8854 66.2010 5.0769
246 73.0331 41.6159 8.2975
247 48.8609 84.1929 9.3599
248 57.8525 83.2917 7.0545
249 23.7284 25.6441 4.3510
250 45.8849 61.3461 4.6513
356
Table B.43: Depot locations and number of vehicles for MS22
Depot index x-coordinate y-coordinate Number of vehicles
1 63.1189 22.4171 1
2 35.5074 65.2451 1
3 99.7003 60.4991 1
Table B.44: Customer locations and service time for
MS22
Customer index x-coordinate y-coordinate Service time (short)
1 58.2249 45.6058 8.4429
2 54.0739 10.1669 4.5251
3 86.9941 99.5390 6.5922
4 26.4779 33.2093 9.6864
5 31.8074 29.7347 8.4562
6 11.9215 6.2045 8.3206
7 93.9829 29.8244 9.5959
8 64.5552 4.6351 2.6481
9 47.9463 50.5428 7.0339
10 63.9317 76.1426 7.6204
11 54.4716 63.1070 8.3760
12 64.7311 8.9892 7.1292
13 54.3886 8.0862 3.9705
14 72.1047 77.7241 1.3122
15 52.2495 90.5135 2.0817
16 99.3705 53.3772 3.5534
17 21.8677 10.9154 8.5441
18 10.5798 82.5809 9.1122
19 10.9697 33.8098 5.0495
20 6.3591 29.3973 9.8968
21 40.4580 74.6313 1.3041
22 44.8373 1.0337 8.7351
23 36.5816 4.8447 5.7570
24 76.3505 66.7916 9.7791
25 62.7896 60.3468 8.8950
26 77.1980 52.6102 2.4520
27 93.2854 72.9709 4.1804
28 97.2741 70.7253 1.5221
29 19.2028 78.1377 4.9970
30 13.8874 28.7977 4.9698
31 69.6266 69.2532 3.9403
32 9.3820 55.6670 9.2296
Continued on next page
357
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 52.5404 39.6521 5.4510
34 53.0344 6.1591 7.3921
35 86.1140 78.0176 6.9818
36 48.4853 33.7584 8.4860
37 39.3456 60.7866 3.3223
38 67.1431 74.1254 7.9232
39 74.1258 10.4813 4.6951
40 52.0052 12.7888 1.5009
41 34.7713 54.9540 8.8358
42 14.9997 48.5229 9.7507
43 58.6092 89.0476 2.0528
44 26.2145 79.8960 5.5748
45 4.4454 73.4341 7.8001
46 75.4933 5.1332 1.9899
47 24.2785 7.2885 1.3048
48 44.2402 8.8527 4.9699
49 68.7796 79.8351 2.1681
50 35.9228 94.3008 9.7444
51 73.6340 68.3716 9.4614
52 39.4707 13.2083 9.3981
53 68.3416 72.2725 9.8538
54 70.4047 11.0353 7.2373
55 44.2305 11.7493 7.3223
56 1.9578 64.0718 4.3418
57 33.0858 32.8814 1.5770
58 42.4309 65.3812 4.9911
59 27.0270 74.9131 5.8869
60 19.7054 58.3186 5.8615
61 82.1721 74.0032 8.0766
62 42.9921 23.4827 6.4127
63 88.7771 73.4958 9.5231
64 39.1183 97.0599 6.6810
65 76.9114 86.6930 8.9095
66 39.6792 8.6235 2.1042
67 80.8514 36.6437 8.3219
68 75.5077 36.9199 9.7984
69 37.7396 68.5028 3.0812
70 21.6019 59.7942 9.2146
71 79.0407 78.9364 7.0873
72 94.9304 36.7653 7.5256
73 32.7565 20.6028 7.1721
Continued on next page
358
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 67.1264 8.6667 8.1705
75 43.8645 77.1934 5.7666
76 83.3501 20.5675 7.7918
77 76.8854 38.8272 5.5320
78 16.7254 55.1779 9.1634
79 86.1980 22.8953 2.1125
80 98.9872 64.1941 8.6700
81 51.4423 48.4480 2.5754
82 88.4281 15.1846 7.8775
83 58.8026 78.1932 5.1340
84 15.4752 10.0606 6.4546
85 19.9863 29.4066 4.2764
86 40.6955 23.7373 4.6175
87 74.8706 53.0872 7.5707
88 82.5584 9.1499 9.5962
89 78.9963 40.5315 8.9092
90 31.8524 10.4846 6.4876
91 53.4064 11.2284 9.7099
92 8.9951 78.4428 6.7072
93 11.1706 29.1570 7.9954
94 13.6293 60.3533 9.0865
95 67.8652 96.4423 3.0391
96 49.5177 43.2485 1.9114
97 18.9710 69.4752 8.4543
98 49.5006 75.8099 4.8202
99 14.7608 43.2642 7.5439
100 5.4974 65.5498 9.4307
101 85.0713 10.9755 3.6688
102 56.0560 93.3760 3.8098
103 92.9609 18.7461 5.9473
104 69.6667 26.6179 5.9732
105 58.2791 79.7830 6.7636
106 81.5397 48.7604 6.3698
107 87.9014 76.8958 2.4506
108 98.8912 39.6007 4.7612
109 0.0522 27.2939 4.3215
110 86.5439 3.7235 1.7224
111 61.2566 67.3295 3.1268
112 98.9950 42.9564 9.9491
113 52.7680 45.1739 9.1837
114 47.9523 60.9857 8.1171
Continued on next page
359
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 80.1348 5.9403 2.2163
116 22.7843 31.5811 5.9531
117 49.8094 77.2722 1.4845
118 90.0852 69.6433 7.0890
119 57.4661 12.5332 8.4005
120 84.5178 13.0151 9.2026
121 73.8640 9.2352 2.3248
122 58.5987 0.7820 3.7438
123 24.6735 42.3109 8.0188
124 66.6416 65.5573 5.3851
125 8.3483 72.2923 5.9426
126 62.5960 53.1209 8.9039
127 66.0945 10.8818 9.8946
128 72.9752 63.1766 1.1724
129 89.0752 12.6500 4.1619
130 98.2303 13.4303 5.8118
131 76.9029 9.8594 7.7304
132 58.1446 14.2027 9.7301
133 92.8313 16.8251 7.2563
134 58.0090 19.6249 3.4594
135 1.6983 31.7480 9.5602
136 12.0860 31.6429 9.1690
137 86.2711 21.7563 5.1168
138 48.4297 25.1042 7.5985
139 84.4856 89.2922 6.0242
140 20.9405 70.3223 9.9450
141 55.2291 55.5738 4.5037
142 62.9883 18.4434 8.9351
143 3.1991 21.2031 9.0394
144 61.4713 7.7347 4.4740
145 36.2411 91.3800 7.5480
146 4.9533 70.6715 9.2138
147 48.9570 55.7789 9.1371
148 19.2510 31.3429 1.7331
149 12.3084 16.6204 1.3001
150 20.5494 62.2497 6.1517
151 14.6515 98.7935 1.0836
152 18.9072 17.0432 2.7850
153 4.2652 25.7792 1.1861
154 63.5198 39.6799 8.1304
155 28.1867 7.3995 2.7175
Continued on next page
360
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 53.8597 68.4096 9.5687
157 69.5163 40.2388 7.9320
158 49.9116 98.2835 8.3492
159 53.5801 40.2184 4.8345
160 44.5183 62.0672 3.7020
161 12.3932 15.4370 7.1226
162 49.0357 38.1345 8.7266
163 85.2998 16.1134 8.8461
164 87.3927 75.8112 9.0736
165 27.0294 87.1111 8.5923
166 20.8461 35.0777 5.3664
167 56.4980 68.5536 5.3969
168 64.0312 29.4149 1.5880
169 41.7029 53.0629 5.1128
170 20.5976 83.2423 6.3600
171 94.7933 59.7490 1.9908
172 8.2071 33.5311 4.0941
173 10.5709 29.9225 3.3766
174 14.2041 45.2593 6.2216
175 16.6460 42.2646 4.9185
176 62.0959 35.9606 4.7359
177 57.3710 55.8319 1.4879
178 5.2078 74.2545 3.3373
179 93.1201 42.4335 3.1976
180 72.8662 42.9356 7.3819
181 73.7842 12.4873 6.9297
182 6.3405 2.4434 2.0726
183 86.0441 29.0185 2.1630
184 93.4405 31.7521 1.7017
185 98.4398 65.3690 7.6172
186 85.8939 95.6936 6.0053
187 78.5559 93.5731 8.5093
188 51.3377 45.7886 1.9551
189 17.7602 24.0478 3.3091
190 39.8589 76.3898 1.4871
191 13.3931 75.9327 6.9090
192 3.0890 74.0648 3.4969
193 93.9142 74.3688 7.3822
194 30.1306 10.5920 2.1727
195 29.5534 68.1560 5.7160
196 33.2936 46.3261 1.4130
Continued on next page
361
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 46.7068 21.2163 1.9118
198 64.8198 9.8519 5.2204
199 2.5228 82.3574 7.3958
200 84.2207 17.5010 6.4121
201 55.9033 16.3570 2.8443
202 85.4100 66.5987 6.5691
203 34.7879 89.4389 7.2924
204 44.6027 51.6558 3.8335
205 5.4239 70.2702 8.2431
206 17.7108 15.3590 2.6022
207 66.2808 95.3457 3.1718
208 33.0829 54.0884 6.3526
209 89.8486 67.9734 8.8141
210 11.8155 3.6563 8.3680
211 98.8418 80.9204 6.3108
212 53.9982 74.8619 1.0206
213 70.6917 12.0187 9.5008
214 99.9492 52.5045 8.1323
215 28.7849 32.5834 4.5940
216 41.4523 54.6449 8.8610
217 46.4840 39.8881 7.0696
218 76.3957 41.5093 3.1813
219 81.8204 18.0738 2.5160
220 10.0222 25.5387 8.7501
221 17.8117 2.0536 3.9398
222 35.9635 92.3676 3.9264
223 5.6705 65.3700 4.6016
224 52.1886 93.2614 7.8716
225 33.5849 16.3512 2.4766
226 17.5669 92.1097 7.1946
227 20.8947 79.4658 6.7898
228 90.5154 57.7394 8.3922
229 67.5391 44.0036 4.4069
230 46.8468 25.7614 2.0071
231 91.2132 75.1946 8.7353
232 10.4012 22.8669 7.4186
233 74.5546 6.4187 6.1751
234 73.6267 76.7330 7.6702
235 56.1861 67.1202 7.7830
236 18.4194 71.5213 5.9958
237 59.7211 64.2061 8.2082
Continued on next page
362
Table B.44 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 29.9937 41.9048 7.0331
239 13.4123 39.0762 5.8160
240 21.2602 81.6140 7.1733
241 89.4942 31.7428 9.5967
242 7.1453 81.4540 6.6498
243 24.2487 78.9074 8.3722
244 5.3754 85.2264 2.7007
245 44.1722 50.5637 7.7633
246 1.3283 63.5661 2.9942
247 89.7191 95.0894 4.7480
248 19.6658 44.3964 8.1179
249 9.3371 6.0019 4.5997
250 30.7367 86.6750 1.4060
363
Table B.45: Depot locations and number of vehicles for MS23
Depot index x-coordinate y-coordinate Number of vehicles
1 42.7911 69.5390 1
2 96.6053 72.0165 1
3 62.0055 34.6895 1
Table B.46: Customer locations and service time for
MS23
Customer index x-coordinate y-coordinate Service time (short)
1 38.7245 4.2298 2.8094
2 14.2187 97.2958 1.3858
3 2.5135 18.9207 6.7525
4 42.1112 66.7120 3.2658
5 18.4100 58.6440 4.7790
6 72.5775 67.5112 2.5465
7 37.0363 36.1022 8.9601
8 84.1560 62.0278 4.0691
9 73.4230 81.1151 2.8461
10 57.1026 1.9257 8.1585
11 17.6855 8.3874 1.2202
12 95.7384 97.4802 1.3580
13 26.5322 65.1350 5.7684
14 92.4581 23.1238 9.4003
15 22.3770 40.3491 6.4199
16 37.3564 12.2021 6.4106
17 8.7500 26.8439 6.7948
18 64.0117 25.7846 9.2974
19 18.0617 33.1665 2.9733
20 4.5051 15.2234 8.9641
21 72.3173 34.8008 1.4394
22 34.7438 12.1658 8.3084
23 66.0617 88.4153 1.2933
24 38.3869 9.4278 4.7354
25 62.7347 93.0041 6.3520
26 2.1650 39.9020 2.7712
27 91.0570 4.7401 8.1648
28 80.0559 34.2374 2.8989
29 74.5847 73.5966 2.5697
30 81.3113 79.4682 6.5246
31 38.3306 54.4906 9.4695
32 61.7279 68.6223 6.9541
Continued on next page
364
Table B.46 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 57.5495 89.3633 2.9341
34 53.0052 5.4792 9.2223
35 27.5070 30.3661 4.4218
36 24.8629 4.6192 1.3148
37 45.1639 19.5477 3.0461
38 22.7713 72.0166 9.1620
39 80.4450 72.1753 8.8209
40 98.6104 87.7799 6.2422
41 2.9992 58.2433 6.0471
42 53.5664 7.0684 1.0098
43 8.7077 92.2745 2.1418
44 80.2091 80.0372 2.9318
45 98.9145 28.5947 8.4414
46 6.6946 54.3663 4.4885
47 93.9398 98.4776 3.8627
48 1.8178 71.5678 3.3560
49 68.3839 83.8970 3.6687
50 78.3736 43.3261 4.8536
51 53.4138 47.0625 2.7317
52 88.5359 56.0713 6.1073
53 89.9005 26.9092 6.9190
54 62.5938 74.9018 7.1702
55 13.7869 50.3888 4.1837
56 21.7802 64.6810 9.6111
57 18.2141 30.7746 3.1936
58 4.1820 13.8725 7.7344
59 10.6942 47.5573 4.5120
60 61.6443 36.2459 8.6028
61 93.9661 78.8113 4.3479
62 35.4456 78.0296 7.3685
63 41.0629 66.8512 4.1109
64 98.4349 13.3504 8.8944
65 94.5579 2.1556 7.7548
66 67.6645 55.9841 4.9098
67 98.8302 30.0819 4.6059
68 76.6831 93.9410 4.3564
69 33.6699 98.0904 4.9893
70 66.2382 28.6620 4.4228
71 24.4165 80.0820 1.6544
72 29.5507 89.6111 4.9625
73 68.0178 59.7527 6.4587
Continued on next page
365
Table B.46 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 52.7847 88.4017 3.7431
75 41.1594 94.3732 4.6598
76 60.2638 54.9158 1.9091
77 75.0520 72.8387 5.2919
78 58.3533 57.6758 3.6317
79 55.1793 2.5857 1.1465
80 58.3571 44.6531 8.9597
81 51.1820 64.6302 2.8928
82 8.2593 52.1203 7.1528
83 71.9570 37.2313 2.3895
84 99.6156 93.7135 9.7688
85 35.4534 82.9533 5.5240
86 97.1259 84.9085 9.0227
87 34.6449 37.2534 7.5384
88 88.6544 59.3185 5.4746
89 45.4695 87.2553 6.4649
90 41.3427 93.3502 4.1436
91 21.7732 66.8464 5.7359
92 12.5655 20.6776 8.1722
93 30.8915 65.3851 3.4631
94 72.6104 7.2052 3.6342
95 78.2872 40.6727 4.1334
96 69.3788 66.6932 8.8838
97 0.9802 93.3726 1.8399
98 84.3213 81.0950 2.8601
99 92.2332 48.4548 3.7248
100 77.0954 75.6749 4.1637
101 4.2660 41.7047 7.5407
102 37.8186 97.1786 8.9769
103 70.4340 98.7975 1.4673
104 72.9513 86.4148 1.7070
105 22.4277 38.8884 1.1304
106 26.9055 45.4742 2.7401
107 67.3031 24.6687 1.2366
108 47.7492 78.4423 5.2189
109 62.3716 88.2838 3.1904
110 23.6445 91.3712 9.2793
111 17.7124 55.8285 7.4425
112 82.9643 59.8868 5.3978
113 76.6922 14.8877 1.7027
114 93.4478 89.9713 5.7706
Continued on next page
366
Table B.46 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 10.7889 45.0394 6.9945
116 18.2228 20.5672 6.4694
117 9.9095 89.9651 4.7760
118 48.9764 76.2586 1.9972
119 19.3245 88.2486 8.3495
120 89.5892 28.4950 3.2437
121 9.9090 67.3226 5.5826
122 4.4166 66.4280 8.2372
123 55.7295 12.2815 5.5885
124 77.2495 40.7318 3.7243
125 31.1940 27.5287 8.7573
126 17.8982 71.6670 1.5165
127 33.8956 28.3384 7.5768
128 21.0146 89.6199 9.1079
129 51.0153 82.6579 5.1764
130 90.6364 39.0027 5.2243
131 62.8924 49.7903 2.3843
132 10.1534 69.4805 9.6562
133 39.0855 83.4369 8.8863
134 5.4617 60.9630 5.3977
135 50.1283 57.4737 4.6637
136 43.1721 32.6042 2.1392
137 99.7560 45.6425 9.3288
138 81.1603 71.3796 1.0502
139 48.5652 88.4405 2.6775
140 89.4448 72.0856 3.9165
141 13.7547 1.8613 1.4517
142 39.0005 67.4776 2.3008
143 92.7356 43.8509 7.5643
144 91.7494 43.7820 5.3405
145 71.3574 11.7037 4.0426
146 61.8337 81.4682 3.1309
147 34.3288 32.4855 5.0578
148 93.6027 24.6228 2.6691
149 12.4774 34.2713 3.9183
150 73.0585 37.5692 3.3757
151 64.6477 54.6554 8.4707
152 83.3152 56.1920 7.2672
153 39.8282 39.5822 4.0018
154 74.9822 39.8131 6.2221
155 83.5221 51.5367 3.5905
Continued on next page
367
Table B.46 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 32.2460 65.7531 3.3757
157 55.2262 95.0915 3.3391
158 97.9129 72.2349 7.0937
159 54.9309 40.0080 5.6784
160 33.0424 83.1871 1.6908
161 61.9472 13.4338 1.5026
162 36.0637 6.0467 3.3286
163 75.6510 8.4247 4.9593
164 41.3901 16.3898 3.5586
165 49.2345 32.4220 7.1089
166 69.4743 30.1727 9.5462
167 97.2734 1.1681 7.9656
168 32.7755 53.9905 6.7253
169 83.7803 9.5373 7.7822
170 73.9072 14.6515 7.7213
171 95.4174 63.1141 6.2743
172 3.1923 85.9320 7.9575
173 35.6869 97.4222 4.5324
174 66.2654 57.0838 6.4476
175 28.1502 99.6850 3.2269
176 23.0383 55.3542 3.6118
177 71.1129 51.5458 1.1740
178 62.4573 33.0682 4.1258
179 59.0609 43.0002 2.2762
180 66.0438 49.1806 4.7038
181 4.7555 7.1037 2.3776
182 34.8785 88.7739 8.4611
183 45.1341 6.4634 7.6528
184 24.0905 43.6185 1.8898
185 71.5045 82.6630 8.3857
186 85.6182 39.4535 3.0440
187 28.1508 61.3475 1.9625
188 73.1051 81.8641 6.9650
189 13.7763 88.6235 9.5912
190 83.6723 93.1112 8.3311
191 13.8602 19.0785 6.6093
192 58.8209 25.8582 3.9544
193 36.6157 89.7866 3.4963
194 80.6760 59.3362 4.9094
195 50.3781 50.3840 4.1527
196 48.9594 61.2810 8.8998
Continued on next page
368
Table B.46 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 87.7049 81.9422 1.0554
198 35.3142 53.1889 7.2680
199 44.9444 20.2075 4.0426
200 96.3530 45.3893 3.7449
369
Table B.47: Depot locations and number of vehicles for MS24
Depot index x-coordinate y-coordinate Number of vehicles
1 79.6179 77.5028 1
2 69.1191 91.4188 1
3 34.5308 78.2551 1
4 94.6817 29.5534 1
5 52.0190 15.1846 1
6 95.3813 84.7911 1
7 7.3596 78.4855 1
8 20.7032 27.0832 1
Table B.48: Customer locations and service time for
MS24
Customer index x-coordinate y-coordinate Service time (short)
1 51.6990 87.7182 6.8329
2 55.6695 78.4852 9.2903
3 15.6495 46.4954 9.0377
4 56.2056 81.3977 9.9746
5 69.4803 89.8444 1.6560
6 42.6456 42.9239 2.1666
7 83.6270 33.4329 9.8341
8 73.1387 59.6647 1.8122
9 36.0031 90.1991 7.1754
10 45.4212 70.2066 9.3607
11 38.6390 37.7455 2.2763
12 77.5555 73.4956 8.9597
13 73.4271 95.4103 1.1779
14 43.0278 54.2813 4.0842
15 69.3753 54.0106 3.1448
16 94.5213 31.1110 9.8611
17 78.4233 7.1235 8.6194
18 70.5572 18.1980 8.1506
19 10.9334 9.2989 9.1025
20 38.9931 46.3489 8.0209
21 59.0905 0.9333 8.5286
22 45.9380 91.5026 3.8898
23 5.0340 64.2742 7.6847
24 22.8688 0.1419 6.9804
25 83.4189 3.0385 3.6027
26 1.5645 20.8470 4.0364
27 86.3711 45.4966 9.1777
Continued on next page
370
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
28 7.8069 12.7266 1.2903
29 66.9043 0.8648 7.2672
30 50.0211 72.7080 2.8789
31 21.7994 35.4116 8.4173
32 57.1616 78.0446 2.9641
33 12.2189 43.6657 1.8968
34 67.1166 43.6555 6.5756
35 59.9586 4.9213 1.9343
36 5.5976 4.9632 8.1916
37 5.6343 9.1100 9.1263
38 15.2501 59.4037 3.8126
39 1.9621 24.1084 3.5343
40 43.5176 84.1369 1.0610
41 83.2221 85.7213 5.4628
42 61.7390 96.3612 9.8963
43 52.0129 48.8900 7.6415
44 86.3868 22.0310 3.7965
45 9.7698 22.6209 6.4037
46 90.8052 53.6788 8.0351
47 10.8017 76.2110 2.0038
48 51.6997 34.7567 6.2140
49 14.3156 46.1232 8.8333
50 55.9371 63.9324 7.2080
51 0.4580 91.7336 3.1867
52 76.6682 16.1573 4.0845
53 84.8709 71.5635 5.9090
54 91.6821 57.7739 1.6082
55 98.6968 43.3299 4.6940
56 50.5133 88.4243 3.1376
57 27.1422 39.3052 5.4008
58 10.0751 17.8975 8.2546
59 50.7849 63.3334 4.4006
60 58.5609 62.4001 5.6618
61 76.2887 32.7942 1.8514
62 8.2963 80.2965 9.1819
63 66.1596 99.9478 2.8687
64 51.6979 98.0978 4.4386
65 17.1048 12.7037 6.9425
66 93.8558 23.2240 7.8254
67 59.0483 2.3632 2.5576
68 44.0635 60.7433 5.6564
Continued on next page
371
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
69 94.1919 11.0809 9.9580
70 65.5914 40.7460 7.3685
71 45.1946 88.4077 1.7251
72 83.9697 54.8133 1.3898
73 53.2624 36.9003 5.4204
74 55.3887 20.8346 5.0194
75 68.0066 44.0943 5.3812
76 36.7190 95.6196 2.4930
77 23.9291 12.4026 4.2459
78 57.8923 47.0763 8.9265
79 86.6887 85.6896 7.6992
80 40.6777 4.3390 4.7509
81 11.2615 69.1625 9.1662
82 44.3846 97.8985 1.8488
83 30.0184 28.3268 2.6319
84 40.1387 13.3780 9.5193
85 83.3364 68.5280 1.9076
86 40.3629 90.9455 4.4923
87 39.0176 61.0869 3.6030
88 36.0449 89.9983 1.6578
89 14.0255 19.3434 2.7515
90 26.0130 75.4425 4.7574
91 8.6815 34.6261 3.6363
92 42.9397 41.8625 7.3192
93 25.7283 15.5720 3.1574
94 29.7555 81.9001 9.6353
95 42.4858 62.4924 3.7492
96 11.9207 73.8560 2.3942
97 49.5067 80.5112 5.9996
98 70.6407 6.7223 8.1149
99 24.3573 95.0790 4.9949
100 78.5070 49.7577 9.9624
101 7.4090 75.5146 4.9293
102 39.3883 74.2405 3.7400
103 0.3394 83.1130 3.2186
104 22.0677 15.6502 9.6474
105 0.1301 45.7309 3.0059
106 18.9180 61.8100 4.5605
107 14.2484 93.2183 3.0207
108 26.8076 83.5088 3.4302
109 17.4892 89.5424 4.7660
Continued on next page
372
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
110 13.8649 58.2519 9.9796
111 59.8886 58.2747 9.1993
112 90.1058 85.4926 5.9538
113 93.9380 3.4866 6.3670
114 22.1184 88.5420 1.7123
115 48.2671 40.7731 6.1897
116 37.6011 3.6382 9.0836
117 52.3780 74.6148 5.1698
118 26.4873 15.4829 4.5856
119 6.8357 14.3908 1.9402
120 43.6327 60.5959 6.8701
121 17.3853 25.4481 9.9253
122 2.6107 32.4154 7.1027
123 95.4678 40.1791 4.8563
124 43.0597 40.6373 6.8932
125 96.1559 38.6191 6.2987
126 76.2414 60.9802 7.7055
127 0.7349 16.6891 6.7678
128 68.0039 18.8092 5.5331
129 70.5951 9.4629 9.4424
130 64.5129 32.3186 6.4481
131 55.2310 76.9597 6.7503
132 21.8109 23.4118 7.3239
133 77.2366 74.0365 8.7485
134 22.8028 69.2818 4.4170
135 37.0865 82.4078 7.4091
136 89.0929 82.7978 5.7117
137 85.6377 29.3368 4.2714
138 40.2434 30.9369 4.9121
139 31.8019 52.3030 7.1884
140 60.8635 32.5299 3.0417
141 91.0195 83.1843 9.8110
142 90.9098 81.0295 9.7810
143 59.1594 55.6998 3.6056
144 33.2571 26.2964 4.0459
145 85.3064 68.0566 9.9680
146 44.2398 23.3653 8.1007
147 90.4355 45.6425 8.1543
148 3.3179 38.4567 6.6913
149 53.2426 53.8601 8.3031
150 71.6497 99.1704 5.0328
Continued on next page
373
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
151 17.9302 75.5220 8.4755
152 33.6533 98.0455 2.1400
153 18.7713 23.4783 5.6194
154 32.1927 52.8559 7.4434
155 40.3857 5.1436 3.2333
156 54.8566 75.6875 5.7871
157 4.8739 60.1980 4.4399
158 55.2732 85.7169 8.2159
159 27.4811 98.8277 7.0377
160 24.1502 92.9484 9.8457
161 24.3145 40.9515 9.4314
162 15.4159 0.0341 6.1865
163 95.6416 54.0878 1.7217
164 93.5661 20.7731 4.7244
165 81.8714 21.9284 2.6276
166 72.8262 32.5806 9.9607
167 17.5812 9.5949 5.6835
168 36.0371 74.7534 8.9675
169 18.8790 74.8509 6.8343
170 0.1198 54.3299 5.1963
171 31.6420 33.8132 1.8575
172 69.9617 83.2334 9.7104
173 62.5255 55.2572 6.5810
174 54.3062 95.7543 2.4040
175 43.9037 89.2833 4.5853
176 28.7427 35.6504 8.9425
177 50.1659 54.6402 5.8511
178 76.1546 34.6682 5.8931
179 76.2408 62.2803 4.9821
180 57.6056 79.6625 2.6537
181 74.7663 74.5875 3.2431
182 64.5535 12.5536 3.5660
183 12.3220 82.2394 5.7656
184 50.4398 2.5151 6.0385
185 34.7261 41.4429 4.7363
186 9.2148 73.1407 9.1511
187 14.7849 78.1374 3.7463
188 19.8170 36.7286 6.8479
189 67.2270 74.4868 3.5990
190 43.1511 89.2267 3.2973
191 69.4404 24.2603 4.2236
Continued on next page
374
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
192 25.6785 12.9597 8.2533
193 0.9759 22.5068 5.8503
194 53.2283 35.0014 6.3106
195 27.9392 28.7085 3.0803
196 94.6230 92.7488 1.9175
197 90.6443 5.1314 6.8018
198 39.2685 59.2667 9.8212
199 2.4855 16.2899 1.9155
200 67.1437 83.8406 2.6908
201 83.7171 16.7561 1.0845
202 97.1500 50.2201 8.5447
203 5.6933 99.9329 5.3321
204 45.0324 35.5407 5.2168
205 58.2470 4.7078 9.1769
206 68.6638 21.3661 4.7543
207 71.9433 39.7839 5.8972
208 65.0041 33.3668 7.2911
209 72.6915 22.9603 1.7115
210 37.3848 93.6120 5.5847
211 58.1582 68.3189 5.3821
212 11.6119 96.2114 8.7029
213 5.7654 43.7973 6.5296
214 97.9765 94.0337 2.0567
215 28.4824 0.5834 6.4619
216 59.4974 61.0307 2.4776
217 96.2161 80.1076 4.5912
218 18.5778 23.2982 5.7912
219 19.3040 93.2469 8.8769
220 34.1644 76.3263 6.9313
221 93.2898 82.6450 8.0886
222 39.0668 57.3464 2.1342
223 27.3217 79.2582 5.7248
224 15.1947 32.9041 9.0953
225 39.7109 22.3462 1.9818
226 37.4722 31.2386 6.7111
227 13.1115 58.4523 1.7276
228 43.5041 82.9914 4.7011
229 9.1513 29.0462 7.4137
230 61.4627 40.2554 1.9038
231 1.0979 86.2057 8.2895
232 57.3260 61.4740 6.7403
Continued on next page
375
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
233 78.9730 99.1188 9.0826
234 23.5367 20.3699 6.5964
235 44.8020 82.7209 4.7315
236 56.9358 67.5862 6.8280
237 6.1401 24.8949 5.4034
238 49.6289 47.5786 1.8438
239 64.2315 39.9075 6.7359
240 22.1266 59.9438 9.5524
241 83.7056 80.0523 5.2874
242 97.1075 10.5069 6.4252
243 84.6373 82.1442 6.3233
244 50.5999 84.1086 3.0274
245 27.8876 35.4506 7.0159
246 74.6617 43.0069 2.4090
247 23.6930 57.2239 7.9683
248 95.7345 70.0825 2.9175
249 62.0260 74.2470 2.5221
250 60.0262 75.7884 7.5318
251 17.2605 38.9129 3.3057
252 9.0347 42.9302 2.4649
253 25.5262 95.6345 6.6320
254 85.8571 57.2971 3.2567
255 91.1067 84.9722 3.3668
256 69.9634 27.6345 8.5954
257 72.5182 62.2324 4.5768
258 22.9886 58.8362 1.9412
259 57.6053 96.3468 2.7447
260 81.0628 8.5903 4.2676
261 40.3843 50.0499 8.8708
262 98.8439 52.1590 6.3979
263 8.9999 9.0166 3.3230
264 32.0941 90.4666 4.2258
265 51.1409 88.4389 8.9879
266 6.0606 43.8990 9.1048
267 72.5688 78.1723 5.0316
268 55.6556 14.8465 3.4197
269 52.9360 61.9816 5.9843
270 82.9982 26.0624 2.6096
271 85.8759 44.5656 8.7373
272 78.9029 84.4000 3.0878
273 31.7833 19.6205 2.5129
Continued on next page
376
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
274 45.2207 30.3852 1.2405
275 75.2228 48.3295 3.9019
276 10.9862 33.7812 5.9965
277 10.9742 79.8486 8.4208
278 26.9884 98.7488 8.2382
279 52.4637 15.9048 1.2197
280 97.2651 23.6880 4.3435
281 71.0409 70.2237 5.4268
282 31.1860 37.5472 5.1945
283 29.1457 97.3705 1.3754
284 85.0357 97.2306 6.5530
285 91.1647 64.3698 6.2023
286 63.9276 86.0099 3.6893
287 25.5370 40.1883 4.9210
288 8.8666 63.1931 2.2297
289 83.8256 98.5237 3.6975
290 58.4719 55.9477 7.8524
291 94.8109 93.3592 1.3177
292 6.1029 72.0343 3.4255
293 58.4641 48.4039 9.9664
294 28.5108 63.9031 5.0225
295 82.7732 88.7637 2.3751
296 19.0986 19.8737 8.9761
297 44.2530 39.5366 1.2824
298 39.3412 99.2175 2.0443
299 82.6574 40.2352 3.2577
300 67.6871 65.8856 7.8371
301 20.7603 90.1348 9.0848
302 31.8105 99.5382 3.0108
303 13.3811 65.3163 7.0597
304 67.1463 10.8436 8.3691
305 57.0991 3.6114 9.5404
306 16.9767 61.8091 8.8688
307 14.7656 56.7144 4.5436
308 47.6080 96.1965 9.4327
309 90.8102 74.6105 4.9321
310 55.2175 66.2516 2.4627
311 3.2940 52.3313 3.7884
312 5.3863 25.9894 7.1300
313 80.5063 96.1994 9.4065
314 45.1375 54.0204 9.5265
Continued on next page
377
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
315 38.2646 3.0270 6.3917
316 78.9644 69.6314 9.5399
317 36.4287 51.9716 4.6362
318 53.2350 5.9031 1.3693
319 71.1657 89.0036 3.6444
320 87.1477 33.0202 1.2875
321 32.8690 22.9701 8.7806
322 65.0118 11.3949 4.8929
323 97.4836 31.0923 1.8353
324 7.5967 22.8432 2.2401
325 58.7019 65.1997 3.1777
326 41.3886 6.6160 3.0071
327 30.9136 27.5431 8.8097
328 26.3834 28.1820 7.8776
329 75.8766 88.0066 4.1024
330 99.5216 44.4330 4.4630
331 18.6571 75.5914 6.3538
332 78.1145 60.3296 5.8161
333 19.5798 78.3266 4.0020
334 99.2359 11.3931 8.6921
335 80.2262 97.8564 3.3908
336 42.4227 84.8597 9.4055
337 72.8864 5.0646 4.5085
338 49.8354 46.6202 7.1476
339 80.8990 32.5653 3.4751
340 35.6509 63.0205 1.2516
341 7.3243 23.0299 9.4655
342 59.0991 57.9885 5.8057
343 91.0188 60.3156 7.0406
344 19.3766 59.9879 6.4678
345 43.2368 44.8428 7.7579
346 74.9160 3.5423 9.8319
347 3.9184 51.3815 7.5490
348 94.6325 40.7730 8.7159
349 76.3673 10.8046 9.9266
350 55.8821 45.9876 7.8351
351 18.3843 45.0883 2.3144
352 49.7949 55.1140 3.9367
353 51.7846 80.5404 1.2591
354 99.4243 70.0850 7.2510
355 85.4852 87.2236 9.6288
Continued on next page
378
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
356 96.2404 5.2192 7.5614
357 67.8941 21.9681 7.6308
358 40.3501 45.9642 2.5715
359 93.4979 95.8534 4.1987
360 47.9485 79.0045 6.1718
361 23.1792 45.1875 5.1395
362 39.6290 33.3428 8.5035
363 70.5077 5.9095 8.3390
364 55.8559 74.0905 3.9156
365 75.6631 50.6795 5.1552
366 99.5481 19.9925 7.0656
367 96.2431 42.7194 6.3570
368 53.5067 16.8690 2.2095
369 96.3870 75.1695 1.1754
370 11.5626 36.8351 2.1260
371 5.1448 94.1818 3.0095
372 30.4349 1.7173 5.0422
373 58.0192 82.9056 5.8108
374 53.0964 62.6591 9.9135
375 90.1208 53.8747 7.4561
376 54.0550 65.0508 9.8205
377 43.1981 72.6630 1.4836
378 54.2667 9.4489 6.7319
379 71.2415 87.7574 9.6434
380 1.6675 1.4362 3.4293
381 80.0921 29.4303 9.5447
382 14.2509 17.9915 9.1201
383 47.8474 92.6294 2.7518
384 25.6835 6.8180 7.6056
385 36.9092 58.1093 2.5738
386 66.1765 63.7151 1.9463
387 16.9609 65.1269 3.8270
388 27.8784 86.4622 4.1389
389 19.8222 5.5953 4.5907
390 19.5072 81.6855 3.5553
391 32.6840 52.8922 3.8252
392 88.0338 69.4351 7.4645
393 47.1102 21.2405 9.5018
394 40.3969 54.3280 1.7901
395 17.9231 70.2520 3.5158
396 96.8925 95.6435 6.3654
Continued on next page
379
Table B.48 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
397 40.7456 44.4542 8.4559
398 84.4487 8.5398 8.0394
399 61.5325 5.7340 6.0151
400 37.6611 62.9450 1.3265
380
Table B.49: Depot locations and number of vehicles for MS25
Depot index x-coordinate y-coordinate Number of vehicles
1 62.0425 61.0092 1
2 28.2840 20.3592 1
3 20.5181 51.9917 1
4 43.9134 5.3824 1
5 2.7250 86.2187 1
6 87.6184 44.2935 1
Table B.50: Customer locations and service time for
MS25
Customer index x-coordinate y-coordinate Service time (short)
1 22.7811 70.6108 7.0243
2 32.1023 83.1360 8.6409
3 82.9562 3.4834 1.5892
4 82.2182 75.7839 4.2469
5 57.0683 95.7112 3.3225
6 57.1830 34.2871 4.8934
7 28.6018 63.8244 3.7546
8 69.9134 34.3006 9.6993
9 79.6258 21.6471 2.1694
10 44.1589 78.6201 2.9569
11 44.6216 72.3090 9.0405
12 46.5662 27.8839 6.5954
13 27.9039 58.2431 4.5835
14 67.5375 42.1006 4.2048
15 90.3665 9.2069 6.8192
16 90.8526 2.4027 7.5978
17 74.7197 49.1146 7.5853
18 26.0512 27.8267 9.6236
19 68.9638 33.9757 1.4136
20 13.1831 28.7350 4.8193
21 12.3501 17.0903 1.0812
22 19.0903 39.9263 7.3342
23 14.5732 69.7650 8.0280
24 58.5044 20.3676 6.0836
25 7.3362 66.6326 1.2097
26 82.2326 44.3066 1.0681
27 72.2903 43.3295 9.9007
28 92.5858 17.5239 2.8148
29 49.2639 19.3202 8.4100
Continued on next page
381
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
30 65.4883 61.6421 4.2486
31 89.0123 26.9011 5.1513
32 53.8526 55.9678 1.9904
33 28.2205 94.4784 8.0314
34 97.5958 71.4472 5.0810
35 3.6426 67.9220 3.6739
36 32.6245 95.9381 4.2256
37 97.3014 77.5334 5.3419
38 36.5033 60.7727 4.8810
39 30.9150 94.8002 7.2894
40 12.0912 5.9642 7.0756
41 91.5766 26.8712 1.0618
42 13.5478 98.6680 1.7109
43 33.2118 77.2207 5.1456
44 89.7480 47.5354 7.9978
45 49.9649 68.0900 8.3509
46 61.5288 41.6935 6.6825
47 58.3133 38.0149 4.2839
48 69.8254 21.3270 8.9875
49 2.9332 38.2938 3.2583
50 52.7883 2.9668 1.5951
51 3.2073 47.2321 7.5444
52 82.7142 33.3373 7.9012
53 33.9986 97.5845 9.0849
54 84.6711 55.5444 7.9014
55 24.6070 84.6304 9.5220
56 58.1491 40.8063 5.8216
57 93.7677 46.2018 9.6380
58 4.7787 82.6307 9.8037
59 5.3978 99.1203 5.6989
60 2.0618 52.3948 8.6082
61 68.1479 92.5437 9.0822
62 59.8629 73.9022 9.3811
63 11.4030 56.7430 5.1188
64 79.6245 96.8778 7.8325
65 61.7851 82.4499 9.4492
66 7.0214 95.9609 8.2963
67 6.9279 64.6346 9.3735
68 13.6007 37.9573 5.0226
69 78.8891 47.6575 8.5050
70 9.2398 91.1890 9.8900
Continued on next page
382
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
71 23.7869 1.4854 4.3268
72 24.3648 15.6694 2.5369
73 10.4822 47.1568 8.4085
74 85.8353 54.2992 6.2835
75 69.8200 5.9691 9.6545
76 73.3742 65.8030 5.4022
77 65.0531 88.9635 3.2817
78 51.6271 10.9633 7.1040
79 32.6388 43.7773 9.2304
80 66.1776 28.0230 6.5537
81 11.7565 98.5246 3.9025
82 14.7817 60.8759 5.4146
83 1.9765 25.3749 4.6671
84 96.4292 13.2615 1.7555
85 97.0373 54.5005 6.3276
86 12.3861 82.7804 8.9111
87 46.7410 83.7006 5.9798
88 65.6694 83.3349 3.6952
89 29.0186 20.3715 9.0731
90 75.4537 54.4418 8.1488
91 55.8118 87.4943 7.9823
92 42.7793 12.1000 6.3907
93 26.7194 85.6351 6.0150
94 75.3736 89.9776 3.6974
95 89.8376 21.7865 5.9289
96 72.8444 7.6979 9.9265
97 40.6830 47.4215 5.3507
98 93.8316 83.5027 7.1630
99 25.5427 46.9394 5.3202
100 53.3163 41.3770 7.7187
101 95.4755 50.2746 2.9028
102 26.7748 12.5440 3.2364
103 25.0085 13.2285 1.8806
104 92.7673 87.0475 7.3780
105 6.8582 60.2950 8.7017
106 29.9400 26.5302 8.1013
107 59.1584 86.4803 7.6856
108 20.3299 5.8109 1.9407
109 63.5883 45.7754 5.6879
110 79.8370 72.2210 8.6197
111 50.1701 33.8999 8.5925
Continued on next page
383
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
112 65.0812 40.1220 4.3997
113 79.5955 52.6980 3.4489
114 23.3374 89.4236 2.1277
115 60.0839 77.8361 7.2222
116 11.2462 6.9368 5.9962
117 51.5766 27.8785 1.0763
118 83.7841 37.9370 4.7443
119 92.0790 86.4673 4.9521
120 49.8228 41.9960 8.0592
121 27.7611 23.9877 8.4700
122 65.2520 59.7655 6.3065
123 91.7299 47.9404 2.2787
124 50.9839 89.8548 6.3398
125 97.4191 93.4709 7.5357
126 19.7279 81.7887 4.8554
127 11.1185 70.8909 2.8971
128 29.7354 74.3221 3.3885
129 39.6419 89.9710 9.9387
130 42.0756 6.5240 5.3268
131 31.1475 33.5911 8.4498
132 69.3843 0.4335 6.4291
133 9.1872 82.8096 8.3606
134 40.2089 50.7435 9.5999
135 29.5181 36.6162 6.8534
136 30.6497 22.6640 6.6488
137 10.5561 53.4832 6.8191
138 59.3828 28.9485 1.5592
139 28.2728 6.8371 9.4438
140 15.5222 8.4971 9.0884
141 0.0659 6.8339 7.2537
142 28.3595 40.9816 3.7937
143 55.0811 12.3381 4.0919
144 87.0902 44.3017 1.6861
145 4.2253 89.8940 5.6785
146 90.4722 35.3639 6.4790
147 13.0974 12.0178 7.5444
148 83.3729 56.9111 1.0007
149 80.0468 87.5033 2.5279
150 91.7880 34.8575 5.1696
151 13.7304 4.1921 4.2567
152 50.4732 14.2340 9.5686
Continued on next page
384
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
153 40.4958 7.6593 9.3897
154 17.3572 74.0527 9.6226
155 57.5184 45.6525 2.8588
156 60.6218 66.8249 2.4373
157 21.4446 69.9246 6.1458
158 51.9932 57.1357 6.3363
159 98.9186 62.8693 7.2875
160 48.9915 87.7764 3.7523
161 69.4873 66.2352 4.5447
162 41.1422 87.5414 4.0320
163 3.4777 46.7517 2.1609
164 29.2832 14.1336 1.7824
165 80.1442 6.8134 5.9405
166 34.6502 71.4242 3.8596
167 8.3316 30.7986 9.9347
168 51.1106 67.1164 7.5121
169 36.6833 65.2421 6.1489
170 73.9480 53.1049 7.4550
171 52.4740 71.5107 9.7890
172 80.4521 50.4811 4.8429
173 81.6911 48.7999 9.2171
174 18.9471 49.7838 9.0758
175 12.3693 93.5976 8.5171
176 82.0996 38.9282 1.4316
177 63.7898 11.7145 4.2335
178 1.6120 24.0424 3.6618
179 89.5955 68.4908 6.6621
180 51.5375 83.9254 2.2257
181 54.4522 97.0145 4.3664
182 60.6442 21.5170 8.7830
183 76.0436 76.0343 3.2525
184 85.5347 58.4103 1.2656
185 38.2868 40.2952 9.9950
186 8.4649 51.0040 6.4463
187 73.3873 49.5644 3.1978
188 33.1989 65.1368 4.9438
189 83.9750 74.3706 7.6158
190 37.1723 30.1953 6.0219
191 82.8215 8.9612 4.9451
192 17.6519 82.5965 6.4319
193 12.9520 38.9587 2.6290
Continued on next page
385
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
194 87.9884 77.5305 8.2791
195 4.4079 17.9369 8.3715
196 68.6720 10.9361 5.3851
197 73.3773 90.5158 7.7955
198 43.7172 87.6351 4.6394
199 37.9839 99.9793 7.5311
200 97.9657 86.4255 2.3861
201 39.8993 3.6878 5.5817
202 44.0187 54.4682 7.0123
203 15.6808 99.7616 2.3732
204 32.6034 51.1008 1.5643
205 31.4062 87.3512 4.0340
206 89.4501 7.0221 5.0135
207 24.7024 98.7539 7.8188
208 31.0679 92.2713 2.1748
209 40.8869 56.4261 9.1136
210 70.8011 43.1462 2.9830
211 14.3638 33.7845 4.4070
212 87.1322 72.0723 4.8048
213 8.3156 1.3656 9.7542
214 46.1738 37.4060 2.5931
215 3.0389 92.2685 8.9405
216 75.3201 54.6480 5.9613
217 70.0043 47.3887 3.8934
218 21.4512 49.6537 9.0986
219 67.9905 30.8971 5.8790
220 55.7293 95.0838 5.1660
221 85.0679 98.1993 8.2718
222 55.8565 51.3563 4.2474
223 90.1774 99.2590 9.7390
224 41.9518 45.5844 5.9997
225 35.8128 42.6041 7.9284
226 48.8988 21.3215 7.1211
227 25.5962 19.3249 2.8468
228 92.9169 83.2754 8.5116
229 46.6757 72.6637 8.7892
230 25.4008 52.9746 1.3737
231 43.1218 82.9081 6.5277
232 70.2530 51.1874 3.4595
233 40.2330 55.1962 7.7204
234 18.1840 21.3285 5.3908
Continued on next page
386
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
235 85.6251 58.7821 8.1314
236 58.4201 14.2763 5.7202
237 37.3579 5.2224 6.3776
238 22.1695 68.3308 2.9803
239 21.8994 60.8559 4.2762
240 52.2232 21.9656 3.6752
241 43.3423 40.6280 8.6646
242 74.1304 62.9908 9.7632
243 7.0450 55.5308 6.6126
244 84.7333 12.7579 9.0305
245 67.9880 16.9198 9.8281
246 13.6652 0.0999 6.8228
247 85.8402 41.8162 8.1894
248 19.9834 48.8486 4.6439
249 60.7340 15.9869 5.3413
250 54.3045 66.6839 1.5750
251 16.2325 1.7920 8.2264
252 0.5653 11.9675 4.1596
253 77.1485 95.2125 8.6435
254 76.4788 97.5854 9.9263
255 42.1069 3.0915 5.3589
256 5.6813 49.3882 4.2073
257 58.5747 86.2722 1.4893
258 17.4155 24.2876 9.2267
259 72.8611 83.4270 7.3447
260 53.4291 81.3591 4.9428
261 25.3064 62.8973 9.7130
262 91.7057 0.2238 7.5144
263 75.8195 37.9724 6.9112
264 88.7031 90.4406 5.6329
265 6.8798 68.0352 8.8935
266 18.3528 37.8823 1.5416
267 73.7073 63.1955 5.2433
268 69.6715 24.3270 3.7991
269 77.6993 57.1413 2.7522
270 50.1903 98.1729 2.3594
271 42.5497 84.9682 9.1128
272 61.1237 28.3444 1.6359
273 85.5772 68.2458 9.6255
274 67.0797 35.8125 7.2990
275 52.3592 98.6927 1.1081
Continued on next page
387
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
276 29.8815 8.3986 1.0439
277 70.3969 25.0306 8.6796
278 38.1611 81.1347 5.2056
279 56.7685 8.4423 8.5305
280 88.7861 53.1254 2.9856
281 84.2949 80.0623 8.2536
282 89.8799 73.8823 3.2372
283 93.9003 14.1663 9.9845
284 81.5435 43.7894 9.4411
285 0.1358 35.0380 5.9856
286 0.3091 47.8497 9.2143
287 8.7469 58.7403 6.7194
288 26.0727 14.5806 8.0209
289 2.2799 90.5331 6.1050
290 42.4085 64.0194 2.7259
291 34.1065 16.2940 9.1562
292 54.1354 56.5911 5.6337
293 92.6169 93.1616 9.9908
294 29.8499 78.3102 4.3960
295 33.8085 68.5687 2.8550
296 85.9480 46.6219 7.5695
297 34.0478 26.0318 3.8209
298 13.8120 56.9268 2.0582
299 50.7799 24.8771 8.9975
300 85.6656 31.9302 7.2381
301 38.4314 91.0802 9.4591
302 69.5691 88.5220 4.7545
303 62.7904 79.4589 8.3419
304 45.0388 92.5810 8.2436
305 47.3618 17.8840 4.2436
306 94.9706 51.7541 9.2243
307 8.3498 62.7005 3.5948
308 27.9829 91.3182 2.4850
309 44.7007 66.3968 5.1028
310 58.7571 38.9193 3.1854
311 87.7634 74.0008 1.0173
312 46.9101 81.7635 6.5381
313 43.7418 60.0345 6.9511
314 74.6185 8.4997 6.9430
315 46.7910 92.2358 7.1243
316 86.0827 5.3598 8.6558
Continued on next page
388
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
317 46.6512 52.7025 1.3358
318 49.8104 11.8853 7.1270
319 48.7431 38.0143 6.1402
320 22.9469 81.2833 7.2119
321 8.5552 24.4096 9.0601
322 6.7383 88.4423 3.4018
323 88.8391 71.2647 1.6170
324 23.3168 37.8148 3.8224
325 86.1596 24.8920 8.1026
326 71.1735 25.2854 5.4851
327 87.2813 76.7244 4.9333
328 93.8002 4.9862 2.5157
329 13.9689 68.5289 3.3811
330 39.3900 62.0278 7.1549
331 98.0563 74.6685 8.3497
332 64.4794 97.7256 7.3497
333 89.6410 38.3914 6.1889
334 48.2230 26.0206 9.9466
335 1.4093 87.7470 5.1507
336 62.2880 80.6096 5.4402
337 23.1095 46.1121 3.4656
338 52.7434 9.0962 6.8959
339 72.4992 56.4269 4.6635
340 60.7416 18.7383 3.6997
341 58.8366 53.1690 6.4489
342 43.3435 35.5033 8.1206
343 24.4173 31.4784 9.7380
344 42.8960 72.6741 7.9605
345 1.0177 51.5773 6.3998
346 60.8821 79.0645 5.0416
347 95.7975 20.4493 2.3813
348 9.5447 67.8106 2.9011
349 3.5591 5.2486 7.3031
350 88.6235 80.1172 9.6056
351 24.6941 67.8569 6.7192
352 0.8915 94.6009 9.0214
353 81.4920 9.1558 2.9466
354 14.0499 90.8438 7.1519
355 87.9866 50.9953 3.8355
356 9.5377 61.4904 1.2285
357 35.2560 31.6071 8.3822
Continued on next page
389
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
358 59.3421 7.7487 4.8940
359 58.5182 85.0614 1.7984
360 66.7682 14.4527 9.4158
361 64.8027 37.0486 4.5170
362 43.3369 62.2391 6.2914
363 13.9759 99.7552 3.1585
364 75.1930 51.7344 6.8821
365 24.1787 99.0511 4.2988
366 65.0459 22.6534 5.3312
367 85.7374 39.8005 4.6152
368 8.4370 69.6569 4.0042
369 97.2089 6.4641 3.4083
370 3.1460 74.7662 7.9106
371 83.5405 42.0400 3.1634
372 83.5713 81.1317 9.6515
373 4.9858 37.9605 9.3120
374 54.5886 31.9068 3.4682
375 94.3170 98.6051 3.0095
376 32.1473 71.8181 3.2691
377 80.6467 41.3183 3.2229
378 60.1399 9.8630 3.1562
379 78.9620 73.4559 4.8543
380 79.9185 63.7306 8.4333
381 4.9565 7.3842 6.5547
382 28.3199 12.0508 2.7449
383 65.3457 98.1596 8.2727
384 48.9655 49.6799 9.8707
385 97.2852 2.2414 2.3374
386 74.8490 5.3832 8.6773
387 56.7841 14.0874 3.1474
388 29.8964 89.3474 4.7525
389 25.6110 46.5820 3.9016
390 88.6564 56.0857 4.9063
391 44.6801 49.4456 3.9468
392 81.5987 6.7785 1.8907
393 9.8337 89.7647 7.0406
394 85.9593 28.8565 1.4442
395 2.7629 26.9047 2.8090
396 89.9156 59.4194 5.4922
397 89.9936 47.5879 3.4788
398 52.4106 36.8311 4.7764
Continued on next page
390
Table B.50 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
399 12.0200 65.5611 6.3729
400 17.7794 93.8200 1.4423
391
Table B.51: Depot locations and number of vehicles for MS26
Depot index x-coordinate y-coordinate Number of vehicles
1 87.5721 9.7281 2
2 63.5186 90.8439 2
Table B.52: Customer locations and service time for
MS26
Customer index x-coordinate y-coordinate Service time (short)
1 54.8009 38.0848 8.9801
2 56.6861 63.4579 8.7247
3 68.0395 36.3229 1.7656
4 37.1379 40.7619 2.5968
5 7.8229 36.8700 1.1206
6 45.6351 46.8399 6.3099
7 4.7844 50.3414 7.3708
8 73.8257 91.0536 7.8303
9 3.8002 20.6431 2.9257
10 95.4244 33.8604 9.6955
11 74.2372 57.4126 5.3595
12 93.7450 48.6932 1.5622
13 51.3364 26.2219 2.6061
14 24.0905 57.9593 4.0444
15 25.9965 87.8328 8.9243
16 75.8974 6.0950 1.3845
17 99.3343 44.0876 4.1987
18 35.6706 8.4258 6.7667
19 75.2858 56.3238 8.4510
20 11.0048 53.9311 1.4016
21 59.7045 76.8058 8.1174
22 43.0595 23.3090 1.4604
23 73.0718 58.7362 3.6678
24 26.1176 45.8974 3.4493
25 9.4808 86.0982 9.2211
26 45.0963 66.0836 6.4492
27 64.0075 35.3879 5.5200
28 13.2039 34.7186 7.6294
29 45.2822 25.3718 2.0091
30 65.2200 95.2528 8.9604
31 82.6998 29.8201 5.7660
32 30.8077 15.8406 1.0494
33 40.2364 36.1297 2.4658
Continued on next page
392
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 88.4231 74.1629 3.3609
35 70.0580 70.5900 1.3498
36 24.1872 70.0892 7.1386
37 75.9832 0.6226 1.2538
38 29.0926 37.4346 5.4995
39 27.7439 90.1496 5.3263
40 0.6108 31.8345 3.5068
41 37.4711 59.7083 6.3144
42 43.6933 29.7795 3.5867
43 30.4298 12.5014 9.2795
44 29.0860 38.8356 1.0546
45 24.2516 81.7688 6.0808
46 93.6684 98.1176 4.3182
47 86.0190 86.1990 4.3422
48 39.7228 8.3821 1.1907
49 47.9419 33.7712 7.1853
50 56.4996 23.6129 5.9911
51 48.9619 31.7805 7.8889
52 26.9812 98.4448 8.1221
53 98.9740 54.8251 3.2190
54 18.3676 74.9251 2.7983
55 86.1657 84.1852 4.3025
56 3.2633 16.6890 7.4761
57 33.1958 90.3098 2.1283
58 74.8747 10.5124 4.8690
59 64.4366 74.5093 1.1472
60 16.9238 72.9372 1.6392
61 95.2205 71.7470 7.3928
62 54.3270 13.3432 8.2265
63 25.1413 44.5789 9.1918
64 57.8572 50.8787 9.2091
65 91.5477 53.0490 6.6658
66 89.5597 85.9717 2.1834
67 48.2507 67.7725 1.5592
68 44.2740 80.5838 7.9979
69 31.1755 53.1243 7.6793
70 5.5314 95.5896 6.6334
71 75.3792 6.6677 7.5619
72 13.1947 54.1518 2.8271
73 35.5922 28.1660 8.1550
74 39.5871 48.0900 9.7711
Continued on next page
393
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 88.5521 68.4864 4.7813
76 2.1240 20.8258 3.2115
77 84.4081 60.8161 5.3211
78 28.8071 32.6176 7.0208
79 25.0343 88.0847 8.6714
80 48.8380 13.3395 9.5079
81 72.9036 10.2408 2.1586
82 20.2616 95.9117 7.2698
83 21.6276 15.2902 1.7208
84 97.6335 15.2538 1.9321
85 59.3236 15.5553 2.1808
86 30.4404 8.9569 5.6355
87 96.7703 45.4425 5.3360
88 89.5970 66.8896 5.0130
89 19.0025 83.1302 8.1836
90 0.1799 79.0235 5.7604
91 71.1764 71.2711 7.0196
92 86.7727 47.2598 5.3500
93 11.8308 70.8588 3.9942
94 3.9023 95.8059 3.3292
95 59.8195 50.5776 9.7633
96 60.4314 30.5053 3.3792
97 51.6432 78.9811 8.1095
98 0.7507 23.6387 5.4736
99 68.8933 23.4303 3.8871
100 94.6020 46.4699 6.5465
101 87.3536 61.9387 1.0620
102 11.3276 61.5329 1.5664
103 35.4569 12.2624 9.2802
104 24.1937 12.3794 9.1555
105 56.0333 28.4459 8.4838
106 61.2727 73.5733 9.2231
107 30.0809 41.1308 7.1124
108 79.8142 82.8982 7.9935
109 79.5642 93.5114 7.2430
110 78.1092 39.9067 2.7897
111 35.1098 5.2211 5.0715
112 5.4297 57.1186 8.1000
113 70.8705 74.7670 1.0173
114 99.2928 32.0244 6.0002
115 16.2476 49.2934 4.8992
Continued on next page
394
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 11.3566 22.1653 1.5257
117 91.2875 93.9274 4.9776
118 48.1657 48.2305 8.5563
119 85.1806 53.9996 6.5643
120 80.9914 22.1057 7.6743
121 18.6760 9.5945 9.4207
122 24.7200 6.0165 3.9278
123 5.4189 81.9509 7.7139
124 60.8961 77.1478 8.8561
125 77.7232 19.5696 4.8996
126 51.1064 89.5118 5.6940
127 2.7750 68.4300 6.8739
128 99.0385 65.6846 5.2211
129 50.0940 99.0381 2.6497
130 33.1997 3.3692 3.0340
131 17.3883 42.4253 4.7076
132 62.5636 48.9984 1.1376
133 57.5135 58.3504 7.7560
134 75.0985 8.3270 1.5591
135 15.3519 66.0155 4.8852
136 35.6787 5.2305 5.8850
137 14.3951 55.6831 6.4913
138 85.0608 71.2025 4.9261
139 33.7870 48.7911 1.7296
140 27.5196 61.7601 3.5556
141 0.6011 21.3778 1.6590
142 80.1912 64.5659 7.5698
143 49.7408 38.0642 4.1174
144 53.7843 10.3713 6.8698
145 87.0913 37.7512 5.3358
146 72.2844 26.2861 4.4433
147 66.8086 24.1286 3.9420
148 17.8828 62.2924 1.9274
149 55.0495 52.2928 4.3337
150 95.9875 41.3238 4.3970
151 59.6022 21.7792 5.3362
152 80.8571 85.8554 8.1606
153 98.4532 86.1008 7.2225
154 88.5924 28.3939 8.6481
155 21.3837 61.5393 5.6105
156 3.4630 77.9490 8.6953
Continued on next page
395
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 45.1124 95.4847 5.1890
158 1.3795 91.9603 3.3836
159 47.3711 38.4816 6.6654
160 95.1197 16.2643 6.0646
161 24.8952 79.6751 5.8704
162 38.6423 11.3817 4.5398
163 43.1433 15.8824 4.7842
164 83.0886 35.5828 2.2341
165 82.4647 84.7759 3.6296
166 45.2999 58.2781 1.0659
167 38.0560 58.6178 9.3943
168 92.5869 92.5838 6.4833
169 74.0844 57.5078 9.0266
170 73.7633 0.9977 4.7874
171 94.6916 80.9377 4.6016
172 51.0100 60.8808 5.9854
173 79.1879 47.9914 6.3663
174 45.2174 26.8440 5.5565
175 84.9199 25.8096 6.2849
176 39.0431 48.1010 2.1954
177 73.8377 22.7341 7.8544
178 97.6439 4.8602 6.8603
179 52.3299 16.9242 4.1598
180 42.9915 25.8446 3.8134
181 20.7158 19.7910 3.4683
182 32.3401 60.5693 2.3458
183 11.0870 82.3704 4.0091
184 37.5210 81.0615 8.4973
185 32.9904 80.2237 3.1022
186 34.2105 70.8113 1.6232
187 81.7119 85.9378 5.4525
188 53.1685 78.1085 2.0994
189 52.1122 20.3797 4.6236
190 77.4310 99.3343 1.8209
191 12.0263 9.3625 7.4849
192 62.5450 65.0619 4.0811
193 34.6649 21.5177 6.0967
194 33.4619 24.3873 6.8906
195 57.4617 33.9688 6.8725
196 86.3938 19.7862 7.3077
197 19.8563 50.6833 3.7099
Continued on next page
396
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 67.2451 95.0758 1.7692
199 90.1831 39.4607 6.7009
200 19.9157 58.4465 3.3979
201 29.8284 60.6537 9.0483
202 49.6520 71.4643 3.7024
203 88.9904 40.1536 7.4355
204 50.1415 85.8691 3.9732
205 27.6995 92.0485 4.2839
206 53.3958 75.0839 6.3311
207 57.4250 28.5592 9.1467
208 41.2804 79.6816 3.3808
209 1.4764 14.2766 9.5484
210 70.2765 50.4550 7.6486
211 50.6747 61.0688 1.0402
212 38.1266 70.3797 8.6566
213 6.4932 38.3340 7.2601
214 35.8580 72.8683 6.0619
215 23.4251 88.7285 4.0394
216 20.3504 5.5848 3.9952
217 81.3780 13.8216 1.6959
218 39.3435 86.3065 5.1247
219 5.3575 42.1746 6.9147
220 37.5052 41.1314 6.1476
221 77.4994 95.9141 4.6190
222 16.5298 75.0245 9.4123
223 91.2219 98.0997 4.2448
224 31.9206 23.3516 9.5294
225 32.9780 9.6227 1.2711
226 20.4236 38.4582 4.9699
227 76.7215 50.0273 7.3064
228 6.9973 57.0256 7.3269
229 95.0034 97.6632 5.5915
230 15.8210 49.2855 6.5102
231 28.6446 40.0883 7.7173
232 68.7129 99.4990 8.2129
233 14.1150 26.0998 4.0305
234 51.2087 66.5325 6.0768
235 72.1327 96.4257 8.6974
236 92.8845 67.1151 6.3024
237 73.2104 29.9175 5.5742
238 74.9848 53.1127 8.6809
Continued on next page
397
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 40.7320 0.1463 7.1542
240 23.9492 88.3789 1.9570
241 52.0850 40.4384 5.5176
242 21.9077 30.1206 1.1725
243 84.2388 95.0582 4.9835
244 66.2933 46.0648 9.1646
245 81.6235 28.7648 1.4020
246 79.3878 8.4627 9.5067
247 46.9105 58.2181 2.6234
248 30.9525 15.3069 4.3292
249 68.7579 7.3094 2.8472
250 98.6852 58.0565 1.8603
251 76.9934 28.7015 4.8947
252 82.9581 36.1920 3.4980
253 70.6085 72.4825 1.9077
254 59.5336 85.8312 5.4903
255 75.2874 34.7916 3.1513
256 49.6722 96.1746 4.1464
257 86.5133 95.3569 6.0244
258 6.8028 20.6037 5.9326
259 96.8546 76.8245 4.7915
260 9.8756 61.5532 4.4695
261 54.6977 91.8922 4.4260
262 40.2970 60.2537 3.5266
263 10.7040 70.2138 2.6192
264 72.4166 74.3675 2.1456
265 61.3682 38.5102 1.1412
266 78.2968 25.1504 7.7778
267 56.6621 3.6760 5.5446
268 81.1319 47.2123 7.4990
269 57.6776 64.5072 7.8499
270 94.4029 27.8970 3.4205
271 87.1452 51.7861 2.7426
272 50.7602 24.5667 1.5773
273 78.8823 29.7508 4.8284
274 47.3031 65.0474 7.3193
275 82.8802 89.1393 9.7959
276 32.2482 86.1106 5.9642
277 97.6147 20.9915 1.3943
278 27.8211 39.9094 6.2393
279 7.2831 88.7883 3.5054
Continued on next page
398
Table B.52 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 75.1224 25.6528 5.8797
281 83.1189 96.6802 4.9899
282 92.2338 61.9157 2.0548
283 32.7024 16.5346 4.4195
284 80.4069 82.6199 7.8835
285 53.8250 65.5693 9.2653
286 46.3295 54.6453 7.2343
287 82.0750 25.1329 9.7356
288 95.1907 4.0156 2.1355
289 7.6273 23.3375 6.8177
290 70.8671 36.1113 4.4816
291 23.4926 63.3455 6.0611
292 39.8896 98.6098 2.7852
293 26.8124 20.7157 4.5453
294 83.2513 75.7084 4.0622
295 99.5374 88.6328 4.2083
296 64.9751 47.2230 4.3574
297 70.3953 15.8914 2.0383
298 93.2303 81.0921 5.5109
299 68.7653 47.6508 8.3522
300 56.8354 11.6288 4.0916
399
Table B.53: Depot locations and number of vehicles for MS27
Depot index x-coordinate y-coordinate Number of vehicles
1 14.9057 75.6670 2
2 2.8279 79.6106 3
Table B.54: Customer locations and service time for
MS27
Customer index x-coordinate y-coordinate Service time (short)
1 3.5016 1.5908 5.4868
2 3.9750 95.7514 2.0622
3 98.8568 2.5692 6.1797
4 68.6182 97.1111 5.6392
5 37.6689 29.7596 4.1975
6 50.4324 52.5073 8.7701
7 76.3496 86.2339 4.0961
8 4.8875 89.6405 5.1119
9 72.5928 18.9011 3.1428
10 70.1328 66.0720 7.9405
11 45.8891 94.1231 3.4606
12 58.2295 97.5707 5.7250
13 33.9090 10.7935 5.7800
14 17.0625 17.8899 8.8605
15 39.9193 74.6551 9.4385
16 91.9777 4.9469 1.4385
17 22.6045 7.1285 9.8096
18 36.1007 48.9126 6.6909
19 32.4562 84.9894 1.6537
20 8.3582 99.7041 2.9064
21 51.2666 0.4393 4.2390
22 83.2865 54.2607 4.8401
23 90.4613 86.1348 7.8233
24 72.3596 90.9139 9.2418
25 38.2996 84.5351 6.6677
26 29.8017 87.8873 9.6032
27 69.1712 74.6182 7.7961
28 88.0457 11.7489 5.7350
29 92.4548 50.9022 8.6510
30 8.1253 16.8832 8.3443
31 48.2673 83.1112 2.1892
32 12.8265 92.8011 7.8465
33 25.2911 16.9484 6.5551
Continued on next page
400
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 88.3962 88.3737 4.5788
35 19.6277 38.7863 8.5714
36 12.1354 38.2569 1.3449
37 54.3695 27.1453 1.8659
38 31.4621 86.7883 9.5329
39 38.2041 74.1502 4.5641
40 79.1539 44.7873 5.7904
41 83.9179 70.9639 9.1328
42 68.0236 94.4331 4.0603
43 41.6922 17.4118 6.9751
44 64.2890 24.4596 7.5462
45 21.4081 64.0929 3.0071
46 61.7271 80.8613 5.9991
47 67.5191 85.3371 5.0971
48 60.1023 39.8118 6.4924
49 34.6310 11.5494 5.8959
50 36.4401 8.0281 5.6652
51 17.1481 36.0468 3.5744
52 79.5362 82.8906 8.9111
53 49.2667 21.4610 9.4289
54 35.4623 79.1040 8.2559
55 77.5061 65.4688 9.7218
56 23.6805 2.6146 5.7181
57 84.4833 78.5776 2.0158
58 81.6527 92.2563 6.8521
59 84.6228 49.2313 2.7180
60 37.0187 83.4012 8.7124
61 38.3230 13.1354 9.4857
62 86.1335 75.9783 1.9310
63 46.3909 92.5736 3.6680
64 57.0548 83.2708 8.1913
65 69.5307 25.9401 4.9754
66 96.0917 21.3022 5.4327
67 54.6313 52.2315 1.2656
68 63.6577 39.7357 6.1538
69 57.0892 47.9110 6.1522
70 92.7112 99.3904 7.6752
71 86.3766 60.4478 1.6895
72 16.9839 94.4909 8.0845
73 17.8699 49.0442 2.7415
74 24.3504 43.7947 5.7783
Continued on next page
401
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 75.1779 77.2656 9.3172
76 19.9134 74.4067 9.8745
77 98.2941 44.2904 9.7776
78 70.9639 5.3000 3.7429
79 17.5436 8.7822 7.7827
80 85.8297 79.7986 2.8572
81 90.9411 65.5582 8.7524
82 96.1663 3.2336 6.9206
83 57.0600 55.7067 1.9199
84 56.2879 71.9802 6.2242
85 17.6661 11.0408 9.6714
86 51.3679 21.6647 8.6039
87 54.8472 81.1020 7.7780
88 16.5277 13.8662 7.3274
89 49.3893 88.1899 3.2196
90 53.5117 92.3556 1.3595
91 19.8807 1.2756 5.1590
92 62.3169 37.7159 2.0564
93 2.6315 16.7812 2.4546
94 31.8791 54.0223 4.7778
95 53.3000 10.1662 6.9950
96 32.6774 3.9268 9.7584
97 60.2190 93.3229 3.5169
98 36.1933 97.1592 5.7825
99 13.4921 36.0928 9.3762
100 91.3814 64.4205 2.5000
101 64.0559 6.7947 8.1032
102 65.8774 20.7912 1.9267
103 67.5330 3.9604 8.9526
104 74.4558 46.9359 5.7001
105 84.2178 15.0097 9.7671
106 51.6657 99.1307 7.8049
107 15.1869 42.7062 7.5031
108 38.0664 95.5372 1.0234
109 82.1019 72.4247 2.8505
110 17.1364 58.0892 3.3433
111 32.9975 54.0258 1.7196
112 96.6472 70.5441 7.6179
113 80.6293 0.5029 8.4039
114 22.2188 78.2516 4.0905
115 99.9773 92.6860 2.2252
Continued on next page
402
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 6.3739 0.8296 6.9930
117 42.5483 82.4628 8.4740
118 40.4338 76.7336 7.0626
119 40.0293 99.7137 2.2551
120 11.1923 22.7653 4.4094
121 42.4311 91.9542 7.1053
122 61.3546 64.1999 5.6433
123 98.8061 10.5320 9.8025
124 21.9901 26.8161 3.4095
125 35.4081 76.3844 8.8022
126 26.6242 80.5510 4.3638
127 29.1498 10.4253 2.2297
128 18.8390 46.9759 1.7442
129 2.2860 21.9062 7.6494
130 44.9404 92.2708 4.3486
131 24.3640 32.0323 4.4246
132 86.8727 85.7544 3.7196
133 52.8611 25.9847 3.6507
134 91.4135 87.8063 3.3383
135 97.3930 18.8268 5.1713
136 58.5426 75.9194 9.8907
137 11.8975 3.1689 4.4657
138 92.6533 64.2339 9.4891
139 59.3561 56.6871 2.5030
140 88.3615 37.6410 9.3250
141 42.4476 21.2548 7.7890
142 60.7257 79.2157 8.7094
143 7.0764 14.5443 6.4215
144 92.4772 48.9142 1.9663
145 64.2079 1.2846 5.0993
146 10.4500 18.6612 6.8913
147 70.0225 48.5230 1.5178
148 39.5804 83.8226 1.1914
149 8.4905 14.1057 3.6082
150 21.4479 73.2217 9.3833
151 24.8799 69.1067 5.6262
152 22.6653 3.4493 8.8777
153 70.3004 48.8857 4.4029
154 75.4153 97.1390 8.9606
155 54.7287 11.2451 5.8130
156 55.3483 74.3214 9.0334
Continued on next page
403
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 63.0573 63.8541 1.9249
158 98.5457 59.4183 2.9084
159 63.4278 49.8623 7.3145
160 60.0456 56.7853 4.2522
161 90.9187 42.6504 1.0126
162 57.0837 7.6239 4.4588
163 33.5420 29.0587 3.8813
164 95.7139 56.1335 4.5401
165 43.9923 63.3333 2.6313
166 60.1543 93.0776 2.8844
167 72.0262 97.7769 6.3435
168 67.8778 9.3597 6.3502
169 21.2759 66.1735 2.5522
170 8.1623 60.2773 9.3970
171 27.4479 47.3818 1.5060
172 86.7518 35.6256 2.8155
173 55.9357 47.5578 5.5743
174 46.4628 67.1022 7.8329
175 43.0301 95.9645 2.3145
176 77.3986 8.9084 9.3797
177 65.3920 79.7742 4.7975
178 65.7729 59.0776 1.5085
179 16.1021 91.2197 7.0678
180 43.2377 10.1129 3.5183
181 50.5086 29.3295 8.0208
182 37.5332 5.1588 9.6656
183 48.0372 50.4128 7.1942
184 34.2421 76.8376 5.4858
185 77.7146 28.2985 1.8913
186 38.3944 22.5360 3.5898
187 71.1556 33.1290 5.8430
188 48.0933 45.3251 1.1020
189 72.9180 73.7385 3.5456
190 93.7559 50.9886 6.3061
191 51.7254 38.2514 2.5484
192 90.3069 90.5483 2.5309
193 21.8193 96.5258 7.0871
194 87.3219 62.8267 6.1263
195 8.2693 13.2031 5.9650
196 46.5403 61.8302 9.7070
197 2.1930 38.3020 6.6558
Continued on next page
404
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 80.8281 99.1194 3.9209
199 17.9210 28.6827 5.6891
200 16.5392 70.6191 8.7844
201 18.1603 53.5206 9.9470
202 69.1437 19.3211 8.5464
203 21.3764 68.9435 4.1266
204 29.8105 5.0455 7.7447
205 76.8335 18.4434 9.4547
206 50.1150 4.5658 7.0127
207 90.9465 88.5042 5.3308
208 5.7853 83.9794 3.5755
209 43.6752 11.8155 6.3564
210 57.2255 41.0415 4.0277
211 56.5067 12.0229 9.6360
212 82.3817 57.2093 4.9787
213 12.6099 94.9390 9.6580
214 30.0117 25.6385 7.0875
215 0.2122 98.9865 7.3547
216 95.1107 34.9808 9.6192
217 76.6299 20.8522 9.4589
218 75.1304 66.5827 8.5038
219 13.8865 97.3345 2.3972
220 34.9320 62.2700 8.4739
221 15.1341 6.3538 5.1773
222 49.6721 37.3510 3.6882
223 80.8652 16.6252 5.7097
224 63.2869 23.1278 8.4847
225 68.8401 5.2209 5.8522
226 63.9570 90.1756 3.3385
227 72.9322 79.3292 4.1863
228 85.9846 37.3014 2.6806
229 62.6955 83.2055 4.1559
230 18.0591 75.3835 2.7075
231 57.3307 62.1863 8.5212
232 16.3566 39.4093 4.4574
233 90.6052 35.9278 1.0855
234 7.7343 8.8852 3.7812
235 33.8535 34.1677 8.5307
236 58.0618 54.8671 3.5320
237 47.5235 46.0547 8.0321
238 80.5320 64.5452 5.7836
Continued on next page
405
Table B.54 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 53.0778 51.3521 2.3852
240 22.7310 81.4426 5.7273
241 70.9485 9.7183 3.5492
242 14.8633 46.3714 7.4338
243 65.8116 58.9817 7.6095
244 63.3983 18.7172 5.0467
245 22.9306 61.1330 2.6387
246 18.2228 5.1942 2.2199
247 16.6353 57.5727 3.4549
248 14.9607 84.2345 6.7208
249 20.2747 49.9726 8.2557
250 95.4959 43.9025 7.0109
406
Table B.55: Depot locations and number of vehicles for MS28
Depot index x-coordinate y-coordinate Number of vehicles
1 0.1314 34.6471 1
2 98.1268 55.7503 2
3 57.0194 29.9785 2
Table B.56: Customer locations and service time for
MS28
Customer index x-coordinate y-coordinate Service time (short)
1 29.3556 24.7546 3.5793
2 11.5207 44.7369 2.2820
3 37.5092 53.2783 3.2129
4 82.8894 35.4651 7.2271
5 84.1777 77.3115 1.6457
6 66.5238 88.1681 5.4879
7 96.0140 73.4092 9.8740
8 94.3118 40.6432 9.1441
9 11.2699 60.4179 6.1769
10 64.8287 64.1105 7.8987
11 48.0804 12.7467 7.7209
12 6.6521 49.6192 7.2580
13 89.7771 31.0469 7.0959
14 49.7230 57.8574 3.5416
15 77.1303 94.3609 6.2368
16 6.0362 42.6940 6.5699
17 26.2457 3.3128 8.3282
18 65.1069 92.9434 1.1439
19 13.3604 92.4982 2.9292
20 63.8546 35.8307 9.8908
21 38.4943 25.9989 8.3560
22 76.5698 78.6860 6.6887
23 65.2916 51.1582 7.1393
24 38.1489 56.2527 8.2740
25 30.0019 68.4794 3.5170
26 34.0140 9.2397 6.9847
27 91.8927 87.2579 1.2639
28 45.6267 94.2938 5.8994
29 44.2497 9.6594 5.7607
30 45.4186 84.5883 8.8585
31 94.5282 90.9396 2.6885
32 21.9119 1.1341 9.3831
Continued on next page
407
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 88.2403 52.3683 9.7872
34 1.9875 65.0345 3.9808
35 34.1765 38.5145 6.6134
36 76.6027 64.9302 5.7435
37 34.2804 76.2853 5.1317
38 61.8806 57.5686 4.2271
39 45.3021 63.1919 4.0084
40 1.0163 27.8204 1.7488
41 59.9081 83.9836 4.5136
42 60.1568 42.6835 3.1541
43 64.9417 63.1622 5.3764
44 34.2721 83.3467 7.3008
45 49.3299 27.0185 2.2354
46 70.1774 40.0801 8.4382
47 88.7803 55.4255 9.3705
48 5.5058 44.3865 8.4586
49 9.8362 9.0384 5.3646
50 64.9783 74.4381 6.9379
51 76.4071 3.2615 5.1076
52 98.7959 42.9743 4.7662
53 12.5325 3.7262 1.3087
54 36.4477 97.5798 9.3416
55 67.6230 52.2340 1.3904
56 37.5758 90.9630 5.2845
57 86.3458 38.3248 4.4717
58 29.1977 88.4452 5.8065
59 13.3475 25.5018 9.9835
60 67.2651 90.9050 9.1223
61 20.2585 89.4560 1.1328
62 86.8515 39.8517 8.0246
63 75.1157 62.5020 5.3676
64 41.9380 56.7597 4.5120
65 0.0231 89.4512 8.4078
66 14.9464 21.4166 8.8698
67 27.3834 0.3859 9.9852
68 87.2425 88.0581 2.7609
69 60.1251 23.5122 8.8297
70 32.1188 24.4865 3.7674
71 28.4293 64.0917 4.7011
72 43.5316 30.4524 8.3471
73 90.3759 82.5621 4.3143
Continued on next page
408
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 92.5106 88.3689 4.8359
75 50.5292 94.5373 1.8210
76 62.7582 39.0795 7.0075
77 71.9264 80.1320 7.5818
78 2.3913 15.7113 3.7074
79 57.4933 62.5165 4.0420
80 4.6534 69.8985 7.6089
81 42.2531 8.5869 9.8691
82 46.7734 53.1180 7.2889
83 2.2628 88.8567 1.8094
84 6.5074 26.3666 5.2366
85 92.3956 23.4786 6.7183
86 53.4143 83.9657 5.7274
87 36.6796 49.5540 2.2721
88 36.3946 15.2366 3.4796
89 15.1374 23.0768 9.8839
90 14.9609 65.7954 8.1550
91 35.0802 56.2948 9.4000
92 33.5966 29.1829 4.1354
93 78.4028 62.2305 2.8822
94 48.6739 71.5905 7.1233
95 46.4798 28.0731 4.1988
96 13.1253 41.2273 4.9454
97 88.6391 36.2206 9.1790
98 67.4557 78.1392 8.5023
99 83.5160 13.5487 4.5225
100 65.6488 90.2070 7.6058
101 98.3917 28.9636 3.6159
102 97.9790 49.9558 3.6292
103 25.0153 78.3590 3.6712
104 62.4571 67.7062 1.2236
105 72.8242 14.9812 9.2606
106 49.8170 69.6619 7.1743
107 84.9828 12.9013 3.1085
108 19.0918 94.5946 5.4762
109 12.4144 88.6412 8.1152
110 0.2790 51.5005 4.4221
111 15.2953 67.9409 2.9673
112 53.4161 97.6793 7.5040
113 51.0634 12.5460 7.9555
114 38.5216 75.2243 7.2395
Continued on next page
409
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 31.0596 82.7052 6.5771
116 0.3555 78.1430 7.8607
117 81.5242 19.0883 5.6033
118 63.8418 42.8641 3.9646
119 44.8339 1.4457 1.0121
120 24.4086 32.5285 6.2258
121 80.3385 13.4702 2.5465
122 82.3971 45.0517 2.7542
123 85.2191 57.2275 2.3529
124 46.7252 79.2023 5.5488
125 97.0699 41.9737 1.1565
126 84.1244 53.2537 5.2409
127 7.8548 92.5704 1.4147
128 23.7599 89.9082 4.9804
129 81.7571 54.4833 2.4720
130 40.5829 90.1124 6.1489
131 46.6312 5.1827 8.3649
132 95.1536 80.8603 1.7681
133 96.5005 33.4905 3.0955
134 76.5285 22.8683 3.2144
135 57.4534 82.2402 4.1674
136 91.5925 34.8235 4.6818
137 49.5432 16.5471 2.0282
138 16.6012 2.8134 4.6649
139 32.5998 95.5370 7.0834
140 29.6436 68.0291 5.8872
141 55.8298 86.0562 4.2142
142 6.7477 93.9094 6.9543
143 6.8978 68.0194 7.1083
144 16.6785 91.7424 2.1840
145 94.7438 25.6692 4.9566
146 81.1088 88.5618 9.4348
147 71.0456 92.0043 6.1320
148 97.0246 30.0063 6.1988
149 99.8427 7.3391 7.8814
150 98.7455 76.7399 3.2226
151 15.0087 8.4952 7.2447
152 95.8479 72.8764 3.6538
153 53.0459 44.7890 6.1363
154 7.4087 65.1249 6.7132
155 31.1821 16.9502 4.5900
Continued on next page
410
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 89.5171 53.1449 3.2400
157 83.4768 63.3801 9.4180
158 0.2349 1.4096 5.0401
159 64.0210 47.0371 5.7861
160 80.3183 88.6326 6.7135
161 24.5131 11.4028 7.0131
162 6.4122 44.2541 4.9511
163 26.3148 65.9548 2.5569
164 10.2720 29.4773 7.2495
165 48.3719 95.0368 9.3243
166 41.8884 69.4286 4.3355
167 38.1289 20.6807 6.7491
168 88.6765 55.4762 9.0071
169 42.0558 87.9278 5.3465
170 28.3848 55.7858 6.6684
171 4.8181 75.2334 5.1852
172 21.9166 89.4901 1.9826
173 23.9176 84.1844 2.0180
174 2.9258 13.0857 1.9710
175 70.2311 18.9154 5.0116
176 0.7636 15.3640 9.4496
177 61.0921 2.8902 6.7043
178 40.8090 0.9085 9.3670
179 24.8947 59.6452 1.5659
180 65.2460 60.9049 3.7625
181 32.0277 91.8923 9.5479
182 10.3672 73.3574 1.0933
183 53.5565 30.1147 2.5104
184 16.4870 49.5574 7.7975
185 88.3439 25.8163 8.5044
186 66.6457 73.2854 6.4527
187 84.7742 11.6761 5.6613
188 76.2661 74.6042 9.4857
189 80.7014 80.9789 7.6709
190 63.2952 74.5234 7.3097
191 71.0427 33.7143 7.7025
192 68.8664 58.4325 8.8644
193 32.0948 46.8952 9.6771
194 53.1648 8.7265 9.8373
195 87.3194 82.8717 9.2677
196 5.4540 68.5945 3.5513
Continued on next page
411
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 50.0401 26.7325 1.5276
198 43.2763 96.9484 8.3890
199 90.4282 18.3774 2.6157
200 63.0183 29.9941 1.3144
201 98.3036 41.1185 7.9419
202 58.5200 23.6489 5.8647
203 84.0637 19.5055 3.9839
204 46.8814 70.5379 6.2039
205 54.5222 18.0548 8.6906
206 17.9104 52.2333 6.7814
207 63.4462 29.6172 4.7809
208 96.2959 46.2782 5.9132
209 53.4014 92.5232 2.6407
210 47.9614 21.5889 3.1265
211 79.3666 0.1009 2.8487
212 9.2714 90.6606 3.3372
213 88.0800 68.0042 9.4837
214 0.3874 51.4952 6.7741
215 51.1529 52.2069 8.4616
216 67.8464 10.2919 4.4989
217 56.5748 99.6880 2.5157
218 47.8459 35.8969 7.6611
219 32.0513 62.5243 8.8552
220 60.1580 39.3367 4.1997
221 91.3153 0.7662 2.6095
222 68.2518 54.5285 9.9678
223 94.6733 50.9110 9.6321
224 9.9089 24.6779 2.4040
225 51.1029 4.5395 9.3604
226 11.0128 84.1730 4.8212
227 54.5262 4.8250 3.0078
228 68.8786 31.6320 2.2276
229 14.7417 78.3419 3.3416
230 77.7561 97.2400 5.9002
231 39.9051 58.6464 1.7399
232 89.8300 77.8044 6.3831
233 30.7044 72.7697 1.2627
234 6.1051 65.0987 5.0942
235 21.9471 66.4615 3.9925
236 8.2833 93.8780 9.4931
237 95.0395 53.5081 3.7279
Continued on next page
412
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 1.6371 39.8440 4.8540
239 11.4668 67.0458 6.9493
240 1.2410 44.0534 4.4298
241 21.6227 13.2874 2.2255
242 1.1428 43.9204 1.8696
243 64.2449 54.7643 3.7465
244 51.6991 39.5136 8.4150
245 24.5542 39.8272 6.6453
246 19.3747 75.1349 2.8534
247 9.0871 52.2350 9.8217
248 36.8442 49.0433 4.9400
249 0.7793 8.8679 8.5168
250 60.2701 25.0852 5.8526
251 47.8855 44.7559 1.2261
252 30.8118 63.7961 1.0614
253 74.4444 70.9445 8.0748
254 83.9349 99.2620 5.0265
255 26.2432 93.2195 3.5986
256 51.4238 9.2229 8.7686
257 44.6774 95.3540 6.9061
258 34.1211 16.2796 3.5622
259 83.9142 97.0455 6.8011
260 98.2493 59.7007 3.3722
261 62.6465 24.0227 2.5730
262 18.1275 7.0295 4.3176
263 12.3017 30.0041 5.8379
264 57.9969 81.3545 9.3377
265 32.8536 7.6710 7.7421
266 26.8186 35.4473 2.3296
267 55.0239 13.2011 1.0260
268 18.0517 15.8180 2.1431
269 67.8492 6.2147 9.2523
270 5.5688 70.1843 7.0491
271 3.4057 8.6482 2.0241
272 28.6518 61.6787 9.6420
273 7.7390 17.3772 2.0744
274 90.0572 65.1401 5.4317
275 84.6606 49.8696 4.2518
276 39.5698 28.4511 5.2300
277 16.9215 83.0560 1.5290
278 43.0452 81.8360 3.9701
Continued on next page
413
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 41.6218 93.8169 3.3807
280 72.8763 0.0326 3.2133
281 40.6474 64.0389 9.5291
282 95.1807 0.7356 1.2920
283 91.1985 10.6421 9.1554
284 95.1414 10.6794 4.3165
285 34.6001 36.7109 6.9629
286 29.0244 23.9608 9.5826
287 88.6701 34.6140 1.8472
288 21.0031 24.9620 7.1678
289 13.0877 38.7064 4.7120
290 52.0516 42.1038 2.0061
291 90.5463 64.0077 5.4265
292 40.2530 78.7553 5.1540
293 21.5761 26.9994 8.8935
294 7.8739 84.3982 6.9422
295 93.3060 74.0468 3.5017
296 60.2872 82.6102 6.9145
297 37.7492 18.2192 6.8087
298 66.4931 6.5436 9.0750
299 79.2190 61.0350 8.9410
300 33.3492 70.1553 4.0166
301 69.2659 11.1618 4.8430
302 20.3816 9.5824 8.2339
303 95.8714 59.7834 9.3078
304 71.1832 81.2233 8.8005
305 16.6907 81.4578 5.4969
306 44.2777 8.9437 6.2603
307 63.2994 73.1279 9.3228
308 92.9967 90.3857 2.4951
309 52.9331 45.2232 4.3692
310 62.6474 7.0688 3.3347
311 68.0819 24.1278 8.4743
312 92.3198 73.1865 1.6316
313 15.2834 4.0492 3.5293
314 40.5721 42.4523 5.9954
315 31.2476 54.0215 6.5707
316 69.3899 95.3828 4.6881
317 89.0688 20.8906 3.3259
318 49.0671 11.6332 4.7507
319 80.5824 64.6220 4.4385
Continued on next page
414
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 32.6439 10.8411 1.8670
321 54.9879 98.3497 2.1816
322 38.8784 24.8344 6.4891
323 89.6829 60.6356 6.9057
324 67.6120 81.6695 8.5690
325 82.8397 83.0054 5.4984
326 11.0089 48.9039 3.7648
327 27.9227 76.0728 2.5279
328 76.7636 91.5108 1.4389
329 21.6057 90.0975 3.0324
330 3.4062 21.4238 4.3027
331 43.6552 54.7061 6.1106
332 93.6864 78.4709 6.1274
333 26.2089 19.4441 8.0090
334 56.9745 74.6889 6.3122
335 35.9553 47.5558 1.9960
336 2.6839 58.3259 6.7661
337 50.0419 26.0548 1.6482
338 82.7015 8.4822 4.2926
339 25.8982 29.8133 3.5857
340 4.5885 91.7129 7.6729
341 24.6472 47.0518 1.6029
342 66.0732 26.9468 7.8145
343 32.9410 76.2970 3.1664
344 65.9496 77.2172 3.0782
345 1.3004 2.1300 1.1079
346 71.8068 87.9986 2.1923
347 39.1119 79.8170 2.8845
348 3.3505 32.4165 2.9276
349 40.6015 66.9044 9.1521
350 71.6308 29.6294 3.5000
351 92.1336 92.9952 1.8739
352 98.4016 28.1960 8.0454
353 98.3421 16.8880 7.0077
354 89.6306 74.5167 6.5141
355 86.5703 47.7134 4.0941
356 80.0961 65.3445 7.2131
357 55.4979 96.6576 3.1020
358 41.8872 31.3027 3.7723
359 12.7123 7.6439 4.2157
360 65.4621 79.1415 2.9503
Continued on next page
415
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 86.3965 36.5384 7.0955
362 27.4598 58.5099 7.6241
363 84.0164 18.3337 1.0902
364 7.0755 7.6919 4.2032
365 37.8792 15.3663 3.1596
366 26.8169 82.6876 9.3485
367 15.2921 30.0957 7.8669
368 63.1000 38.3884 4.4145
369 31.6375 65.0749 7.1736
370 95.9112 81.7371 7.2899
371 49.8674 76.6266 6.3136
372 73.8609 37.4176 9.6585
373 1.2756 18.9862 8.0321
374 60.5353 64.6502 5.8458
375 57.6451 0.3605 1.8472
376 80.7379 28.2888 8.9741
377 65.4968 63.8601 3.3175
378 87.8228 59.2075 5.1716
379 90.2373 32.5289 3.9772
380 15.2233 98.8951 7.8110
381 19.2580 12.3236 8.2256
382 79.0976 73.5877 8.2281
383 6.0705 15.6617 8.8897
384 38.9827 43.4647 1.7873
385 29.9966 83.2243 7.0112
386 73.4180 35.9910 5.5218
387 10.4209 7.6238 4.0201
388 79.2575 55.6926 6.2971
389 78.2729 27.3930 4.1674
390 53.2398 13.2055 2.8605
391 25.3352 69.9655 3.3594
392 7.0955 48.5905 1.8878
393 62.5803 18.2716 2.3506
394 2.4681 10.1215 3.8892
395 6.2042 20.1584 6.3495
396 12.9612 13.4746 2.3836
397 45.0614 32.3789 1.5636
398 67.2336 95.0545 1.0700
399 85.6111 53.2131 7.9683
400 49.8445 24.7686 7.1384
401 4.8785 43.7276 2.0845
Continued on next page
416
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
402 31.3832 66.9088 7.4733
403 64.1631 54.7696 2.4567
404 78.6387 60.9054 2.0814
405 28.9150 86.3135 7.1304
406 49.7868 38.0696 2.3034
407 81.8435 74.8956 1.5204
408 59.5128 15.6697 2.2145
409 53.6425 5.8124 1.1330
410 33.0873 33.9707 2.7021
411 41.1690 81.7176 1.6378
412 79.4006 37.7548 1.3407
413 34.3208 97.2605 3.7708
414 46.2607 60.5319 5.6416
415 36.7824 33.8236 4.5416
416 67.9571 92.7984 9.9568
417 56.7779 89.8425 4.9564
418 65.1777 85.0706 2.3630
419 49.1114 25.6792 8.0025
420 39.8458 28.5496 7.6706
421 47.7484 77.9947 1.7888
422 6.6588 70.1395 5.2338
423 41.1028 49.2512 3.6355
424 96.9092 96.7668 4.6617
425 78.0721 47.6161 4.8721
426 72.9018 99.4906 8.8414
427 76.5651 49.0579 7.3653
428 75.6581 50.3453 1.1287
429 84.3270 76.8773 1.2213
430 77.0157 38.8084 3.1329
431 97.8661 45.3259 6.3844
432 11.1359 13.2854 9.3358
433 39.6077 75.8506 4.0097
434 49.2061 56.5237 4.9873
435 25.8095 64.8637 1.8922
436 3.6966 79.8058 7.4364
437 97.4381 22.0448 7.4947
438 72.6426 85.7891 8.0422
439 14.7965 90.4729 9.4784
440 14.7895 29.2020 1.4281
441 70.4824 72.5870 8.2032
442 38.0994 33.9446 5.2011
Continued on next page
417
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
443 7.6411 27.2681 3.5123
444 41.0840 17.0275 1.4025
445 14.2991 66.4018 8.0880
446 79.8920 53.5852 9.0921
447 93.0248 82.9109 7.9812
448 0.4719 26.7362 8.5371
449 65.0041 17.6156 4.0998
450 67.8532 43.1186 2.7207
451 25.3623 47.5655 4.4060
452 84.3181 78.5221 3.3070
453 29.3959 13.0652 1.1932
454 2.6860 5.1356 3.6395
455 9.3307 62.7506 3.1638
456 79.7885 2.9088 2.8233
457 71.1403 13.6195 4.1340
458 78.3407 69.4556 5.8343
459 62.3923 51.5679 2.1188
460 82.5415 54.2582 2.7346
461 3.5023 80.8484 5.3976
462 40.5475 79.3686 4.6631
463 24.9669 50.1867 7.6143
464 48.0897 27.6632 3.6991
465 88.0839 11.9665 8.2642
466 28.0685 88.6598 9.2230
467 59.9143 97.0289 7.8860
468 2.6226 94.2526 4.0079
469 15.5199 63.8128 7.4740
470 83.3911 9.0590 1.3023
471 19.4893 7.4708 6.5406
472 82.9788 18.2451 2.0097
473 33.8075 3.1688 1.4554
474 67.1117 72.4936 1.4969
475 5.2366 14.4159 1.2360
476 73.4309 63.5927 9.5989
477 49.9482 78.9848 5.7269
478 94.3300 56.6253 7.8063
479 28.9772 37.7414 6.3084
480 37.6560 82.1586 7.6502
481 11.3755 30.4881 3.8748
482 96.4851 31.9373 8.6332
483 43.2512 78.4980 5.4428
Continued on next page
418
Table B.56 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
484 8.4563 50.3736 2.0335
485 71.6676 26.0997 8.3105
486 50.6787 73.2476 7.0015
487 32.8088 16.2950 4.4360
488 75.3524 92.1075 7.4693
489 83.6006 22.2223 4.7677
490 25.3716 8.3609 1.5034
491 53.4425 7.3702 6.2650
492 43.5165 76.9552 3.6894
493 15.7704 81.7677 4.6861
494 60.0481 74.0426 6.2748
495 93.7451 75.8249 3.8406
496 10.7759 96.1195 2.3262
497 89.9981 46.6425 9.9238
498 55.0465 78.6996 1.9674
499 42.7357 42.2568 4.0083
500 15.2381 94.3730 1.3416
419
Table B.57: Depot locations and number of vehicles for MS29
Depot index x-coordinate y-coordinate Number of vehicles
1 64.8590 93.2912 2
2 47.4655 9.6444 2
Table B.58: Customer locations and service time for
MS29
Customer index x-coordinate y-coordinate Service time (short)
1 15.9073 43.6377 9.3017
2 66.5256 1.2682 4.3583
3 68.4203 22.9023 9.9024
4 79.2409 26.3680 5.8911
5 34.8624 51.1385 6.0698
6 25.0075 21.5085 2.6911
7 34.5003 34.6110 2.9395
8 32.8633 74.7817 5.3678
9 92.7486 41.3619 2.9755
10 75.6072 5.5753 9.4319
11 28.8239 39.0028 3.4986
12 60.6180 47.4484 9.5779
13 76.6029 82.5321 8.3344
14 84.6152 30.3644 4.1464
15 90.1981 82.1790 1.1945
16 59.5707 56.5680 4.0691
17 6.8536 5.4382 4.4596
18 21.8043 26.0014 1.8396
19 86.9408 58.9104 9.7233
20 41.4218 47.9734 2.7104
21 66.1209 19.8651 2.4816
22 78.3485 23.9013 5.5633
23 24.7886 78.0193 5.5741
24 55.4425 61.7310 1.4633
25 22.9585 14.4129 4.3031
26 0.6913 71.6132 6.2632
27 76.6639 40.1506 9.9528
28 2.1833 46.2385 4.9162
29 39.3103 70.7282 7.2640
30 25.2540 40.1211 1.1483
31 20.4217 1.4385 2.3729
32 66.2279 7.4640 9.0958
33 91.4742 59.1068 1.4174
Continued on next page
420
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 0.6903 44.6002 1.2639
35 74.6423 92.6621 6.1700
36 79.9671 9.4893 4.0636
37 90.7799 37.5419 2.9737
38 97.4574 54.5999 9.1359
39 11.9863 11.1678 7.1478
40 51.8970 90.4463 4.3448
41 82.1975 63.3277 4.6101
42 63.7023 90.5412 2.8447
43 95.3910 63.0553 3.1393
44 94.6926 1.4228 8.9592
45 96.6605 31.6478 9.2912
46 6.7344 11.1871 8.0348
47 43.7535 62.9463 3.1772
48 32.0840 6.0709 6.2524
49 13.4052 67.3995 2.8167
50 13.4585 47.7439 2.1436
51 80.5948 30.5546 7.1890
52 52.4764 51.6333 9.1967
53 94.4257 70.7028 7.7585
54 98.8340 81.3611 8.4062
55 40.9894 31.5808 3.0261
56 37.1188 31.1302 4.4807
57 22.6854 34.4977 4.7682
58 44.6031 66.6305 9.4221
59 26.6221 86.1072 1.9500
60 45.9096 76.1779 5.7816
61 43.2905 87.5838 6.5907
62 25.9623 87.1235 3.5231
63 13.3715 17.2790 2.7799
64 41.9228 85.0224 4.6755
65 50.6861 95.9588 4.2634
66 32.4325 77.0207 2.4571
67 68.4689 87.5015 9.0417
68 44.3094 6.7413 4.9643
69 43.5663 64.6792 7.0328
70 79.3024 32.4097 2.8938
71 81.5556 64.0347 5.2403
72 75.2113 87.9751 1.4492
73 78.9256 37.3638 5.4634
74 50.1267 76.6738 3.4275
Continued on next page
421
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 55.5182 16.8087 7.1576
76 63.0750 51.9725 7.7320
77 9.7989 62.7456 4.5248
78 24.5676 71.3914 6.0294
79 61.5725 30.6396 7.5902
80 30.4960 26.3687 6.5046
81 76.6968 91.6004 6.2311
82 26.7229 61.5034 1.6354
83 3.9506 9.3175 4.3682
84 29.6562 62.7697 1.3023
85 55.6365 19.2028 4.6553
86 96.9074 77.6965 6.9216
87 68.9125 86.4501 6.1772
88 71.7881 33.3582 9.7836
89 55.9029 13.5414 4.9748
90 53.3354 76.5467 8.0005
91 87.5724 31.8614 6.1251
92 39.3099 25.2380 1.1899
93 45.8067 20.0075 5.6105
94 20.8245 6.9010 4.6680
95 75.7273 55.1911 2.9785
96 54.6692 40.3812 3.0741
97 35.7388 75.0116 4.9469
98 70.0998 48.7184 9.2790
99 10.9222 38.4786 3.8713
100 0.6611 6.1409 3.5590
101 59.7302 21.3691 4.2740
102 65.9176 54.3873 5.4939
103 58.0006 41.0645 8.3217
104 90.9952 90.0963 3.1134
105 63.6006 5.6290 1.2004
106 52.5561 44.3509 3.7101
107 25.9623 53.7813 3.6826
108 5.1171 13.4061 8.4334
109 73.1950 54.0947 2.2276
110 16.4291 85.7368 8.3312
111 28.0397 19.8017 8.7498
112 25.9427 15.5609 5.9765
113 54.7096 6.1378 1.1668
114 54.1268 66.1074 5.5704
115 78.8113 1.8603 7.4228
Continued on next page
422
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 86.9606 29.1103 7.2797
117 78.7541 97.3824 9.0411
118 96.9428 76.4640 7.3107
119 18.0468 24.3684 9.4356
120 93.0599 68.2116 1.0980
121 4.5152 13.7855 8.3777
122 24.0646 62.9812 1.3084
123 0.8855 85.7015 5.6454
124 67.1594 89.9798 6.8800
125 90.4813 34.8368 7.7871
126 57.2416 48.6310 3.5200
127 15.5461 67.9517 6.4275
128 50.2367 70.4122 8.9990
129 56.7733 46.0884 6.7891
130 18.8272 36.4272 8.0746
131 32.4196 28.0265 5.4203
132 71.6037 7.6204 4.6311
133 55.2929 44.4625 8.8970
134 14.2282 16.5706 7.3736
135 38.0364 39.8749 8.4384
136 39.6569 92.0585 1.0960
137 57.6742 51.1334 1.8600
138 1.9402 91.4142 5.8896
139 57.7580 9.1934 8.7060
140 93.2196 99.3037 3.3792
141 10.6873 9.6434 7.9799
142 73.2150 31.3147 6.7413
143 97.0523 78.5375 7.5255
144 60.8886 60.2400 9.0518
145 71.9666 46.5908 7.9119
146 30.2752 29.8131 2.8616
147 45.9022 13.3173 1.3897
148 4.8029 29.5009 2.3821
149 38.5352 16.6627 7.4648
150 36.1716 31.7104 2.1578
151 28.7584 10.9840 2.9871
152 81.6713 83.2088 5.0820
153 45.0528 97.1593 5.1873
154 80.6633 21.8271 1.8081
155 79.0173 70.6078 5.5606
156 28.2958 3.9014 1.6886
Continued on next page
423
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 6.8309 61.6295 2.4987
158 5.4931 66.9364 7.7294
159 63.7523 3.7202 4.0111
160 42.4286 0.3335 3.7455
161 90.5531 14.2464 8.3699
162 41.7321 86.2405 9.8384
163 15.4058 27.6037 9.7207
164 53.9999 53.1692 6.1896
165 93.7091 52.2221 3.1013
166 66.0955 56.7618 3.6289
167 39.4657 33.3033 7.0639
168 25.8991 41.3417 6.1636
169 84.7912 41.4348 2.7973
170 94.5056 98.3922 9.6238
171 37.7000 5.7739 4.0254
172 6.7280 39.6543 2.3470
173 18.1582 79.1321 3.9554
174 57.5748 59.4185 2.0179
175 18.5885 30.9563 7.9472
176 29.1448 90.1803 8.1331
177 46.1664 9.3127 6.2836
178 34.6977 31.9027 1.7127
179 31.8166 88.6962 2.7361
180 45.9915 65.7432 7.9786
181 23.5895 68.4517 4.1805
182 2.7752 47.3949 8.5505
183 65.8453 14.1244 2.2050
184 15.8804 95.0925 7.2833
185 80.2663 88.2626 2.7131
186 40.8580 43.7439 4.5713
187 32.7392 83.4957 4.0505
188 74.6015 32.5143 9.3042
189 74.6352 36.7639 8.5456
190 17.3955 79.4839 6.6657
191 11.7545 9.9309 8.7894
192 17.4038 95.1782 2.9466
193 62.7409 0.1474 1.5841
194 84.1890 29.5396 7.1020
195 51.0083 4.8455 5.8161
196 16.5764 44.2740 5.6561
197 71.4305 78.9846 3.3015
Continued on next page
424
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 90.7037 91.3521 8.6754
199 21.8538 53.3254 8.4088
200 87.0961 80.4076 1.1491
201 21.1836 56.2660 5.2724
202 83.6665 75.0876 9.4971
203 85.9302 0.9230 5.1276
204 52.3377 47.6785 8.6498
205 47.7363 25.0330 5.8200
206 88.9883 30.7918 4.9069
207 6.5076 96.6949 1.2199
208 50.9456 20.8804 5.5392
209 62.0798 52.0476 8.8884
210 73.3567 22.5546 9.1742
211 22.9996 56.7198 3.5668
212 2.1872 99.8164 2.1943
213 13.8989 13.1865 1.0012
214 76.9507 95.4677 3.8616
215 96.9765 12.3878 5.7710
216 38.6794 18.6238 8.4626
217 99.3428 64.6503 7.0623
218 32.6393 12.8169 9.2171
219 13.7161 8.1321 7.8053
220 38.4754 65.9227 2.5166
221 56.2636 2.7399 9.6761
222 63.3835 98.5180 4.1344
223 54.1606 53.9331 6.3864
224 31.4993 37.3835 7.5825
225 15.9327 70.6735 8.8373
226 15.2616 94.7411 4.0006
227 13.6951 38.2277 5.1674
228 70.9803 69.2909 2.5020
229 46.4864 60.2071 5.1975
230 11.3271 77.5258 5.1073
231 70.0879 59.1834 2.1504
232 17.9986 37.6180 6.7594
233 80.3668 85.0649 9.0684
234 51.3956 22.5735 4.8469
235 54.8438 79.6958 2.5826
236 20.7845 99.6881 3.6541
237 78.4589 28.1311 1.5286
238 52.6490 71.0381 1.5416
Continued on next page
425
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 57.1023 66.4642 1.2399
240 42.2041 41.4836 5.9542
241 72.1156 49.8270 6.0675
242 7.3138 94.9123 3.7414
243 59.4862 95.3182 7.7906
244 86.1977 73.2923 7.0399
245 44.8801 38.4680 9.4585
246 65.2577 4.0083 5.3664
247 30.3473 58.2934 5.6628
248 60.7440 56.4713 8.1028
249 27.8902 35.5183 6.1405
250 79.9562 88.0201 7.8985
251 79.6169 62.4530 9.2815
252 95.4087 62.4016 2.8928
253 44.4338 29.5741 6.4730
254 45.6883 7.4680 5.1915
255 59.9817 29.3706 6.5503
256 84.2622 23.4740 2.8278
257 3.1200 34.5897 7.0984
258 18.7270 84.8490 1.1558
259 94.3594 16.0364 3.0395
260 94.7922 15.7864 9.2302
261 45.2984 50.8659 7.9159
262 81.0833 60.3301 5.7998
263 92.8879 16.1397 1.6154
264 67.2717 63.5454 2.7963
265 37.2332 84.3941 1.1082
266 40.5696 78.2269 9.6991
267 43.8824 26.4566 8.4898
268 67.8649 31.4699 5.0078
269 46.5070 18.3196 9.9145
270 95.3264 44.7473 8.1486
271 35.4698 32.6679 5.3975
272 33.9021 27.9816 2.1753
273 89.5860 93.1764 2.9102
274 54.5434 39.9692 8.4800
275 74.9284 37.9423 3.9141
276 12.4877 59.2846 7.6489
277 45.3235 6.8507 2.4389
278 7.4749 20.5238 7.5832
279 66.3341 72.3618 1.4832
Continued on next page
426
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 70.3652 57.5148 7.4295
281 91.8951 20.0233 2.0956
282 66.0072 84.3480 9.8564
283 69.0105 42.3730 6.3379
284 85.3724 54.4751 3.4259
285 46.7902 52.7967 4.8880
286 45.8479 18.5108 9.3746
287 80.6104 8.1690 5.5710
288 82.4767 46.4094 1.5769
289 19.0436 3.0555 6.9320
290 2.5673 43.4984 5.0425
291 5.6815 55.7865 2.3245
292 14.2936 63.8782 7.9771
293 17.1419 3.4217 5.7814
294 62.5845 70.9900 1.7910
295 2.9515 16.9324 9.1041
296 47.2332 59.3382 8.8134
297 67.8443 60.8065 1.5067
298 11.4789 77.2360 6.7605
299 23.6064 5.6274 9.0034
300 28.9081 85.4725 4.1295
301 17.2756 38.4284 7.0005
302 32.3706 39.9619 5.0901
303 80.1110 32.5417 5.0219
304 29.9634 55.5390 1.1533
305 77.5626 29.5420 8.7528
306 55.2771 36.6120 9.4404
307 55.4692 34.9048 5.3090
308 73.0647 63.0224 6.1285
309 77.3625 66.4442 9.9352
310 90.0847 99.2096 4.6372
311 13.8167 94.4361 2.9786
312 79.4077 35.0348 8.7985
313 18.9413 19.2998 7.2012
314 2.8974 91.9576 2.5432
315 12.7387 28.8692 1.0812
316 13.3736 55.0859 2.5217
317 12.8311 91.9324 2.8575
318 93.5260 9.0049 9.1146
319 27.3230 25.7696 7.3823
320 94.2679 42.7048 2.1874
Continued on next page
427
Table B.58 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
321 63.8151 57.7723 4.8268
322 87.2531 89.9521 6.9530
323 36.7073 21.8226 3.9014
324 23.6202 96.7032 6.3769
325 18.7318 43.3981 2.8958
326 54.5649 78.4822 2.7066
327 25.5116 52.5234 2.8748
328 30.5824 33.1277 7.4201
329 1.5549 43.1594 3.2743
330 58.7488 71.7902 3.4301
331 96.2558 91.6212 5.3358
332 84.9848 89.0028 2.9861
333 0.7940 13.4706 4.1920
334 63.4026 11.9913 6.7396
335 35.9291 89.3452 7.7478
336 11.4060 65.3086 5.4318
337 54.0818 4.0278 6.5565
338 41.6421 50.4716 3.8751
339 51.7098 89.4453 3.7225
340 88.6123 38.5728 2.2761
341 14.9396 29.2052 8.5991
342 43.4677 23.4037 3.5934
343 5.9039 20.0948 9.1795
344 38.1030 38.0306 2.0189
345 72.2369 59.4790 6.5247
346 9.5119 26.8386 3.5551
347 66.7190 62.2443 5.5732
348 29.6401 80.4567 5.8499
349 59.8563 10.3971 1.4694
350 15.1852 72.9240 4.9337
428
Table B.59: Depot locations and number of vehicles for MS30
Depot index x-coordinate y-coordinate Number of vehicles
1 13.7563 63.9193 1
2 52.4102 68.2423 1
3 61.1506 55.3530 1
4 35.8528 50.2519 1
5 49.0485 30.5918 1
6 54.8631 58.2473 1
7 39.7564 29.7359 1
8 49.7726 76.5131 1
9 56.8686 58.7746 1
10 34.3808 54.4136 1
Table B.60: Customer locations and service time for
MS30
Customer index x-coordinate y-coordinate Service time (short)
1 59.0190 72.3647 8.8736
2 24.3187 33.5261 5.1413
3 46.6143 80.2990 1.0276
4 41.6672 43.7594 5.1845
5 56.3837 25.8043 8.4166
6 56.8673 39.6886 8.8470
7 56.7582 65.5750 3.7097
8 43.9370 67.5988 3.1240
9 40.0121 52.6705 8.4842
10 40.1735 54.7900 4.9398
11 64.2257 60.5484 5.5638
12 19.1165 25.6826 2.6693
13 46.5449 40.3048 2.3635
14 54.5063 19.4975 9.1613
15 39.1205 42.5149 9.9347
16 57.9538 65.8212 4.5107
17 48.8113 61.9574 8.4413
18 34.3616 88.1305 9.5865
19 52.6894 52.7788 9.0446
20 45.5303 14.0585 8.5691
21 43.1688 78.1567 7.1496
22 38.1446 71.3713 2.5462
23 51.0241 40.2895 3.1380
24 19.2312 53.7102 4.9086
25 43.3611 62.9909 1.2256
Continued on next page
429
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
26 40.9409 56.4118 3.4178
27 34.8017 61.6061 9.8214
28 60.8783 48.1214 3.8142
29 37.7621 49.3529 6.1458
30 59.0106 51.4681 6.5050
31 66.2640 36.8391 9.1138
32 47.3855 73.7160 4.5644
33 54.6300 50.1055 7.2349
34 60.6586 61.4413 2.8404
35 48.6504 35.7511 1.5657
36 59.0145 32.0794 6.6015
37 28.9573 48.4839 7.1922
38 68.5071 45.7871 3.6711
39 33.5073 69.9137 6.1441
40 19.5194 60.1011 3.8460
41 73.0750 59.0086 8.2855
42 48.9546 25.9177 4.2895
43 57.4820 33.8718 7.2891
44 43.9457 53.3675 6.7008
45 32.9903 44.2020 9.6812
46 -1.2165 71.5015 2.8072
47 60.4380 72.3526 6.3836
48 45.2219 40.3200 1.7533
49 46.7110 64.5856 5.8997
50 56.7601 73.2575 8.6153
51 26.3442 55.3498 1.3663
52 37.8426 77.0564 3.9642
53 69.1221 67.7072 7.3841
54 59.9644 53.5684 8.7428
55 28.6453 64.6134 5.5081
56 13.2789 53.2401 9.9528
57 40.4792 43.0851 4.8578
58 53.5666 55.9743 3.4061
59 65.7063 50.6037 5.2566
60 51.5621 43.9228 2.4476
61 31.2948 79.5170 2.4301
62 55.1026 53.6879 3.4151
63 30.4611 95.5063 7.8141
64 33.9839 45.0639 6.4826
65 39.1044 59.4049 9.7024
66 29.5101 76.3770 7.9599
Continued on next page
430
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
67 45.4839 95.4872 6.1558
68 35.0008 55.0594 5.0520
69 45.2386 36.8290 3.5835
70 42.2930 63.3897 7.7715
71 43.1702 28.0016 1.8492
72 41.6077 45.4359 1.9611
73 70.5550 54.5311 7.6140
74 60.1718 74.8259 4.1913
75 50.9845 73.9524 6.2257
76 25.5509 49.5406 3.6897
77 22.9033 65.3989 7.4231
78 17.2541 44.6453 4.2444
79 93.4199 61.0187 7.4661
80 66.2062 81.9216 9.9579
81 54.2830 52.6127 1.7533
82 33.7627 44.9911 5.2139
83 30.8939 41.6661 1.8442
84 59.1273 61.9412 7.5265
85 76.0847 72.2881 9.2084
86 21.7776 85.4280 1.7777
87 42.5100 50.9008 5.6796
88 48.5951 52.7173 5.9737
89 16.8000 39.4549 7.1663
90 64.0208 76.8665 3.6969
91 43.0890 48.7425 6.4169
92 81.8697 42.1127 2.7865
93 43.4850 86.4040 6.9108
94 56.8197 63.4980 7.2852
95 30.9595 61.9390 5.1371
96 39.5856 33.2405 2.4189
97 30.5213 57.2331 4.7961
98 56.5429 58.6691 6.3645
99 71.6973 31.7959 3.9010
100 40.1060 46.2368 8.4766
101 57.2729 43.2513 2.1042
102 41.5940 58.7977 3.2606
103 51.7018 33.2173 9.4385
104 69.9375 68.1504 6.8969
105 52.0047 79.7479 7.7762
106 32.7193 44.9374 8.2977
107 35.7149 49.8551 1.4358
Continued on next page
431
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
108 47.1688 58.4439 4.7324
109 46.8055 70.0542 7.5294
110 35.5697 58.7003 2.2514
111 53.0111 56.6174 6.6930
112 71.1088 41.9532 3.2215
113 45.8138 46.1417 8.5598
114 46.5905 60.2231 8.5300
115 13.3080 78.0475 5.0777
116 37.0914 59.4732 4.5528
117 26.7788 29.8995 9.6544
118 43.5628 57.2177 1.0736
119 58.7598 48.4647 4.5859
120 75.3878 45.9324 5.3900
121 79.9749 46.3469 6.5632
122 48.0519 35.3372 1.6301
123 44.6634 44.6533 2.2842
124 63.6253 36.9264 6.8880
125 58.1693 43.9173 2.9649
126 62.7542 51.9545 2.0722
127 62.9713 52.9057 1.3882
128 25.3282 46.4057 2.4900
129 59.0061 47.4565 5.6000
130 48.4743 50.5615 8.8054
131 37.3291 57.6380 7.8963
132 38.4401 71.3605 2.2146
133 71.3576 60.3348 1.5843
134 36.5044 45.2221 7.0520
135 29.3864 59.9669 5.3399
136 53.5781 45.9078 5.4588
137 83.5129 20.3210 3.8214
138 50.4259 10.8793 3.9115
139 55.1383 21.4401 9.1819
140 34.3625 46.0479 5.0530
141 77.9036 39.6729 7.7377
142 52.0831 37.9973 2.6673
143 58.8350 50.6776 1.7643
144 34.1322 39.0170 2.8633
145 64.2340 39.4914 6.0302
146 56.4858 60.1604 6.9553
147 30.7333 63.0389 9.4529
148 50.6623 90.6097 1.3622
Continued on next page
432
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
149 42.4900 55.0401 2.4729
150 51.8208 50.9720 4.9431
151 45.8241 40.4311 3.9310
152 46.8350 46.7465 1.8094
153 32.7848 49.1578 8.2929
154 44.6118 20.7371 4.5960
155 62.7754 45.7107 6.8978
156 79.0779 62.4924 6.1016
157 30.6580 40.4873 1.0281
158 89.6235 58.2372 6.8622
159 75.4346 66.5240 3.8539
160 52.8085 67.9523 3.3934
161 44.9799 62.9474 5.1440
162 38.3558 12.3360 6.6084
163 63.8795 40.5937 8.2167
164 38.4232 65.0249 6.0505
165 42.3020 56.5779 1.2232
166 64.7270 50.0809 8.1419
167 57.2657 57.2820 3.4578
168 64.9458 68.8345 8.4062
169 58.4122 52.5628 7.1970
170 43.3184 37.3562 6.4351
171 41.4359 46.9973 4.4826
172 63.2728 46.5368 1.5898
173 38.8135 64.9458 9.9873
174 69.7777 56.8718 6.9494
175 63.1784 59.1253 3.0626
176 54.7954 52.4639 1.8303
177 50.0538 43.9622 3.1688
178 56.0936 51.0190 9.1231
179 97.3100 53.6118 2.9561
180 48.1261 26.6980 5.3157
181 24.0568 52.9812 9.1831
182 81.9184 65.4597 2.7440
183 60.1641 48.1637 5.0319
184 39.2015 76.2066 6.5602
185 93.6222 59.3415 6.3479
186 59.1825 42.9943 6.9929
187 54.9034 47.4342 3.4091
188 37.0359 45.4134 4.8148
189 32.2512 54.0187 8.1939
Continued on next page
433
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
190 20.5264 62.5781 9.3908
191 42.9513 45.1348 5.2275
192 32.4483 57.6408 3.7567
193 60.7959 79.2548 4.9543
194 44.7062 65.5248 3.7617
195 79.4832 63.7544 3.4751
196 75.1764 36.4199 2.2487
197 52.7335 41.0966 2.4989
198 45.2873 54.0425 5.4455
199 69.2028 48.3225 1.7793
200 30.8915 22.9159 9.3416
201 61.2283 24.7596 2.3363
202 38.8481 67.1032 2.4443
203 43.3280 37.3645 7.4595
204 38.8033 84.6391 7.0741
205 59.5938 12.9669 4.2267
206 37.0318 57.4794 1.8141
207 32.2740 50.0104 1.0742
208 59.2163 37.3960 4.3550
209 42.9429 56.7387 8.0948
210 56.0265 36.7691 5.0256
211 44.1352 64.3297 1.8966
212 54.4923 51.1145 8.2525
213 7.2592 22.6769 6.9351
214 57.7644 9.5875 5.0713
215 80.8927 45.2695 5.8003
216 67.3215 69.0968 5.7400
217 65.1816 53.0195 6.6671
218 46.0045 50.9042 6.8191
219 53.0166 61.4626 2.7265
220 54.0708 26.7765 8.2156
221 51.6065 73.7561 2.7691
222 36.1589 35.1025 4.7016
223 44.1291 50.6294 3.1212
224 47.0871 43.9405 3.4498
225 41.9891 52.4926 1.0780
226 63.9473 17.5914 9.3545
227 92.3058 75.3982 5.6820
228 27.9444 59.0968 5.1771
229 52.1390 83.4988 5.7118
230 25.9603 73.6112 4.0313
Continued on next page
434
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
231 71.7085 50.1913 3.9914
232 73.4985 34.3492 9.8946
233 22.2910 21.0182 5.2635
234 82.3947 50.2828 7.7217
235 31.9217 53.6527 7.0296
236 53.7803 67.4303 8.1603
237 68.3155 34.1503 3.4529
238 52.4531 63.2466 3.5552
239 88.2611 51.1905 7.4553
240 95.8760 37.1052 2.6617
241 52.3053 62.9027 8.5033
242 18.2156 54.4276 2.5270
243 43.9168 46.0816 9.5794
244 35.8648 81.2882 7.5029
245 37.2541 60.1540 2.2082
246 31.2051 48.1621 8.6778
247 51.3031 54.6243 9.3852
248 85.1105 51.4508 6.0777
249 38.0692 52.8932 4.5894
250 45.3247 57.5599 4.9744
251 69.4413 39.9414 7.3151
252 70.2137 36.7163 3.3404
253 58.0923 56.0108 1.2568
254 67.1003 81.4182 9.5317
255 64.5121 44.8863 9.9655
256 43.6374 33.1213 8.0153
257 57.1482 46.0242 9.9046
258 45.0145 41.9331 5.3880
259 35.0022 44.5443 2.1518
260 60.5791 57.9253 5.1793
261 51.1242 47.8333 7.6833
262 46.8813 40.0941 7.0605
263 54.8621 42.6039 8.8658
264 66.4616 27.9578 7.8243
265 56.5489 35.6746 6.5546
266 53.2425 26.4500 3.4734
267 54.6631 41.4002 4.0274
268 50.8537 31.9150 8.5215
269 37.0922 38.2140 4.4730
270 63.1130 44.9724 1.7231
271 73.4818 29.9927 8.7903
Continued on next page
435
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
272 41.0984 49.6773 4.9184
273 82.1293 55.6728 2.5487
274 47.0625 33.9462 1.0387
275 45.9375 68.5654 6.8725
276 35.0400 23.5649 4.3272
277 36.7944 43.4701 4.3849
278 34.1171 25.2552 4.9721
279 55.8984 44.2562 5.6451
280 76.6171 27.9347 3.7010
281 58.7912 40.4194 5.3049
282 64.2367 37.6549 1.0562
283 72.3641 30.2500 2.5429
284 8.3411 15.5857 3.7320
285 47.2073 59.4177 7.7002
286 55.8836 83.3357 6.2280
287 61.9542 87.0555 7.3109
288 28.2525 41.7970 8.2420
289 33.2355 49.2333 8.6679
290 63.1781 42.2375 2.0595
291 48.0571 51.2658 6.9154
292 59.2182 34.6872 7.7766
293 33.9893 18.0089 7.3192
294 22.7700 49.3926 6.4461
295 62.6867 29.5812 1.3444
296 69.8885 18.2928 2.7564
297 77.2010 89.5708 3.9761
298 24.4635 46.1109 6.7855
299 27.7191 56.7313 2.9566
300 25.4359 69.8745 1.6922
301 49.3056 21.9207 9.8253
302 39.7415 56.8858 2.8608
303 71.9026 58.3624 9.8493
304 25.7489 51.3844 6.4933
305 20.9608 52.6300 3.2318
306 53.4217 41.2010 5.6616
307 69.8822 62.0510 7.4155
308 36.6196 35.8343 3.3388
309 28.9061 36.7269 2.0322
310 47.5111 62.0890 5.9470
311 22.7259 78.1091 2.9701
312 50.2891 43.5601 3.8096
Continued on next page
436
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
313 63.8065 41.5820 9.7582
314 53.6290 56.8012 3.7827
315 18.1793 67.8726 9.5162
316 41.0530 66.1330 4.6951
317 44.9661 54.5024 1.0930
318 80.2264 39.4266 3.7906
319 65.2475 60.4961 2.3969
320 49.0487 48.6794 9.9467
321 71.8227 72.9492 5.0522
322 32.5877 26.5298 5.9070
323 44.1956 52.3539 3.3610
324 73.5427 71.4953 8.9429
325 75.0397 41.7511 1.9275
326 62.1729 39.5863 8.4121
327 58.1792 34.4394 4.8446
328 40.2312 45.3546 9.2831
329 62.4150 46.6579 5.7521
330 36.1974 52.2790 8.8375
331 59.5753 35.2775 4.1753
332 54.6974 51.3756 4.6014
333 68.9884 39.9354 6.3813
334 42.9022 43.8545 9.2037
335 60.6023 36.0305 2.1969
336 63.2196 45.2921 1.3795
337 35.0270 97.3100 4.6094
338 52.6041 97.3100 6.3614
339 76.6209 69.1153 9.2771
340 51.8740 63.1210 3.6440
341 44.8563 28.6977 5.9054
342 57.6110 40.2568 8.0351
343 45.4150 39.6766 3.9466
344 57.3857 58.9217 1.8574
345 47.7539 58.0498 4.9751
346 49.6945 51.8079 1.2617
347 57.6798 44.3286 7.0785
348 72.7053 34.5692 2.0043
349 57.5312 50.0887 2.7968
350 77.4731 68.9858 5.7715
351 16.1940 57.1227 6.6462
352 42.5124 53.0172 4.3624
353 53.9332 60.9580 6.4581
Continued on next page
437
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
354 36.0805 59.7374 8.6175
355 28.7341 23.0591 7.3175
356 60.2839 50.3129 4.5359
357 60.2117 42.9007 6.1468
358 54.8230 16.0995 3.2480
359 56.5886 27.8575 7.5461
360 35.4906 44.6686 4.0900
361 41.7052 63.7572 1.7077
362 48.2221 46.1785 3.7201
363 38.5362 54.3708 3.7036
364 55.5313 35.0337 1.2090
365 89.4204 14.0450 2.5850
366 41.9628 51.5653 8.7483
367 60.7908 34.1470 6.9035
368 32.7596 69.5432 8.7088
369 72.3259 78.9183 3.4385
370 33.8477 43.8051 9.0635
371 53.4786 69.8811 2.8791
372 39.6901 65.8941 9.6775
373 58.5336 26.4159 4.7292
374 50.1892 49.4441 3.0661
375 49.2669 54.3520 8.3653
376 97.3100 58.7166 4.2440
377 39.4992 61.2798 5.5137
378 49.2187 61.2399 7.7291
379 94.7171 61.3066 8.4866
380 30.8885 44.7903 4.5502
381 59.2166 56.3207 1.8697
382 32.0590 12.4517 3.3885
383 67.1773 30.5275 8.1275
384 55.4588 70.0328 9.4317
385 60.8687 38.9877 6.1143
386 45.3523 55.4593 9.4422
387 54.0865 75.1355 6.3752
388 74.5419 35.1849 9.8916
389 12.0816 34.0119 7.8611
390 22.7785 41.7880 2.6705
391 56.9245 57.3509 5.6509
392 39.0872 46.5873 6.7614
393 45.0609 33.7032 8.8206
394 25.0514 23.7842 6.4011
Continued on next page
438
Table B.60 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
395 34.9194 43.8290 9.9970
396 43.2636 46.3142 2.1626
397 37.9034 41.0798 3.6403
398 35.5586 45.6338 5.2919
399 42.9692 31.7431 2.1662
400 34.2889 59.1539 3.0531
439
Table B.61: Depot locations and number of vehicles for MS31
Depot index x-coordinate y-coordinate Number of vehicles
1 63.1931 99.2175 1
2 98.5237 40.2352 1
3 55.9477 65.8856 1
4 93.3592 90.1348 1
5 72.0343 99.5382 1
6 48.4039 65.3163 1
7 63.9031 10.8436 1
8 88.7637 3.6114 1
9 19.8737 61.8091 1
10 39.5366 56.7144 1
Table B.62: Customer locations and service time for
MS31
Customer index x-coordinate y-coordinate Service time (short)
1 43.4400 54.6002 2.6296
2 13.7282 57.6633 7.0481
3 30.0724 46.3749 3.9321
4 56.0888 63.2687 8.1153
5 90.2074 24.6996 5.9141
6 62.3375 32.0847 3.0750
7 55.1624 -1.2028 7.1809
8 40.9669 58.6901 1.4417
9 52.0381 33.4829 6.1534
10 66.0380 45.7812 9.9439
11 45.7671 66.8211 4.2667
12 81.5293 50.8502 6.0285
13 29.6624 42.6595 9.3455
14 43.7294 35.8588 3.3389
15 50.8738 45.9938 8.4923
16 17.4344 60.0488 2.5761
17 59.4237 24.7291 8.9186
18 51.2966 48.8609 3.5167
19 51.3450 63.0399 8.6453
20 63.2451 26.3212 8.2604
21 67.3948 61.1561 2.7021
22 63.3697 61.3873 9.8070
23 42.1863 35.2977 3.2835
24 49.2235 24.9249 8.0069
25 55.8909 57.2190 8.2971
Continued on next page
440
Table B.62 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
26 29.0533 63.4709 5.4816
27 32.7328 59.6490 9.2415
28 42.8840 62.7142 1.9089
29 51.2945 30.2979 2.2224
30 79.8488 59.7308 8.7249
31 63.2877 40.3332 1.1678
32 42.6250 40.6439 7.5550
33 39.5151 24.0684 8.3499
34 75.5633 68.3368 2.0460
35 95.5590 52.9176 5.3970
36 52.7907 66.7269 4.1270
37 42.0189 75.1835 7.9650
38 26.4558 31.0460 3.5676
39 66.2498 60.7170 8.4196
40 54.8286 49.7873 2.5575
41 69.4235 65.2377 8.7728
42 34.8549 68.4616 9.3345
43 54.0096 63.6745 2.7199
44 39.0992 36.3731 1.4532
45 71.2492 47.8919 5.9360
46 40.8135 54.4024 1.0857
47 48.5432 99.3100 8.4553
48 44.2030 70.4436 9.1769
49 66.5660 88.6773 7.3477
50 57.1406 56.9083 3.1900
51 33.2636 53.5305 6.3031
52 39.4552 60.2194 9.4501
53 32.5715 41.2037 9.0595
54 58.4285 70.6934 6.4560
55 55.5326 47.3728 8.1314
56 22.7431 27.1066 8.5255
57 18.2193 64.5140 6.0413
58 49.3267 23.8578 1.0063
59 61.6199 19.2625 3.2615
60 52.8134 54.8068 4.8875
61 24.2701 34.1515 4.8759
62 24.1366 34.8211 8.8771
63 64.4513 47.3008 1.6088
64 47.5771 41.8516 4.0592
65 43.5626 46.2870 2.5936
66 71.9367 54.5344 3.2143
Continued on next page
441
Table B.62 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
67 36.7256 30.5245 7.5504
68 52.2574 29.5961 3.5938
69 56.9634 15.0087 3.1361
70 63.6647 43.4960 2.2569
71 35.7608 61.0714 2.9866
72 55.9553 38.2956 8.3579
73 95.8078 58.3555 4.4041
74 24.7837 59.0052 6.9896
75 57.2330 66.5125 9.4223
76 46.1705 66.4896 4.8383
77 36.2152 38.5193 6.4464
78 36.1336 35.7194 9.7263
79 58.2983 50.8065 4.2819
80 88.5938 38.9191 6.9800
81 36.7696 74.2124 3.8328
82 59.0160 72.9974 8.9714
83 40.6823 51.5856 3.6599
84 82.9428 42.8812 3.6583
85 59.0777 58.5135 9.1637
86 47.7016 39.0621 5.4360
87 60.3313 47.9164 2.8643
88 49.9070 41.1589 1.2324
89 68.4533 51.7598 2.5319
90 46.9068 68.8058 3.7211
91 31.3097 62.3746 9.6530
92 54.1075 69.0601 8.0529
93 76.0173 34.7548 7.0593
94 30.0563 52.9967 8.5665
95 45.9609 33.6109 4.7877
96 66.7471 56.4138 7.3336
97 17.9979 55.4283 5.3316
98 60.4241 71.6052 8.3852
99 62.5493 68.3205 4.9365
100 53.5581 60.8871 8.7398
101 37.1628 41.5821 1.0801
102 49.8811 42.0668 9.9643
103 51.5531 15.8073 3.4768
104 65.5875 42.5283 1.3016
105 61.0586 24.1467 2.3689
106 44.1628 65.4971 5.3164
107 76.9980 65.0323 8.9996
Continued on next page
442
Table B.62 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
108 49.1528 52.3048 3.5508
109 36.4550 43.6932 8.0571
110 42.6930 52.3844 2.5335
111 64.3102 76.7506 7.5816
112 53.2536 72.4853 3.2196
113 64.8144 42.5260 1.7366
114 51.1537 52.8069 8.6762
115 91.4470 31.3251 7.1790
116 22.2393 56.6788 9.6230
117 43.0679 62.3177 9.8655
118 48.5963 65.0007 5.8125
119 51.4875 24.4797 9.1538
120 74.2691 58.4103 5.2898
121 53.6576 35.5964 9.0070
122 48.0854 43.7241 1.2146
123 51.1434 63.1335 2.1585
124 62.5249 54.9701 7.6658
125 38.5095 47.2710 4.5192
126 57.5136 60.1122 4.5427
127 23.9163 77.2416 6.4166
128 48.6867 39.6084 1.2150
129 34.3035 27.4983 4.4890
130 39.1190 30.6293 1.5107
131 54.7088 34.2620 7.2061
132 31.2487 38.8132 5.6835
133 33.5171 59.6114 1.6848
134 24.7357 15.2372 4.6563
135 12.8582 53.9327 4.8719
136 47.4746 37.0263 6.9338
137 69.3791 68.3260 2.9655
138 46.9677 35.7406 1.7298
139 46.1008 50.1260 5.2090
140 32.5544 34.3736 7.5580
141 76.3886 38.6407 6.5259
142 45.8431 45.6643 9.1054
143 71.5670 46.1867 3.2750
144 56.0330 41.2531 2.9809
145 45.6158 68.8053 3.1222
146 68.0357 59.1690 8.2912
147 66.3739 80.9191 7.3217
148 48.1426 45.3784 8.9065
Continued on next page
443
Table B.62 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
149 71.5992 67.7772 7.3991
150 79.6883 15.0127 6.9497
151 48.9064 60.6414 4.9562
152 45.7387 56.1911 6.0651
153 56.7440 43.7637 9.9128
154 55.8626 61.5891 9.6158
155 63.4585 64.6271 4.0314
156 45.7402 67.2268 2.3991
157 61.9186 56.9965 4.7537
158 67.4766 60.0178 5.9903
159 52.9591 38.7664 1.2678
160 52.5550 31.7470 8.8004
161 29.0946 45.5397 9.0497
162 30.4533 53.1092 5.4747
163 25.6426 65.8491 2.8836
164 29.2619 36.8247 7.4944
165 47.4150 41.8420 7.2974
166 23.0848 99.3100 5.1467
167 87.4344 39.6236 2.5353
168 62.3214 82.0050 8.1493
169 15.5392 66.0191 8.9965
170 30.7575 40.7033 2.2826
171 48.2135 48.2241 9.4570
172 21.4520 46.4140 1.0023
173 42.3351 57.8915 4.9492
174 68.1833 72.7607 1.1005
175 47.2687 22.7033 3.1106
176 48.8793 83.7288 7.3629
177 33.3068 62.9632 7.2475
178 40.7390 40.8516 3.3861
179 27.4741 47.8998 3.9392
180 56.0702 54.9930 1.8391
181 42.4632 54.9362 1.3744
182 63.0561 70.0130 7.8335
183 70.6206 68.1695 3.9239
184 67.9533 44.0216 5.6964
185 49.4193 47.8345 9.5670
186 41.6002 62.2290 7.0208
187 29.5997 52.0055 5.2581
188 51.9752 68.9389 6.8443
189 65.9912 38.5538 6.9907
Continued on next page
444
Table B.62 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
190 44.3178 57.8614 3.0713
191 47.1114 54.8057 8.2440
192 60.2717 73.1976 5.5251
193 64.3987 27.5750 4.9063
194 26.3848 50.0125 7.3813
195 53.3325 50.8916 5.9974
196 53.2638 10.9682 3.2950
197 47.4811 70.8016 1.6768
198 64.8797 96.8205 6.3019
199 43.9302 46.1303 7.0682
200 36.2302 54.7839 6.2921
445
Table B.63: Depot locations and number of vehicles for MS32
Depot index x-coordinate y-coordinate Number of vehicles
1 31.4177 22.8672 1
2 61.4209 76.9550 1
3 67.2946 54.4023 1
4 80.3702 31.2142 1
5 41.1835 40.6804 1
Table B.64: Customer locations and service time for
MS32
Customer index x-coordinate y-coordinate Service time (short)
1 82.7075 48.4180 5.8033
2 73.4386 73.0536 5.2535
3 58.2806 71.7280 3.9143
4 51.3805 47.9031 4.8789
5 24.1920 40.0521 7.8841
6 81.0527 24.6559 9.9682
7 52.2338 61.1974 3.3852
8 24.2333 50.3807 8.1286
9 57.2214 30.3702 2.2115
10 51.7159 44.4237 1.3198
11 40.4942 19.5091 5.0855
12 58.2177 57.1665 6.0668
13 38.2081 47.1001 3.0779
14 27.5329 77.1874 2.3029
15 20.7616 27.3429 7.0939
16 43.9365 66.1751 4.1866
17 39.5484 52.3940 5.5943
18 57.3358 51.3767 7.2524
19 24.9560 61.9444 6.3576
20 46.5294 69.8914 5.5550
21 24.9146 32.1490 7.9876
22 80.1623 71.9817 7.1668
23 48.0505 29.8333 3.8754
24 70.4368 32.0981 8.4893
25 58.2491 38.7907 6.9474
26 65.1432 62.2744 6.2836
27 30.7630 32.1673 1.1717
28 70.9593 55.5786 8.5326
29 74.2089 56.8647 2.0260
30 15.3865 52.5687 8.5638
Continued on next page
446
Table B.64 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 47.0585 59.2428 4.0375
32 39.1320 30.4526 4.8649
33 52.6089 66.7931 8.1440
34 35.8296 51.8920 2.2741
35 54.6508 62.1675 6.4729
36 59.9516 33.6081 9.3757
37 54.0786 50.8672 6.7280
38 48.0276 64.6267 1.4299
39 28.5099 66.9024 7.2851
40 50.9594 48.5942 3.3140
41 41.3178 19.1078 7.2181
42 28.6829 31.7197 4.2686
43 49.0629 53.6438 5.8770
44 46.5053 63.2374 2.9993
45 53.2017 57.7187 9.1494
46 66.5389 39.7895 4.3619
47 59.6041 87.4067 1.7093
48 71.7631 51.2058 1.2784
49 37.8449 64.4252 6.6421
50 35.5904 43.0717 9.4330
447
Table B.65: Depot locations and number of vehicles for MS33
Depot index x-coordinate y-coordinate Number of vehicles
1 57.8128 41.3045 1
2 39.0451 52.6906 1
3 21.3840 32.3032 1
4 74.5087 57.5082 1
5 61.5690 45.4534 1
6 41.4884 48.3091 1
7 51.8898 26.1816 1
8 46.1699 37.2598 1
9 25.6378 56.8356 1
10 1.9611 36.8345 1
11 49.2089 52.6940 1
12 42.2922 82.9651 1
13 40.3892 63.2544 1
14 35.9005 67.2894 1
15 19.7127 89.3388 1
Table B.66: Customer locations and service time for
MS33
Customer index x-coordinate y-coordinate Service time (short)
1 18.2596 27.2642 3.8794
2 34.6750 27.9887 7.7066
3 29.9342 22.0640 3.6004
4 27.0229 26.1030 2.1192
5 27.0040 47.2798 5.6267
6 18.1542 24.9369 4.4876
7 33.2759 30.9192 9.8075
8 27.8866 21.1455 3.6264
9 22.8239 20.6010 6.3311
10 23.4607 22.1184 6.1422
11 24.1522 29.7046 6.5427
12 17.6080 18.3205 6.0482
13 31.1781 9.5588 3.5187
14 36.6017 25.4435 2.3666
15 45.6158 21.3632 7.5971
16 29.1993 27.3334 1.3573
17 18.1460 25.7050 8.2146
18 26.6748 31.0760 4.6578
19 16.6079 32.5063 8.4701
20 19.8902 13.9530 9.7393
Continued on next page
448
Table B.66 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
21 19.5086 12.2952 4.8023
22 18.0564 29.1869 1.4851
23 28.1515 27.5533 8.0833
24 15.7055 17.1737 6.6707
25 30.5603 35.3117 5.5794
26 31.6278 25.2751 6.1092
27 33.6458 26.0297 3.7827
28 24.8297 27.2828 7.7242
29 30.1579 31.2847 4.0299
30 40.0255 37.7041 8.9502
31 25.4416 22.8169 4.0029
32 23.5176 10.5776 8.1641
33 39.7707 33.4455 8.2431
34 4.0933 17.2689 1.4521
35 21.1951 35.3640 4.6225
36 45.2531 20.0876 9.6867
37 21.0712 37.4290 4.7294
38 20.3306 18.2835 3.9747
39 14.7794 15.7283 6.7274
40 31.6079 32.9745 8.7222
41 7.4172 13.6412 8.0946
42 18.3384 30.6715 5.8457
43 29.7248 28.6485 7.6750
44 24.9880 23.8061 7.6575
45 30.1994 22.1539 5.0032
46 26.0537 42.1484 8.6537
47 30.6739 21.8789 5.4508
48 14.2715 23.4150 9.5334
49 26.8174 17.1772 8.1801
50 11.9453 18.2211 2.1974
51 31.5273 20.1365 3.1399
52 22.4119 39.2460 2.1495
53 30.4610 21.7465 5.8071
54 20.5211 19.2495 1.5103
55 27.7387 21.2648 5.2172
56 33.7839 30.9531 9.8442
57 8.5025 14.0356 7.1400
58 9.4384 30.2260 8.8381
59 9.7304 13.9059 5.4659
60 32.0716 23.9096 3.5890
61 28.3766 9.7759 2.6472
Continued on next page
449
Table B.66 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
62 19.1462 29.4660 9.6510
63 37.4921 30.7739 7.8064
64 26.1483 19.2704 9.5532
65 11.7765 27.6465 7.0414
66 16.5071 26.3570 2.6745
67 13.4564 34.6593 3.6086
68 32.9574 26.0699 1.5239
69 19.9907 33.6622 1.3966
70 15.2342 24.0269 3.5160
71 20.1907 19.5975 2.5342
72 18.0297 24.6835 7.0939
73 32.1081 23.3390 9.1218
74 28.9778 32.3472 4.1679
75 27.5193 24.5321 1.9014
76 28.4648 17.9897 8.1370
77 25.3581 23.7096 5.2159
78 17.0929 34.9050 7.1861
79 29.5134 21.5424 7.1477
80 18.1573 19.5115 4.7929
81 16.0675 33.1999 6.9341
82 16.0492 25.8436 6.7008
83 32.2463 21.9775 5.7263
84 33.1754 18.8431 2.7215
85 10.3431 12.6680 5.6072
86 23.7659 26.2781 7.7350
87 27.0995 22.3582 4.7784
88 19.9135 27.6577 7.6373
89 31.3415 12.8621 7.1782
90 27.1202 36.0153 9.6015
91 23.7264 29.0600 3.7712
92 20.3549 11.9448 4.0807
93 30.6418 33.8088 4.4833
94 32.0775 20.1035 1.2356
95 28.9109 27.5185 6.7019
96 23.0018 26.8289 6.0873
97 32.6749 17.6817 4.2896
98 17.4427 1.1550 4.7931
99 26.2037 29.4630 5.1598
100 36.6367 22.1497 3.8299
101 23.4192 20.0178 3.0310
102 17.9680 28.4909 2.0434
Continued on next page
450
Table B.66 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
103 41.1953 19.2527 2.2057
104 22.9423 30.5933 9.5187
105 28.6802 26.2575 5.4319
106 18.3032 16.7390 7.7339
107 27.3967 31.9736 3.7984
108 28.8918 28.9542 1.0693
109 25.0380 35.4347 6.5406
110 27.7174 17.5615 4.2182
111 35.0382 17.5394 6.8395
112 13.2990 27.6110 8.6138
113 26.7130 30.5586 1.9122
114 8.4067 31.9010 6.2947
115 25.2367 25.0542 6.2414
116 41.0876 23.0342 5.6962
117 32.8428 30.4402 5.0914
118 24.9423 41.3711 9.7003
119 22.1813 32.3715 2.6408
120 29.4022 25.7045 6.0345
121 33.8075 20.2124 6.6383
122 25.1228 29.1646 1.2712
123 38.4563 20.9658 6.7805
124 18.2012 26.9870 8.5435
125 8.3520 31.4854 4.5562
126 18.7651 32.7023 4.9361
127 23.3391 29.9011 1.7639
128 21.8937 36.4828 6.2324
129 17.9386 40.4267 8.8451
130 36.1437 9.1861 2.8622
131 11.5307 10.1776 1.8515
132 20.9015 17.3113 2.6916
133 16.9225 8.3506 7.0105
134 21.0491 22.0242 7.5918
135 19.4486 22.1967 6.6791
136 28.9865 27.0869 5.2139
137 16.3245 27.3847 3.8293
138 18.1612 19.2819 6.7732
139 25.8427 18.2224 6.0582
140 34.0332 31.6117 6.9735
141 9.5456 21.8171 2.1239
142 39.9979 13.5733 7.0662
143 17.6802 25.0859 7.1228
Continued on next page
451
Table B.66 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
144 30.3978 26.7011 9.3711
145 33.7464 21.5748 8.4594
146 36.0258 30.5297 2.6029
147 20.6887 26.8815 9.5432
148 25.2026 23.2263 2.7966
149 23.6469 24.6330 2.9591
150 19.9528 28.8182 1.0767
151 71.3215 69.8804 3.7056
152 66.2088 77.0141 3.4702
153 73.7035 79.5779 6.2780
154 76.0762 78.8970 4.5690
155 79.2452 76.5955 2.6776
156 74.7490 73.0850 4.5353
157 71.1886 70.1732 2.3913
158 79.9695 79.0040 8.4907
159 74.0539 71.7764 2.3478
160 81.7252 78.5135 7.1159
161 74.2516 84.0642 7.7508
162 74.9476 56.2556 1.1340
163 74.2345 90.0373 2.2802
164 67.3230 69.7328 1.2759
165 67.2754 85.9705 8.2783
166 66.9898 87.9299 1.4243
167 89.8736 62.7591 6.9956
168 73.3318 76.4745 5.1043
169 82.8368 100.0000 8.2270
170 77.9096 73.2114 4.2260
171 90.4940 79.0524 1.2280
172 82.7256 77.7574 2.9673
173 64.7753 85.5659 7.3982
174 72.2730 84.0876 5.9403
175 82.4304 67.1129 8.8272
176 77.4015 71.3458 7.6495
177 93.8766 77.8602 1.9291
178 74.6009 74.5133 9.7429
179 62.0678 96.1248 7.6484
180 78.7007 78.6554 1.1247
181 67.4015 78.6460 7.1121
182 75.4120 68.0194 5.3695
183 83.9837 64.1041 1.3125
184 77.5682 81.6179 2.0300
Continued on next page
452
Table B.66 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
185 77.4970 73.3561 1.6896
186 73.3565 80.4096 6.4704
187 73.7798 68.0710 3.1012
188 74.1411 82.4663 2.2781
189 51.6752 59.8876 5.7716
190 78.2773 88.0557 9.3727
191 83.2521 82.0542 6.5521
192 64.1864 75.9180 7.2090
193 62.3169 65.3242 3.1098
194 80.1751 71.6872 2.8616
195 62.4373 77.1191 1.3363
196 61.0050 85.0649 6.9703
197 81.5748 66.3872 5.5653
198 69.5476 85.7929 5.3722
199 85.3742 98.0677 8.7553
200 64.2311 70.8721 9.6896
453
Table B.67: Depot locations and number of vehicles for MS34
Depot index x-coordinate y-coordinate Number of vehicles
1 93.1616 60.0345 1
2 78.3102 8.4997 1
3 68.5687 92.2358 1
4 46.6219 5.3598 1
5 26.0318 52.7025 1
6 56.9268 11.8853 1
7 24.8771 38.0143 1
8 31.9302 81.2833 1
9 91.0802 24.4096 1
10 88.5220 88.4423 1
11 79.4589 71.2647 1
12 92.5810 37.8148 1
13 17.8840 24.8920 1
14 51.7541 25.2854 1
15 62.7005 76.7244 1
16 91.3182 4.9862 1
17 66.3968 68.5289 1
18 38.9193 62.0278 1
19 74.0008 74.6685 1
20 81.7635 97.7256 1
Table B.68: Customer locations and service time for
MS34
Customer index x-coordinate y-coordinate Service time (short)
1 34.7950 28.5498 7.8372
2 28.3145 24.6422 3.2201
3 41.2604 14.6478 7.0864
4 17.4612 20.7921 7.8337
5 19.3154 27.7154 6.2757
6 41.8191 15.7381 8.4020
7 28.7862 28.9015 9.3415
8 24.6491 27.6884 6.7381
9 28.8181 25.8335 1.1704
10 22.7988 27.5120 2.6591
11 22.5668 25.1985 1.2407
12 21.7767 24.8162 9.4150
13 20.3834 24.9270 5.3602
14 17.1356 32.7455 8.1531
15 24.5013 24.2464 5.1115
Continued on next page
454
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
16 20.2110 2.9905 5.4479
17 37.0155 20.9488 4.8314
18 26.9627 26.6331 9.0259
19 33.5115 32.9977 8.8686
20 23.8347 36.5027 6.6984
21 24.3204 17.1545 3.6305
22 35.4854 31.3406 3.6251
23 37.2378 26.9827 3.2095
24 25.2745 23.2636 7.3391
25 39.1040 25.2062 7.9715
26 28.9644 24.7659 8.4039
27 28.0711 26.1697 8.2557
28 43.2667 26.9799 3.2839
29 37.7974 19.4038 8.2045
30 32.5605 16.2917 6.6674
31 28.3522 33.0481 3.0835
32 20.5135 23.1687 4.4297
33 24.0399 36.7878 5.0788
34 40.1833 17.2984 5.5050
35 8.1541 20.0488 5.8651
36 19.6919 36.8440 4.1063
37 23.4266 36.7301 3.6229
38 26.2356 16.4250 7.3318
39 10.1343 26.7209 9.4067
40 29.4089 36.1759 6.3476
41 31.0811 36.1060 6.3378
42 17.1655 14.2925 7.6486
43 22.8393 38.4865 4.3538
44 14.8871 30.5137 5.0794
45 38.5379 26.8946 5.5844
46 28.1126 23.1202 9.3584
47 22.9092 16.9501 5.0571
48 17.2879 25.7918 6.7369
49 25.8222 22.8606 5.1343
50 39.0357 44.2511 5.9840
51 27.2938 26.5838 1.3711
52 27.9441 23.5550 8.2198
53 14.9969 24.8831 7.0436
54 26.3844 19.8938 2.8029
55 31.4680 42.2650 1.1313
56 13.4880 30.3085 7.8685
Continued on next page
455
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
57 34.4023 25.6241 6.1076
58 45.5453 34.3606 6.8879
59 12.0174 24.7239 6.7127
60 7.7779 24.1854 7.6090
61 24.3950 20.3615 8.9859
62 31.3259 19.8708 6.9932
63 24.3195 38.3713 2.0861
64 23.6794 31.4041 7.4236
65 25.0542 25.7244 5.0250
66 16.1283 39.2030 6.7688
67 11.3007 25.1969 6.8401
68 38.1796 27.4170 7.1054
69 27.4385 13.1675 1.5294
70 15.1033 28.9606 3.0156
71 33.9661 12.9390 2.5118
72 14.1886 16.7643 9.3568
73 23.9852 32.9115 5.6371
74 31.1731 27.9269 7.0603
75 17.9940 17.7310 7.0102
76 22.0877 21.6823 1.7332
77 25.2469 27.1370 3.0257
78 41.2698 26.8335 3.5577
79 28.8252 10.7380 9.2239
80 21.6724 14.9520 3.0619
81 23.1218 10.2257 3.2376
82 22.6643 24.3959 7.0866
83 35.8894 10.6574 6.8364
84 22.6302 30.8490 7.3331
85 18.4024 16.6211 8.5339
86 27.0052 15.7798 7.5457
87 24.2113 39.9213 1.1749
88 31.6103 43.0199 6.2537
89 32.9953 18.1727 9.2879
90 34.0592 24.6913 1.8251
91 30.3931 41.3584 5.9910
92 30.2713 20.4978 9.3772
93 40.8606 39.3125 2.7951
94 15.3331 31.8317 5.7279
95 22.1058 25.4627 2.1407
96 10.8745 22.0573 7.7385
97 32.6616 39.1096 3.8320
Continued on next page
456
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
98 25.1794 30.9254 2.6846
99 22.5055 19.7270 9.8236
100 10.6582 28.2727 7.4154
101 26.5286 17.6837 8.4308
102 22.8356 26.2412 7.1490
103 13.7101 37.7657 7.2046
104 15.3546 29.4321 5.7779
105 18.6501 18.6694 2.6997
106 22.9142 27.8999 5.4371
107 11.2603 19.1850 6.0359
108 23.4834 41.8276 8.4545
109 30.1307 10.0525 2.8258
110 21.8610 19.5041 5.7497
111 19.1830 31.4288 8.2703
112 27.5344 18.1638 4.1959
113 34.1757 25.1491 5.9298
114 21.2783 30.4545 7.4569
115 21.1107 35.4808 2.8226
116 13.0348 17.2743 6.7938
117 16.8524 23.5844 1.0008
118 30.0491 21.0694 5.6186
119 24.0529 24.0481 6.1285
120 31.3713 28.0791 1.0633
121 30.5825 19.8449 9.0323
122 28.1315 31.6676 8.4987
123 31.3888 28.5558 7.9765
124 37.6956 21.0639 8.0932
125 29.8069 27.2996 4.3627
126 84.7950 28.5498 2.3708
127 78.3145 24.6422 4.1703
128 91.2604 14.6478 6.8059
129 67.4612 20.7921 9.3874
130 69.3154 27.7154 1.8399
131 91.8191 15.7381 7.6490
132 78.7862 28.9015 1.4974
133 74.6491 27.6884 7.8144
134 78.8181 25.8335 5.1714
135 72.7988 27.5120 1.4050
136 72.5668 25.1985 8.5783
137 71.7767 24.8162 2.4824
138 70.3834 24.9270 2.0357
Continued on next page
457
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
139 67.1356 32.7455 3.4440
140 74.5013 24.2464 3.8295
141 70.2110 2.9905 6.4548
142 87.0155 20.9488 7.0972
143 76.9627 26.6331 9.8888
144 83.5115 32.9977 9.9393
145 73.8347 36.5027 7.8178
146 74.3204 17.1545 3.4755
147 85.4854 31.3406 9.5861
148 87.2378 26.9827 4.6997
149 75.2745 23.2636 2.9496
150 89.1040 25.2062 6.6622
151 78.9644 24.7659 1.1338
152 78.0711 26.1697 1.3897
153 93.2667 26.9799 2.6224
154 87.7974 19.4038 2.8042
155 82.5605 16.2917 7.4742
156 78.3522 33.0481 4.9858
157 70.5135 23.1687 8.6094
158 74.0399 36.7878 4.5081
159 90.1833 17.2984 8.5380
160 58.1541 20.0488 7.7358
161 69.6919 36.8440 6.2547
162 73.4266 36.7301 2.4452
163 76.2356 16.4250 5.7596
164 60.1343 26.7209 5.1640
165 79.4089 36.1759 4.4159
166 81.0811 36.1060 1.8391
167 67.1655 14.2925 3.3323
168 72.8393 38.4865 4.0225
169 64.8871 30.5137 4.3760
170 88.5379 26.8946 2.3163
171 78.1126 23.1202 3.8509
172 72.9092 16.9501 3.5310
173 67.2879 25.7918 8.3811
174 75.8222 22.8606 4.0788
175 89.0357 44.2511 8.8480
176 77.2938 26.5838 3.4123
177 77.9441 23.5550 7.9789
178 64.9969 24.8831 6.4829
179 76.3844 19.8938 1.1617
Continued on next page
458
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
180 81.4680 42.2650 7.3136
181 63.4880 30.3085 1.1418
182 84.4023 25.6241 7.1550
183 95.5453 34.3606 8.9011
184 62.0174 24.7239 4.8863
185 57.7779 24.1854 6.6821
186 74.3950 20.3615 6.2744
187 81.3259 19.8708 3.0467
188 74.3195 38.3713 8.0619
189 73.6794 31.4041 3.5887
190 75.0542 25.7244 9.3194
191 66.1283 39.2030 3.6863
192 61.3007 25.1969 5.8267
193 88.1796 27.4170 4.0028
194 77.4385 13.1675 3.1356
195 65.1033 28.9606 5.9072
196 83.9661 12.9390 1.9692
197 64.1886 16.7643 2.2344
198 73.9852 32.9115 1.8498
199 81.1731 27.9269 3.7980
200 67.9940 17.7310 8.3137
201 72.0877 21.6823 5.6220
202 75.2469 27.1370 8.7983
203 91.2698 26.8335 9.8244
204 78.8252 10.7380 3.9399
205 71.6724 14.9520 2.9766
206 73.1218 10.2257 5.6640
207 72.6643 24.3959 4.1771
208 85.8894 10.6574 8.7353
209 72.6302 30.8490 3.3402
210 68.4024 16.6211 8.5935
211 77.0052 15.7798 6.2452
212 74.2113 39.9213 7.4746
213 81.6103 43.0199 4.0917
214 82.9953 18.1727 1.0835
215 84.0592 24.6913 2.7320
216 80.3931 41.3584 5.5665
217 80.2713 20.4978 1.2182
218 90.8606 39.3125 5.9504
219 65.3331 31.8317 3.4857
220 72.1058 25.4627 7.2662
Continued on next page
459
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
221 60.8745 22.0573 8.9322
222 82.6616 39.1096 1.2221
223 75.1794 30.9254 4.0709
224 72.5055 19.7270 4.7927
225 60.6582 28.2727 1.7201
226 76.5286 17.6837 1.7142
227 72.8356 26.2412 1.6514
228 63.7101 37.7657 9.1031
229 65.3546 29.4321 9.7238
230 68.6501 18.6694 4.5218
231 72.9142 27.8999 3.8223
232 61.2603 19.1850 5.9798
233 73.4834 41.8276 8.1284
234 80.1307 10.0525 8.1848
235 71.8610 19.5041 8.7693
236 69.1830 31.4288 8.1817
237 77.5344 18.1638 1.0574
238 84.1757 25.1491 9.2791
239 71.2783 30.4545 1.1617
240 71.1107 35.4808 1.2647
241 63.0348 17.2743 7.4031
242 66.8524 23.5844 5.8457
243 80.0491 21.0694 5.7213
244 74.0529 24.0481 5.5202
245 81.3713 28.0791 1.5911
246 80.5825 19.8449 3.0704
247 78.1315 31.6676 2.0534
248 81.3888 28.5558 9.9079
249 87.6956 21.0639 1.6346
250 79.8069 27.2996 1.5402
251 84.7950 78.5498 6.9542
252 78.3145 74.6422 4.0965
253 91.2604 64.6478 2.1566
254 67.4612 70.7921 6.7342
255 69.3154 77.7154 7.7184
256 91.8191 65.7381 8.2474
257 78.7862 78.9015 3.4212
258 74.6491 77.6884 4.9058
259 78.8181 75.8335 4.6163
260 72.7988 77.5120 6.4733
261 72.5668 75.1985 7.9308
Continued on next page
460
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
262 71.7767 74.8162 9.4701
263 70.3834 74.9270 2.1832
264 67.1356 82.7455 3.3015
265 74.5013 74.2464 4.4048
266 70.2110 52.9905 9.9436
267 87.0155 70.9488 4.0686
268 76.9627 76.6331 9.0960
269 83.5115 82.9977 3.1373
270 73.8347 86.5027 2.9800
271 74.3204 67.1545 9.9197
272 85.4854 81.3406 9.5599
273 87.2378 76.9827 6.7440
274 75.2745 73.2636 5.5372
275 89.1040 75.2062 4.2231
276 78.9644 74.7659 7.9161
277 78.0711 76.1697 8.0593
278 93.2667 76.9799 1.2603
279 87.7974 69.4038 1.4720
280 82.5605 66.2917 3.9108
281 78.3522 83.0481 8.1972
282 70.5135 73.1687 6.6721
283 74.0399 86.7878 9.8452
284 90.1833 67.2984 2.4242
285 58.1541 70.0488 6.5501
286 69.6919 86.8440 3.7785
287 73.4266 86.7301 1.7657
288 76.2356 66.4250 8.8915
289 60.1343 76.7209 6.3163
290 79.4089 86.1759 3.7281
291 81.0811 86.1060 2.5126
292 67.1655 64.2925 4.0589
293 72.8393 88.4865 1.6070
294 64.8871 80.5137 6.8814
295 88.5379 76.8946 3.1986
296 78.1126 73.1202 7.8213
297 72.9092 66.9501 3.6911
298 67.2879 75.7918 4.7693
299 75.8222 72.8606 1.5025
300 89.0357 94.2511 1.2777
301 77.2938 76.5838 2.6792
302 77.9441 73.5550 3.4382
Continued on next page
461
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
303 64.9969 74.8831 1.5962
304 76.3844 69.8938 4.0014
305 81.4680 92.2650 1.4492
306 63.4880 80.3085 1.9118
307 84.4023 75.6241 1.6468
308 95.5453 84.3606 9.1406
309 62.0174 74.7239 3.8062
310 57.7779 74.1854 6.3259
311 74.3950 70.3615 4.3986
312 81.3259 69.8708 9.5641
313 74.3195 88.3713 7.6816
314 73.6794 81.4041 8.9838
315 75.0542 75.7244 6.3901
316 66.1283 89.2030 7.2067
317 61.3007 75.1969 4.5200
318 88.1796 77.4170 3.0095
319 77.4385 63.1675 2.1813
320 65.1033 78.9606 2.5523
321 83.9661 62.9390 9.4474
322 64.1886 66.7643 1.3103
323 73.9852 82.9115 8.9160
324 81.1731 77.9269 5.7009
325 67.9940 67.7310 8.2742
326 72.0877 71.6823 5.0282
327 75.2469 77.1370 4.1189
328 91.2698 76.8335 7.8144
329 78.8252 60.7380 4.2419
330 71.6724 64.9520 6.0095
331 73.1218 60.2257 8.9985
332 72.6643 74.3959 8.5615
333 85.8894 60.6574 3.1962
334 72.6302 80.8490 4.9206
335 68.4024 66.6211 8.4570
336 77.0052 65.7798 2.3743
337 74.2113 89.9213 7.8216
338 81.6103 93.0199 8.8886
339 82.9953 68.1727 5.5191
340 84.0592 74.6913 6.1324
341 80.3931 91.3584 8.6633
342 80.2713 70.4978 9.8618
343 90.8606 89.3125 8.1119
Continued on next page
462
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
344 65.3331 81.8317 4.1561
345 72.1058 75.4627 5.5171
346 60.8745 72.0573 3.2969
347 82.6616 89.1096 5.5888
348 75.1794 80.9254 1.7076
349 72.5055 69.7270 1.5031
350 60.6582 78.2727 6.7149
351 76.5286 67.6837 6.5521
352 72.8356 76.2412 1.7333
353 63.7101 87.7657 6.4857
354 65.3546 79.4321 5.9020
355 68.6501 68.6694 8.7033
356 72.9142 77.8999 6.7842
357 61.2603 69.1850 3.4447
358 73.4834 91.8276 1.9608
359 80.1307 60.0525 1.5446
360 71.8610 69.5041 6.5969
361 69.1830 81.4288 7.2916
362 77.5344 68.1638 3.4745
363 84.1757 75.1491 4.7977
364 71.2783 80.4545 4.2924
365 71.1107 85.4808 1.7394
366 63.0348 67.2743 1.6279
367 66.8524 73.5844 2.0880
368 80.0491 71.0694 7.1007
369 74.0529 74.0481 2.9704
370 81.3713 78.0791 3.1355
371 80.5825 69.8449 1.0777
372 78.1315 81.6676 7.5440
373 81.3888 78.5558 6.0493
374 87.6956 71.0639 5.9678
375 79.8069 77.2996 7.6803
376 34.7950 78.5498 8.4217
377 28.3145 74.6422 4.5406
378 41.2604 64.6478 2.2235
379 17.4612 70.7921 2.7617
380 19.3154 77.7154 7.4827
381 41.8191 65.7381 7.0267
382 28.7862 78.9015 1.5386
383 24.6491 77.6884 4.4585
384 28.8181 75.8335 5.4211
Continued on next page
463
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
385 22.7988 77.5120 7.9675
386 22.5668 75.1985 2.3303
387 21.7767 74.8162 5.3698
388 20.3834 74.9270 1.6465
389 17.1356 82.7455 8.0870
390 24.5013 74.2464 4.5436
391 20.2110 52.9905 3.1255
392 37.0155 70.9488 1.7251
393 26.9627 76.6331 1.7110
394 33.5115 82.9977 9.3469
395 23.8347 86.5027 2.8424
396 24.3204 67.1545 9.6092
397 35.4854 81.3406 4.0577
398 37.2378 76.9827 9.6397
399 25.2745 73.2636 4.0883
400 39.1040 75.2062 1.5708
401 28.9644 74.7659 6.5123
402 28.0711 76.1697 6.0005
403 43.2667 76.9799 9.1581
404 37.7974 69.4038 2.8110
405 32.5605 66.2917 8.0892
406 28.3522 83.0481 4.1295
407 20.5135 73.1687 9.7494
408 24.0399 86.7878 8.5245
409 40.1833 67.2984 7.4062
410 8.1541 70.0488 2.9341
411 19.6919 86.8440 1.1390
412 23.4266 86.7301 2.8904
413 26.2356 66.4250 5.8282
414 10.1343 76.7209 1.9761
415 29.4089 86.1759 8.6839
416 31.0811 86.1060 9.1977
417 17.1655 64.2925 4.0035
418 22.8393 88.4865 5.2223
419 14.8871 80.5137 1.0261
420 38.5379 76.8946 3.7982
421 28.1126 73.1202 5.3670
422 22.9092 66.9501 3.3595
423 17.2879 75.7918 7.1480
424 25.8222 72.8606 9.2007
425 39.0357 94.2511 6.1345
Continued on next page
464
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
426 27.2938 76.5838 3.3875
427 27.9441 73.5550 9.3562
428 14.9969 74.8831 1.5782
429 26.3844 69.8938 6.6367
430 31.4680 92.2650 9.5345
431 13.4880 80.3085 5.6475
432 34.4023 75.6241 9.6103
433 45.5453 84.3606 3.4482
434 12.0174 74.7239 5.7429
435 7.7779 74.1854 9.2007
436 24.3950 70.3615 2.9322
437 31.3259 69.8708 8.4411
438 24.3195 88.3713 2.2449
439 23.6794 81.4041 4.9398
440 25.0542 75.7244 8.8775
441 16.1283 89.2030 7.3388
442 11.3007 75.1969 5.4732
443 38.1796 77.4170 6.4864
444 27.4385 63.1675 1.7005
445 15.1033 78.9606 3.1729
446 33.9661 62.9390 1.2321
447 14.1886 66.7643 8.6183
448 23.9852 82.9115 1.1338
449 31.1731 77.9269 5.9537
450 17.9940 67.7310 2.0770
451 22.0877 71.6823 6.2915
452 25.2469 77.1370 6.5999
453 41.2698 76.8335 7.7232
454 28.8252 60.7380 3.7894
455 21.6724 64.9520 9.2485
456 23.1218 60.2257 8.0404
457 22.6643 74.3959 1.9094
458 35.8894 60.6574 3.5299
459 22.6302 80.8490 9.1675
460 18.4024 66.6211 1.9998
461 27.0052 65.7798 8.1084
462 24.2113 89.9213 1.9205
463 31.6103 93.0199 7.9115
464 32.9953 68.1727 6.9585
465 34.0592 74.6913 7.9579
466 30.3931 91.3584 9.3878
Continued on next page
465
Table B.68 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
467 30.2713 70.4978 2.5920
468 40.8606 89.3125 1.1838
469 15.3331 81.8317 8.5028
470 22.1058 75.4627 5.2587
471 10.8745 72.0573 1.9778
472 32.6616 89.1096 1.8015
473 25.1794 80.9254 2.0362
474 22.5055 69.7270 2.5118
475 10.6582 78.2727 9.7526
476 26.5286 67.6837 3.5740
477 22.8356 76.2412 6.3912
478 13.7101 87.7657 8.6699
479 15.3546 79.4321 3.2031
480 18.6501 68.6694 7.5445
481 22.9142 77.8999 4.6071
482 11.2603 69.1850 3.7954
483 23.4834 91.8276 6.8842
484 30.1307 60.0525 4.5264
485 21.8610 69.5041 2.0740
486 19.1830 81.4288 9.8068
487 27.5344 68.1638 5.6643
488 34.1757 75.1491 5.5699
489 21.2783 80.4545 3.9252
490 21.1107 85.4808 2.7754
491 13.0348 67.2743 8.7660
492 16.8524 73.5844 3.4108
493 30.0491 71.0694 5.8481
494 24.0529 74.0481 5.9632
495 31.3713 78.0791 9.6693
496 30.5825 69.8449 3.4262
497 28.1315 81.6676 3.3915
498 31.3888 78.5558 3.7899
499 37.6956 71.0639 6.0157
500 29.8069 77.2996 4.4037
466
Table B.69: Depot locations and number of vehicles for MS35
Depot index x-coordinate y-coordinate Number of vehicles
1 52.1650 14.9865 2
2 9.6730 65.9605 2
3 81.8149 51.8595 2
4 81.7547 97.2975 2
5 72.2440 64.8991 2
Table B.70: Customer locations and service time for
MS35
Customer index x-coordinate y-coordinate Service time (short)
1 41.0389 41.3323 3.2119
2 19.4352 50.3338 7.0856
3 87.6474 50.5795 3.3516
4 35.6304 63.3027 9.6534
5 44.6872 33.0219 5.4782
6 71.7948 52.2203 4.8500
7 57.2265 61.9088 6.1101
8 44.2896 27.4769 6.5173
9 0.7980 53.7462 8.2629
10 3.8427 59.8172 8.9271
11 72.4981 54.8959 2.4398
12 0.7980 64.1321 1.8026
13 37.9099 68.6688 3.8182
14 51.0509 7.9000 6.4662
15 38.0876 22.4084 4.4086
16 53.4161 44.8744 9.3299
17 52.0691 70.9520 1.5131
18 25.1717 64.4245 9.9461
19 26.5161 52.9422 7.0026
20 26.3801 36.8097 6.5543
21 38.8084 72.2001 2.3310
22 70.1248 88.8311 1.2610
23 38.0460 74.1516 6.1522
24 22.8294 44.4415 1.2698
25 41.8518 43.4774 7.4038
26 32.7551 42.4720 2.9263
27 37.8852 52.1714 3.2967
28 55.0573 46.9385 9.6273
29 45.1021 57.9359 2.6370
30 63.1214 35.6330 8.1861
Continued on next page
467
Table B.70 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 35.1934 72.6949 1.3604
32 69.1178 42.4162 3.7824
33 67.8145 64.1452 9.7038
34 63.4916 55.5814 3.4029
35 99.0714 40.7869 2.0969
36 26.0270 32.6818 6.4664
37 44.5802 68.6273 6.8082
38 62.5821 28.9890 8.8698
39 27.1617 38.9976 9.0760
40 78.5253 51.1311 1.4786
41 51.7040 53.2537 7.8356
42 54.0241 53.6268 8.7301
43 44.6799 55.0518 5.3355
44 44.7857 49.6159 1.6759
45 64.4147 49.1452 1.8165
46 50.5009 36.2323 2.8019
47 52.7480 24.5504 8.0046
48 39.5382 42.2181 4.6655
49 31.7789 53.4952 8.4434
50 31.5121 39.5802 2.3317
51 64.3942 46.9462 7.5962
52 48.7107 67.1628 2.3490
53 70.2353 34.1796 8.5459
54 68.5583 44.8823 5.9083
55 50.1142 47.7471 9.6505
56 24.4562 41.4126 1.6795
57 62.8278 45.6432 9.4045
58 43.8104 65.6914 4.2348
59 53.7597 52.7056 1.6024
60 31.3774 52.4342 9.6934
61 68.1511 58.8669 6.8451
62 49.4574 21.9649 4.7856
63 40.7912 64.5955 6.3680
64 31.6565 58.0636 4.1238
65 24.2631 61.8667 2.9586
66 48.5678 69.5702 1.3406
67 74.8598 53.2040 2.3808
68 62.3717 54.5678 4.3604
69 67.6930 24.4988 8.8913
70 10.8257 54.1504 4.9703
71 60.2600 67.7369 6.7399
Continued on next page
468
Table B.70 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
72 37.5321 23.2757 4.4903
73 53.2070 29.4220 8.5348
74 35.1898 53.8271 7.8969
75 62.7475 75.1027 2.1303
76 73.3711 57.4105 1.8340
77 73.7063 52.5990 6.9429
78 41.8634 45.3989 4.3990
79 52.9563 54.3527 1.9701
80 53.2676 42.6096 6.6143
81 26.3448 43.4684 6.5944
82 45.1403 70.8446 9.2046
83 46.7031 65.7993 6.4552
84 23.5383 62.3518 5.3681
85 63.4078 58.4636 6.1907
86 38.3896 55.3429 9.8389
87 36.0819 49.7922 5.6671
88 54.0619 99.9800 4.1383
89 46.4055 57.6169 9.8459
90 69.4307 29.2925 9.9281
91 69.1325 67.7784 9.0654
92 48.2521 34.4379 7.6742
93 37.9624 44.1613 6.9826
94 6.9085 50.4834 7.6003
95 61.1148 46.9591 4.9232
96 46.8778 76.0843 4.5967
97 51.3749 51.4090 2.9610
98 82.2170 23.2676 8.9347
99 57.3161 48.3609 9.4786
100 79.9113 49.3104 9.5406
101 35.9937 62.2362 1.9580
102 64.8005 50.5136 1.5218
103 48.3318 46.1275 2.4735
104 59.0755 42.8935 5.7473
105 44.9413 56.2135 1.6277
106 60.0054 53.9409 1.0913
107 41.8339 16.2718 1.8251
108 37.6773 87.6392 6.4669
109 21.4685 12.8426 1.5048
110 53.2354 44.3739 6.9229
111 85.6393 33.3323 6.1824
112 63.9931 77.7361 1.6645
Continued on next page
469
Table B.70 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
113 27.4234 59.8339 3.1741
114 67.8693 54.6344 4.1608
115 33.9841 42.9547 2.1406
116 47.9325 77.8367 7.6547
117 26.0551 42.1394 5.0111
118 82.6817 70.2141 1.1585
119 53.2950 48.8968 7.1354
120 70.1308 39.1274 8.9275
121 1.5332 44.5490 2.2584
122 36.2464 31.9561 8.2977
123 27.0171 33.2320 3.2757
124 67.6363 60.8485 1.2195
125 57.8103 45.7157 5.7765
126 54.5412 65.7396 9.4137
127 31.6929 72.0298 7.9240
128 54.6312 34.5862 4.6428
129 38.3076 49.9992 7.4603
130 84.1969 50.9153 5.3319
131 55.8975 34.8145 4.9706
132 63.7264 40.0903 9.4812
133 76.2843 44.1633 6.2090
134 41.5338 29.1625 8.0525
135 45.3003 34.5035 7.4333
136 49.4420 46.0039 2.2795
137 72.2280 61.5060 7.2363
138 31.2085 60.8592 4.5428
139 44.1637 30.1316 2.1499
140 54.9844 76.8638 6.7681
141 49.6185 50.4077 5.4776
142 54.3666 82.4808 1.5758
143 79.1702 32.9917 5.7118
144 54.7608 35.6381 3.8309
145 63.8561 49.9806 8.6940
146 66.3201 51.1806 1.0811
147 69.2734 91.4381 2.8233
148 58.8926 40.3138 8.9254
149 83.3773 86.5406 2.9624
150 33.9295 88.6547 3.8592
470
Table B.71: Depot locations and number of vehicles for MS36
Depot index x-coordinate y-coordinate Number of vehicles
1 79.7742 29.3295 3
2 59.0776 5.1588 3
3 91.2197 50.4128 3
4 10.1129 76.8376 3
Table B.72: Customer locations and service time for
MS36
Customer index x-coordinate y-coordinate Service time (short)
1 9.0190 22.3647 4.0957
2 25.6813 16.4739 8.2007
3 46.6143 30.2990 6.1398
4 8.3328 6.2406 8.3191
5 6.3837 25.8043 1.7756
6 6.8673 39.6886 2.7292
7 6.7582 15.5750 6.6655
8 43.9370 17.5988 1.5748
9 40.0121 2.6705 7.6867
10 40.1735 4.7900 6.4306
11 14.2257 10.5484 8.1860
12 30.8835 24.3174 2.4454
13 3.4551 9.6952 7.6414
14 4.5063 19.4975 7.8134
15 10.8795 7.4851 8.9318
16 7.9538 15.8212 4.8632
17 48.8113 11.9574 2.6873
18 34.3616 38.1305 3.7273
19 2.6894 2.7788 3.8868
20 4.4697 35.9415 4.9781
21 43.1688 28.1567 4.2570
22 38.1446 21.3713 6.6304
23 1.0241 40.2895 9.4494
24 19.2312 3.7102 3.5821
25 43.3611 12.9909 3.2014
26 40.9409 6.4118 9.2877
27 34.8017 11.6061 9.3359
28 10.8783 48.1214 3.7895
29 12.2379 0.6471 1.6883
30 9.0106 1.4681 8.0279
31 16.2640 36.8391 2.1767
Continued on next page
471
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
32 47.3855 23.7160 5.1533
33 4.6300 0.1055 4.9615
34 10.6586 11.4413 6.4450
35 1.3496 14.2489 2.1432
36 9.0145 32.0794 6.3914
37 21.0427 1.5161 2.1891
38 18.5071 45.7871 2.0380
39 33.5073 19.9137 4.9697
40 19.5194 10.1011 3.4399
41 23.0750 9.0086 9.4970
42 1.0454 24.0823 5.6498
43 7.4820 33.8718 5.0076
44 43.9457 3.3675 3.7773
45 17.0097 5.7980 5.2264
46 0.0010 21.5015 8.0150
47 10.4380 22.3526 2.5193
48 4.7781 9.6800 1.2021
49 46.7110 14.5856 7.3786
50 6.7601 23.2575 6.4463
51 26.3442 5.3498 4.7231
52 37.8426 27.0564 9.2329
53 19.1221 17.7072 5.2946
54 9.9644 3.5684 9.2460
55 28.6453 14.6134 5.4722
56 13.2789 3.2401 9.3480
57 9.5208 6.9149 7.3329
58 3.5666 5.9743 7.2518
59 15.7063 0.6037 1.0413
60 1.5621 43.9228 5.8620
61 31.2948 29.5170 4.7167
62 5.1026 3.6879 6.6532
63 30.4611 45.5063 5.8918
64 16.0161 4.9361 2.9440
65 39.1044 9.4049 5.9689
66 29.5101 26.3770 8.7647
67 45.4839 45.4872 1.0445
68 35.0008 5.0594 2.1258
69 4.7614 13.1710 7.9756
70 42.2930 13.3897 1.1835
71 6.8298 21.9984 2.2837
72 8.3923 4.5641 3.8837
Continued on next page
472
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
73 20.5550 4.5311 9.1428
74 10.1718 24.8259 6.5274
75 0.9845 23.9524 1.1431
76 24.4491 0.4594 3.8025
77 22.9033 15.3989 2.7349
78 32.7459 5.3547 3.4792
79 43.4199 11.0187 1.2404
80 16.2062 31.9216 8.4758
81 4.2830 2.6127 7.8785
82 16.2373 5.0089 7.4904
83 19.1061 8.3339 8.4045
84 9.1273 11.9412 7.8809
85 26.0847 22.2881 2.0851
86 21.7776 35.4280 4.4590
87 42.5100 0.9008 1.2513
88 48.5951 2.7173 1.0117
89 33.2000 10.5451 1.0630
90 14.0208 26.8665 2.5101
91 6.9110 1.2575 2.3539
92 31.8697 42.1127 5.6394
93 43.4850 36.4040 4.7699
94 6.8197 13.4980 6.3443
95 30.9595 11.9390 3.4928
96 10.4144 16.7595 6.3354
97 30.5213 7.2331 6.2663
98 6.5429 8.6691 2.0943
99 21.6973 31.7959 1.7073
100 9.8940 3.7632 1.2886
101 7.2729 43.2513 2.5135
102 41.5940 8.7977 5.7175
103 1.7018 33.2173 8.5723
104 19.9375 18.1504 3.7577
105 2.0047 29.7479 2.7204
106 17.2807 5.0626 1.5861
107 14.2851 0.1449 9.5141
108 47.1688 8.4439 3.2029
109 46.8055 20.0542 6.6286
110 35.5697 8.7003 2.8601
111 3.0111 6.6174 3.1757
112 21.1088 41.9532 7.6907
113 4.1862 3.8583 2.4040
Continued on next page
473
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
114 46.5905 10.2231 8.4086
115 13.3080 28.0475 1.8459
116 37.0914 9.4732 9.8182
117 23.2212 20.1005 6.8790
118 43.5628 7.2177 3.5570
119 8.7598 48.4647 8.8051
120 25.3878 45.9324 1.2713
121 29.9749 46.3469 7.8484
122 1.9481 14.6628 9.0656
123 5.3366 5.3467 6.5699
124 13.6253 36.9264 7.4867
125 8.1693 43.9173 5.1747
126 12.7542 1.9545 7.8300
127 12.9713 2.9057 1.0643
128 24.6718 3.5943 2.7414
129 9.0061 47.4565 1.8231
130 48.4743 0.5615 2.5114
131 37.3291 7.6380 9.4802
132 38.4401 21.3605 8.6449
133 21.3576 10.3348 2.2355
134 13.4956 4.7779 6.9465
135 29.3864 9.9669 1.3464
136 3.5781 45.9078 2.3335
137 33.5129 20.3210 2.6629
138 0.4259 10.8793 6.8083
139 5.1383 21.4401 8.7090
140 15.6375 3.9521 8.6804
141 27.9036 39.6729 5.4463
142 2.0831 37.9973 8.0279
143 8.8350 0.6776 3.4719
144 15.8678 10.9830 9.7064
145 14.2340 39.4914 9.9148
146 6.4858 10.1604 1.7600
147 30.7333 13.0389 3.9681
148 0.6623 40.6097 3.4147
149 42.4900 5.0401 2.9433
150 1.8208 0.9720 7.9032
151 4.1759 9.5689 4.2855
152 3.1650 3.2535 2.3862
153 17.2152 0.8422 2.4852
154 5.3882 29.2629 9.0403
Continued on next page
474
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
155 12.7754 45.7107 9.5121
156 29.0779 12.4924 5.6572
157 19.3420 9.5127 1.1654
158 39.6235 8.2372 4.7738
159 25.4346 16.5240 2.0988
160 2.8085 17.9523 9.5666
161 44.9799 12.9474 3.4316
162 11.6442 37.6640 9.0429
163 13.8795 40.5937 9.0567
164 38.4232 15.0249 7.9798
165 42.3020 6.5779 9.1794
166 14.7270 0.0809 1.1501
167 7.2657 7.2820 9.6336
168 14.9458 18.8345 1.6773
169 8.4122 2.5628 3.5662
170 6.6816 12.6438 5.3931
171 8.5641 3.0027 9.7351
172 13.2728 46.5368 6.1130
173 38.8135 14.9458 3.4657
174 19.7777 6.8718 2.1618
175 13.1784 9.1253 2.3967
176 4.7954 2.4639 3.4193
177 0.0538 43.9622 4.9050
178 6.0936 1.0190 4.5631
179 49.7980 3.6118 4.8272
180 1.8739 23.3020 6.5295
181 24.0568 2.9812 5.0212
182 31.9184 15.4597 1.1082
183 10.1641 48.1637 1.3084
184 39.2015 26.2066 4.5889
185 43.6222 9.3415 9.8151
186 9.1825 42.9943 5.8849
187 4.9034 47.4342 9.2115
188 12.9641 4.5866 3.9174
189 32.2512 4.0187 3.6146
190 20.5264 12.5781 8.9108
191 7.0487 4.8652 8.0123
192 32.4483 7.6408 4.5497
193 10.7959 29.2548 8.9409
194 44.7062 15.5248 4.8310
195 29.4832 13.7544 5.1974
Continued on next page
475
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
196 25.1764 36.4199 4.8244
197 2.7335 41.0966 5.0969
198 45.2873 4.0425 7.2588
199 19.2028 48.3225 1.8602
200 19.1085 27.0841 7.6011
201 11.2283 24.7596 2.1702
202 38.8481 17.1032 5.4688
203 6.6720 12.6355 3.3369
204 38.8033 34.6391 6.3250
205 9.5938 12.9669 3.0486
206 37.0318 7.4794 9.5961
207 32.2740 0.0104 1.5671
208 9.2163 37.3960 2.6492
209 42.9429 6.7387 6.6182
210 6.0265 36.7691 3.6227
211 44.1352 14.3297 2.2347
212 4.4923 1.1145 2.7004
213 42.7408 27.3231 9.6096
214 7.7644 9.5875 3.6695
215 30.8927 45.2695 3.1348
216 17.3215 19.0968 6.9414
217 15.1816 3.0195 1.0387
218 46.0045 0.9042 1.7035
219 3.0166 11.4626 3.7863
220 4.0708 26.7765 3.0157
221 1.6065 23.7561 7.2576
222 13.8411 14.8975 7.3021
223 44.1291 0.6294 8.6663
224 2.9129 6.0595 6.0315
225 41.9891 2.4926 6.1330
226 13.9473 17.5914 5.7783
227 42.3058 25.3982 8.7300
228 27.9444 9.0968 5.0171
229 2.1390 33.4988 4.4504
230 25.9603 23.6112 6.3582
231 21.7085 0.1913 3.7454
232 23.4985 34.3492 1.9100
233 27.7090 28.9818 4.3475
234 32.3947 0.2828 2.9994
235 31.9217 3.6527 6.7890
236 3.7803 17.4303 7.9899
Continued on next page
476
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
237 18.3155 34.1503 4.8703
238 2.4531 13.2466 6.5896
239 38.2611 1.1905 3.5117
240 45.8760 37.1052 5.3024
241 2.3053 12.9027 3.8327
242 18.2156 4.4276 8.4445
243 6.0832 3.9184 7.6885
244 35.8648 31.2882 2.2988
245 37.2541 10.1540 1.6144
246 18.7949 1.8379 5.7892
247 1.3031 4.6243 7.6956
248 35.1105 1.4508 8.5216
249 38.0692 2.8932 7.4860
250 45.3247 7.5599 8.9886
251 19.4413 39.9414 2.4657
252 20.2137 36.7163 2.8112
253 8.0923 6.0108 8.9377
254 17.1003 31.4182 5.1576
255 14.5121 44.8863 2.6834
256 6.3626 16.8787 7.5239
257 7.1482 46.0242 8.9520
258 4.9855 8.0669 8.1821
259 14.9978 5.4557 8.5868
260 10.5791 7.9253 5.8424
261 1.1242 47.8333 2.8863
262 3.1187 9.9059 5.7740
263 4.8621 42.6039 8.5897
264 16.4616 27.9578 2.9381
265 6.5489 35.6746 7.4505
266 3.2425 26.4500 8.7640
267 4.6631 41.4002 5.2414
268 0.8537 31.9150 5.1445
269 12.9078 11.7860 9.4828
270 13.1130 44.9724 6.6551
271 23.4818 29.9927 8.2575
272 8.9016 0.3227 4.6139
273 32.1293 5.6728 3.8925
274 2.9375 16.0538 4.4093
275 45.9375 18.5654 7.4707
276 14.9600 26.4351 2.7376
277 13.2056 6.5299 5.4099
Continued on next page
477
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
278 15.8829 24.7448 2.0869
279 5.8984 44.2562 2.2593
280 26.6171 27.9347 9.5248
281 8.7912 40.4194 6.6785
282 14.2367 37.6549 4.9479
283 22.3641 30.2500 7.3699
284 41.6589 34.4143 5.7668
285 47.2073 9.4177 6.8718
286 5.8836 33.3357 8.0037
287 11.9542 37.0555 6.5622
288 21.7475 8.2030 5.5188
289 16.7645 0.7667 5.3684
290 13.1781 42.2375 1.9913
291 48.0571 1.2658 9.2489
292 9.2182 34.6872 4.8936
293 16.0107 31.9911 4.8430
294 27.2300 0.6074 1.2636
295 12.6867 29.5812 5.5938
296 19.8885 18.2928 9.6733
297 27.2010 39.5708 3.4782
298 25.5365 3.8891 7.6907
299 27.7191 6.7313 2.0512
300 25.4359 19.8745 7.9240
301 0.6944 28.0793 7.8915
302 39.7415 6.8858 5.8669
303 21.9026 8.3624 2.5239
304 25.7489 1.3844 9.3711
305 20.9608 2.6300 2.8739
306 3.4217 41.2010 1.1778
307 19.8822 12.0510 6.4145
308 13.3804 14.1657 6.4663
309 21.0939 13.2731 5.2197
310 47.5111 12.0890 6.3668
311 22.7259 28.1091 7.5111
312 0.2891 43.5601 4.6730
313 13.8065 41.5820 6.3785
314 3.6290 6.8012 4.8314
315 18.1793 17.8726 2.0966
316 41.0530 16.1330 4.1496
317 44.9661 4.5024 5.9207
318 30.2264 39.4266 2.1439
Continued on next page
478
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
319 15.2475 10.4961 1.7335
320 0.9513 1.3206 3.6051
321 21.8227 22.9492 7.0913
322 17.4123 23.4702 5.1134
323 44.1956 2.3539 5.4929
324 23.5427 21.4953 1.5263
325 25.0397 41.7511 1.6625
326 12.1729 39.5863 4.0409
327 8.1792 34.4394 4.0246
328 9.7688 4.6454 9.8646
329 12.4150 46.6579 7.7650
330 36.1974 2.2790 6.8188
331 9.5753 35.2775 8.9458
332 4.6974 1.3756 5.6070
333 18.9884 39.9354 4.3858
334 7.0978 6.1455 8.9539
335 10.6023 36.0305 3.2119
336 13.2196 45.2921 2.4760
337 35.0270 49.7980 6.9274
338 2.6041 49.7980 3.3006
339 26.6209 19.1153 2.4184
340 1.8740 13.1210 3.4895
341 5.1437 21.3023 3.6884
342 7.6110 40.2568 1.0531
343 4.5850 10.3234 3.0579
344 7.3857 8.9217 7.0311
345 47.7539 8.0498 9.8350
346 49.6945 1.8079 3.3053
347 7.6798 44.3286 6.5726
348 22.7053 34.5692 9.7465
349 7.5312 0.0887 5.4295
350 27.4731 18.9858 3.7092
351 16.1940 7.1227 6.3739
352 42.5124 3.0172 5.8904
353 3.9332 10.9580 2.1679
354 36.0805 9.7374 5.9700
355 21.2659 26.9409 2.3416
356 10.2839 0.3129 3.3269
357 10.2117 42.9007 5.7584
358 4.8230 16.0995 8.3204
359 6.5886 27.8575 7.4668
Continued on next page
479
Table B.72 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
360 14.5094 5.3314 5.5074
361 41.7052 13.7572 9.0458
362 1.7779 3.8215 9.5565
363 38.5362 4.3708 5.1612
364 5.5313 35.0337 3.5884
365 39.4204 14.0450 9.3373
366 41.9628 1.5653 5.4670
367 10.7908 34.1470 8.8960
368 32.7596 19.5432 2.9191
369 22.3259 28.9183 2.0296
370 16.1523 6.1949 2.1188
371 3.4786 19.8811 6.1669
372 39.6901 15.8941 5.1974
373 8.5336 26.4159 4.3663
374 0.1892 49.4441 7.7915
375 49.2669 4.3520 5.1004
376 49.1515 8.7166 7.3543
377 39.4992 11.2798 9.3656
378 49.2187 11.2399 8.3842
379 44.7171 11.3066 1.3586
380 19.1115 5.2097 9.6957
381 9.2166 6.3207 8.9917
382 17.9410 37.5483 6.7490
383 17.1773 30.5275 1.0986
384 5.4588 20.0328 9.7953
385 10.8687 38.9877 4.4698
386 45.3523 5.4593 4.5969
387 4.0865 25.1355 5.5926
388 24.5419 35.1849 5.9647
389 37.9184 15.9881 9.6300
390 27.2215 8.2120 8.6986
391 6.9245 7.3509 5.2903
392 10.9128 3.4127 8.9003
393 4.9391 16.2968 4.5089
394 24.9486 26.2158 1.4425
395 15.0806 6.1710 3.7669
396 6.7364 3.6858 3.8819
397 12.0966 8.9202 5.1517
398 14.4414 4.3662 5.3932
399 7.0308 18.2569 7.3607
400 34.2889 9.1539 4.3057
480
481
Table B.73: Depot locations and number of vehicles for MS37
Depot index x-coordinate y-coordinate Number of vehicles
1 0.0139 4.2229 3
2 52.8695 0.4531 3
3 3.7563 0.0022 3
4 1.1959 87.1996 3
5 55.6227 31.4835 3
Table B.74: Customer locations and service time for
MS37
Customer index x-coordinate y-coordinate Service time (short)
1 2.2662 6.7158 9.4730
2 1.1445 86.2278 3.4137
3 3.6360 75.8513 7.7086
4 9.3115 86.1210 9.1817
5 40.0943 4.1422 6.2610
6 13.2562 2.4451 9.1585
7 5.5968 69.7158 1.5101
8 74.2406 0.9265 6.0106
9 89.9352 0.2242 1.0267
10 24.7990 14.1027 2.3784
11 0.2302 74.2355 4.6674
12 23.6375 6.5222 3.1010
13 5.6191 1.0044 5.8178
14 97.3813 0.0488 3.8045
15 2.3597 81.2323 7.3777
16 35.2182 21.9116 6.2835
17 15.3307 5.3793 3.1527
18 0.7213 29.3989 1.5765
19 32.7703 49.7151 1.0303
20 0.0128 3.7090 2.7017
21 0.6274 33.2321 5.4208
22 0.0095 0.8467 6.5482
23 69.3252 88.1184 2.1050
24 59.2269 36.0689 2.1973
25 0.1650 0.4650 3.8276
26 6.9130 8.6807 1.7907
27 0.1738 25.3628 4.6791
28 18.7240 80.4272 3.5409
29 85.5725 14.8314 6.6753
30 1.6853 24.5873 2.9778
Continued on next page
482
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 96.9903 31.5569 6.8883
32 4.2804 78.6835 2.7412
33 0.9067 0.3570 1.8514
34 29.5178 6.6785 9.2652
35 92.2147 3.0511 6.0242
36 24.1455 33.4109 4.7588
37 0.0257 70.6605 1.9940
38 5.2108 11.8133 5.9747
39 0.4595 52.3263 2.0015
40 1.2371 3.4786 3.1242
41 0.0142 16.6265 2.2479
42 73.3276 5.8766 3.9542
43 49.9228 72.1322 4.1180
44 5.1901 30.9080 9.3588
45 57.6044 56.8480 8.9948
46 42.8379 0.1334 8.1104
47 24.0483 2.1771 1.6702
48 6.1206 45.2341 4.7782
49 4.6376 1.0086 4.5705
50 0.0701 0.0040 4.7164
51 3.9888 8.3197 9.7656
52 16.5171 82.2298 3.1411
53 9.7684 1.8003 1.9772
54 26.8901 18.4945 8.2003
55 13.5417 4.6482 1.4033
56 54.0201 0.0019 9.6396
57 0.0918 12.5315 8.2148
58 9.9712 56.5640 9.6454
59 20.5188 1.7370 7.8917
60 0.6557 0.0097 6.4741
61 22.8469 1.4973 9.9014
62 0.0140 28.8454 6.0630
63 19.0831 3.5744 5.4630
64 59.7681 28.6838 3.2774
65 12.4795 0.0002 2.7637
66 8.4619 37.0251 5.4346
67 0.3312 5.9831 7.3980
68 0.0023 0.0038 9.8886
69 43.3231 6.6931 4.0116
70 50.4560 36.7535 2.9815
71 2.5297 78.2086 4.1075
Continued on next page
483
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
72 0.1529 95.2810 1.8245
73 5.2773 95.1083 6.6844
74 56.9504 72.0061 4.4037
75 59.6473 64.8794 8.9863
76 29.4396 51.3847 4.8387
77 88.5123 17.0934 9.0170
78 83.8876 7.3493 3.0181
79 0.1431 0.2054 8.1724
80 27.2460 28.0524 8.7245
81 11.1149 64.4894 4.8439
82 0.0294 2.0706 6.2997
83 72.3597 59.3051 1.8253
84 12.2934 0.0354 3.2552
85 45.8855 5.4350 6.3439
86 0.0220 1.9285 5.6852
87 1.8079 0.3576 9.2265
88 27.5983 25.1239 6.9696
89 0.2385 3.1667 5.4969
90 26.0361 88.2283 6.7132
91 5.7041 12.4008 1.7772
92 44.8924 40.2942 1.3673
93 27.8337 0.0002 7.7641
94 5.5520 22.1833 3.9138
95 2.7005 19.1553 1.5984
96 3.9352 52.6298 9.3093
97 77.5965 28.0970 1.4892
98 9.4985 67.7364 1.6115
99 8.6642 73.4781 6.1618
100 9.3692 0.3528 4.9528
101 84.4664 0.7142 1.2463
102 1.0521 49.4868 1.4473
103 68.7069 0.0224 3.1470
104 0.0008 5.9240 2.1457
105 3.9919 2.6991 6.6730
106 44.9503 39.5738 5.2877
107 4.0284 0.1132 1.9900
108 23.6954 49.7877 4.9189
109 9.2973 47.9550 9.1169
110 0.0001 15.0907 6.0925
111 21.5009 1.6262 7.5758
112 21.7698 0.0357 9.8286
Continued on next page
484
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
113 27.3887 24.5083 6.2939
114 4.0255 0.0015 5.5285
115 12.0041 0.0239 5.7843
116 34.5614 0.2177 6.4566
117 69.9760 9.1499 7.8789
118 0.0167 30.3920 6.4056
119 0.0952 62.7466 7.5033
120 27.4350 12.3838 4.9169
121 44.6068 0.0116 6.8187
122 96.4310 3.0910 2.5903
123 0.1968 26.4153 8.8883
124 4.8418 48.6305 3.2652
125 30.9231 2.4175 4.2084
126 5.3055 12.3408 3.7301
127 64.3761 54.8216 9.7098
128 2.4891 21.0781 2.7306
129 0.2378 15.4357 1.8808
130 30.4347 3.6223 7.2441
131 0.8314 6.9777 1.8642
132 65.5137 50.0578 2.7945
133 42.3831 4.0427 6.4635
134 7.3760 9.9000 7.3874
135 0.0000 4.9764 9.0147
136 0.3339 31.3837 6.4238
137 2.0534 18.3037 8.7621
138 66.4025 27.6883 7.0836
139 21.7354 11.8453 8.0650
140 3.3134 6.3263 5.8298
141 2.2977 10.8862 1.0400
142 8.2492 0.0295 2.7875
143 73.8173 6.9441 4.9485
144 79.1724 91.0112 6.0246
145 12.9012 47.5869 4.4662
146 24.7179 38.7449 6.8217
147 37.2104 44.8840 6.2711
148 0.0014 43.3078 7.8970
149 19.0042 59.9654 2.5717
150 0.0101 45.6812 5.5280
151 7.5436 93.7339 4.4441
152 10.2329 0.1381 9.7948
153 0.0012 6.2135 9.4248
Continued on next page
485
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
154 0.0276 11.9140 9.0346
155 78.8777 1.7192 4.9918
156 15.2396 0.0051 7.7637
157 4.9349 92.5096 9.1846
158 4.8207 38.3331 4.3599
159 0.3469 0.3239 2.0466
160 0.3349 0.3235 5.7261
161 4.3170 35.0140 4.0701
162 3.7922 5.5304 8.6446
163 48.1942 0.0446 2.6761
164 11.5316 6.9346 2.8787
165 10.0414 0.2924 5.7739
166 0.2261 50.9929 1.7586
167 69.6429 80.5001 3.1669
168 30.6942 0.0000 6.7110
169 58.2517 27.4676 1.9997
170 28.2931 31.2401 6.4661
171 95.2523 1.6314 9.0078
172 94.0587 59.9463 5.4162
173 1.5654 2.5401 3.8216
174 24.3638 0.0019 7.8593
175 38.6214 0.0812 9.5907
176 12.3633 50.7950 6.8130
177 61.3753 36.0036 5.3679
178 0.6959 48.0797 4.9436
179 0.1913 24.2880 2.6774
180 0.0000 56.2364 4.9882
181 0.3578 0.0043 5.3931
182 15.2411 6.6664 8.7502
183 13.3146 1.5563 7.4481
184 5.7163 11.1213 6.5830
185 2.9963 68.3423 1.8080
186 0.0000 2.2113 2.0059
187 54.1827 21.5075 6.1803
188 26.0205 0.0018 5.1549
189 9.0120 0.3738 5.9090
190 1.4542 57.9908 1.3421
191 51.8527 0.7403 6.2136
192 55.9417 57.1349 6.6608
193 61.8885 3.8640 5.3373
194 10.2012 30.2269 2.4447
Continued on next page
486
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
195 91.4647 0.0144 7.7894
196 59.5341 39.5947 8.1415
197 0.0485 12.4612 3.6223
198 1.3413 83.9362 5.5685
199 54.6482 2.4332 3.1419
200 6.6839 5.3395 2.7342
201 10.1398 0.1472 8.2783
202 86.1541 89.8215 1.6001
203 89.8647 8.0908 2.7628
204 44.8197 0.0605 9.7730
205 18.9647 36.8103 6.1758
206 76.8387 13.0160 6.2489
207 12.1606 3.5316 9.5502
208 0.4575 42.7850 1.9004
209 3.4645 58.4289 8.9086
210 2.6049 1.6332 9.0231
211 17.4020 15.2637 2.9263
212 0.0307 8.2407 2.5026
213 0.0328 0.3922 6.8151
214 0.4639 21.6520 2.6231
215 85.0458 82.3845 2.0489
216 53.3586 0.1251 4.2880
217 35.8601 72.8955 4.6214
218 91.3366 16.6797 1.8083
219 99.5288 7.8050 7.1539
220 96.2835 0.3538 5.9220
221 0.3381 1.5169 9.8736
222 88.0537 8.9536 2.9147
223 14.9264 15.1235 9.2709
224 0.0407 4.4607 6.9865
225 3.0319 46.2096 7.6913
226 71.7328 68.5385 4.4061
227 58.1698 39.5596 5.2729
228 0.0000 6.7137 1.9564
229 26.2402 22.0545 8.9541
230 51.8135 26.3504 5.0059
231 1.4730 0.2071 7.0141
232 0.0264 12.2166 7.5539
233 1.8222 2.9927 3.5708
234 0.1084 19.3677 6.3432
235 11.3183 84.0187 4.3348
Continued on next page
487
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
236 7.3499 7.7821 8.1607
237 5.5432 0.0036 1.6618
238 69.7310 80.2889 9.9346
239 7.4383 79.1408 7.9843
240 2.2870 4.6001 1.0663
241 0.0112 1.7574 9.0005
242 1.0527 48.7183 8.7771
243 1.3682 13.3889 7.2783
244 0.0025 17.8004 8.9649
245 34.6408 32.1129 5.1908
246 0.0000 0.0789 4.3440
247 22.8010 66.4376 1.7472
248 6.7962 83.8396 9.9750
249 1.5428 0.0901 8.8285
250 27.7755 60.5243 1.0006
251 3.2853 75.2071 7.1198
252 0.1114 0.0001 6.8939
253 15.3616 14.3617 4.7063
254 0.4482 27.5063 5.2873
255 68.9492 5.7131 4.4944
256 29.6017 27.3741 5.0685
257 60.9245 44.3939 1.2408
258 44.3603 19.0791 4.8276
259 52.5585 25.2339 1.9522
260 25.3579 2.1532 1.3880
261 35.8558 59.2358 6.0051
262 32.6604 7.7764 6.5016
263 3.3060 25.1984 7.6495
264 15.0271 57.8982 3.3123
265 66.5782 1.9724 7.5363
266 0.0162 6.4385 7.4193
267 12.5301 17.0266 5.5339
268 8.1050 8.7449 9.0349
269 73.9456 0.0738 8.0145
270 25.0265 41.2464 5.4537
271 94.9967 0.0035 7.8536
272 20.0407 7.9364 7.0034
273 59.4052 0.0052 9.8030
274 10.3039 92.9136 2.0536
275 16.2077 14.2515 8.8239
276 0.5745 75.2652 6.1107
Continued on next page
488
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
277 25.5397 5.6291 2.0814
278 89.2942 69.1868 9.7330
279 15.2285 1.6585 8.5597
280 11.0326 75.1213 1.5608
281 49.9935 71.5862 3.5027
282 0.0797 6.3291 4.6867
283 68.3331 24.4164 6.6413
284 0.0000 18.2861 9.2719
285 13.3848 71.5745 4.7364
286 31.2306 0.9823 7.4035
287 18.1079 0.0000 9.7379
288 10.9530 68.2824 4.9192
289 3.2926 1.2998 6.7184
290 21.7711 1.4682 9.1140
291 76.1431 26.3272 8.8443
292 31.7938 2.8240 2.2844
293 84.8561 56.2784 2.8054
294 0.0973 69.0078 6.5884
295 13.3455 84.4908 7.9753
296 0.1336 5.9683 3.2213
297 16.2112 51.4539 4.3251
298 32.6778 0.3878 4.0699
299 0.3204 24.4335 5.1075
300 47.0114 34.1511 2.5374
301 6.3546 0.0633 7.7105
302 72.4877 14.9873 1.8818
303 2.8947 70.1568 9.0124
304 0.0228 1.8330 1.7388
305 1.0571 1.2942 8.0337
306 0.0568 59.1979 8.6381
307 85.8446 12.1685 5.0579
308 0.0004 0.3537 6.4479
309 0.1508 1.2289 4.1902
310 0.0002 28.4831 7.8319
311 1.0110 17.8404 6.3050
312 0.0001 2.4853 6.5041
313 26.5165 24.0996 8.5885
314 13.8181 36.6916 5.1129
315 1.4804 2.2124 8.9451
316 0.7273 7.0074 5.4422
317 0.0750 4.7519 6.6057
Continued on next page
489
Table B.74 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
318 5.0016 47.7097 6.0595
319 0.0000 0.2487 7.4949
320 21.8931 73.4040 5.9209
321 10.9802 2.4297 8.0600
322 2.9252 12.4669 5.0172
323 41.2569 48.1135 9.2072
324 59.1328 31.0374 1.7793
325 1.8074 0.3362 9.9904
326 13.5986 33.8055 7.5482
327 8.9179 0.2147 6.0257
328 3.9726 84.6446 2.2854
329 59.0889 69.6477 8.5387
330 94.8392 13.6595 7.5272
331 24.5861 31.3613 4.7564
332 0.5957 93.1983 3.4585
333 0.1862 0.1975 3.8324
334 19.5080 42.5671 6.2353
335 3.5461 56.5716 7.2042
336 1.9289 47.7167 8.7748
337 16.6592 0.6955 2.8977
338 0.5882 7.8756 5.5608
339 31.2345 0.0003 4.8254
340 0.0173 3.4419 3.1573
341 0.0040 0.2444 7.8177
342 2.3521 9.1440 8.1272
343 0.0464 18.7419 4.4729
344 73.0392 49.6837 3.8625
345 60.6798 7.3949 5.3283
346 6.1957 15.1025 3.5066
347 0.4845 79.3263 2.4223
348 7.9758 72.6771 4.5587
349 7.2105 16.1730 3.5691
350 38.7044 73.1735 3.1875
490
Table B.75: Depot locations and number of vehicles for MS38
Depot index x-coordinate y-coordinate Number of vehicles
1 94.7922 92.8879 2
2 45.2984 67.2717 2
3 81.0833 37.2332 2
Table B.76: Customer locations and service time for
MS38
Customer index x-coordinate y-coordinate Service time (short)
1 21.9105 30.1033 6.7827
2 35.4233 14.9131 9.6123
3 14.4828 9.6406 2.6770
4 21.5956 28.8237 9.1857
5 31.8399 18.5288 6.1187
6 24.3372 20.9102 2.7416
7 29.8033 29.5865 7.3381
8 39.4795 25.1528 6.8642
9 21.4470 26.3744 3.9871
10 15.8681 34.8692 5.6941
11 38.0190 33.8825 1.2229
12 21.3550 25.0299 1.2005
13 27.6524 20.5694 8.1867
14 20.1503 15.0518 1.9703
15 11.9267 27.6314 7.1993
16 17.1055 44.2756 7.9752
17 35.9353 33.7257 8.1234
18 21.5405 26.8746 7.3852
19 23.7485 15.8509 9.5188
20 27.5003 14.7845 3.6822
21 34.8068 20.5831 9.9624
22 26.2700 1.0320 5.9900
23 22.8459 28.4782 6.9048
24 17.8961 35.3625 9.5081
25 29.8568 25.9215 3.0217
26 7.5974 22.2743 9.8337
27 15.2085 36.2741 2.5356
28 31.1360 21.4355 9.4695
29 28.7239 20.1719 9.6126
30 14.3597 32.7164 2.5751
31 29.4751 25.0459 1.4888
32 28.9122 19.7126 3.4139
Continued on next page
491
Table B.76 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 15.1308 32.1527 5.9141
34 24.4019 20.9935 7.9767
35 38.3507 37.4142 6.4338
36 20.8873 19.7551 3.8449
37 13.7705 20.0504 4.9002
38 26.3230 19.7609 8.5850
39 20.3320 27.9688 6.6352
40 22.0108 35.8757 3.4529
41 28.4180 28.0473 5.6308
42 24.5431 31.4340 8.9956
43 21.8213 35.4611 2.5687
44 16.4023 23.9305 8.3806
45 18.1646 32.9052 2.6307
46 16.4707 23.9625 1.8754
47 19.9570 42.4995 1.2818
48 39.6710 27.1690 1.0916
49 26.2305 20.4543 9.7070
50 20.4220 25.8369 8.9923
51 23.9345 18.8925 1.4472
52 27.0444 12.2987 7.0319
53 27.3006 27.9148 9.7896
54 27.6560 26.9405 2.9824
55 34.0878 30.4500 1.7565
56 22.1343 17.9587 4.2298
57 27.9593 18.2907 7.5986
58 19.8449 20.9104 6.4193
59 9.5087 16.6191 5.0623
60 20.2339 47.4280 9.2152
61 36.8165 28.0961 1.0286
62 22.0450 19.5573 5.5907
63 33.5157 28.5360 2.3001
64 30.0152 35.2461 5.5418
65 20.0229 30.6466 6.1139
66 40.9446 32.6387 6.7795
67 32.2786 29.0062 2.8624
68 32.5215 12.4405 4.0617
69 17.4197 18.6676 3.9473
70 19.6077 33.8320 6.5347
71 30.3870 23.3493 6.3207
72 34.9979 27.1600 7.1913
73 24.7802 29.6244 2.4979
Continued on next page
492
Table B.76 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 39.2661 16.4882 6.8700
75 23.9350 26.5843 7.9177
76 30.9838 21.3768 4.5619
77 25.0281 12.7153 4.5664
78 34.1163 28.2769 7.2291
79 22.2743 17.9660 3.1391
80 24.7385 20.8097 9.5399
81 12.4307 13.8398 2.2218
82 27.5188 19.9753 5.6036
83 25.7478 28.6628 1.3729
84 29.4008 38.0959 3.8117
85 27.8183 15.5704 3.8959
86 19.4222 27.8777 9.5349
87 30.5337 29.3616 2.8661
88 46.7513 33.6997 5.4041
89 19.6545 35.4989 5.0021
90 32.7690 15.7843 8.3876
91 20.1853 25.5114 1.1573
92 17.4298 35.2558 8.0966
93 15.6432 29.5425 5.8671
94 29.7947 36.6665 1.4093
95 25.2770 35.1374 5.6247
96 32.2808 44.5317 5.0106
97 23.4166 3.1665 5.4223
98 15.2053 22.2346 6.9390
99 23.3471 22.1781 5.5483
100 24.3853 13.1365 7.6767
101 70.6564 80.2495 9.4946
102 86.8519 78.1276 8.1939
103 75.4941 66.5426 4.9395
104 83.0049 59.2512 1.8128
105 88.6242 63.0520 9.4021
106 72.5811 77.2995 4.4054
107 71.5865 72.4899 7.8303
108 64.0240 81.3292 8.2341
109 72.6892 71.8338 8.2381
110 69.0442 63.9808 6.3621
111 73.1726 75.8028 3.9249
112 73.1201 84.1754 7.7351
113 68.9303 77.2118 5.2882
114 65.4610 73.4504 5.6403
Continued on next page
493
Table B.76 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 71.8526 71.4922 5.3209
116 75.1219 85.5677 4.8162
117 67.5361 82.6192 2.5842
118 77.9353 71.4196 3.5250
119 73.7989 63.7801 8.8990
120 72.8279 67.3871 8.8647
121 82.5978 77.7777 5.4063
122 94.2182 65.8951 6.4565
123 82.0637 71.7754 7.4592
124 80.3558 73.9797 2.2602
125 75.0393 69.5019 6.2475
126 76.0816 69.7960 2.7550
127 79.8452 73.1141 1.5700
128 70.3918 70.4097 1.5751
129 62.5620 63.8145 9.4588
130 78.5759 81.1382 5.6817
131 69.1511 67.3371 2.3510
132 78.2810 83.6253 6.8193
133 68.0788 72.1383 6.2540
134 64.5549 72.4343 3.8110
135 63.3047 85.7964 7.0493
136 77.3425 77.1757 4.5735
137 91.2878 71.6477 2.9756
138 76.6703 68.1087 3.1674
139 79.0875 70.6899 4.4774
140 76.1984 78.3326 1.3015
141 76.9175 82.0595 4.1205
142 94.7123 75.4001 5.9684
143 68.4894 70.8923 6.0260
144 73.6759 77.7953 1.6013
145 69.3858 80.5935 6.2375
146 80.9504 71.4861 5.2827
147 77.1266 87.0261 6.9574
148 72.2728 71.9643 8.0749
149 81.1842 82.4857 2.7103
150 66.6191 83.0695 9.6536
151 75.9952 75.4719 5.8156
152 76.6703 74.2944 9.2307
153 88.1154 82.2668 6.8110
154 79.4886 59.9695 2.3812
155 75.2755 75.2812 1.4696
Continued on next page
494
Table B.76 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 63.8188 75.5762 1.1355
157 62.7424 78.0466 2.7673
158 79.9219 67.6262 5.7494
159 69.1651 63.2485 2.3290
160 72.9901 53.0135 1.6582
161 67.7549 79.5425 5.9936
162 76.5134 83.9834 9.8315
163 76.8990 71.2972 2.4658
164 89.5393 94.8277 2.4094
165 90.1490 69.6585 2.4730
166 83.8469 64.0727 1.7064
167 84.0332 73.7859 7.4656
168 65.2527 75.8815 5.0164
169 85.6314 80.6863 5.5911
170 67.1536 76.0087 6.4463
171 61.6712 68.6365 8.9476
172 99.9730 62.3081 2.0972
173 77.6556 70.1109 3.6123
174 69.4755 63.6355 1.5611
175 75.0660 81.0300 2.2918
176 75.5751 74.1364 1.6117
177 57.7498 59.5583 2.6658
178 69.0371 78.0466 7.9181
179 79.4110 67.3133 9.0791
180 75.2962 86.2531 5.6644
181 61.1425 75.4350 8.6017
182 70.9042 76.9103 3.0588
183 73.7494 68.4385 4.8554
184 75.6778 79.3585 4.3146
185 61.0102 75.5409 7.2644
186 77.1278 76.8014 9.4994
187 87.7421 72.3311 2.9610
188 61.7273 80.3615 7.7770
189 78.6566 54.6733 5.6785
190 86.1971 76.3807 7.8407
191 78.1696 83.7351 8.9278
192 79.9089 73.4111 3.1373
193 71.0413 79.8178 9.4572
194 73.4568 70.0375 1.2444
195 65.4607 76.4396 6.0536
196 73.9874 70.1335 9.0141
Continued on next page
495
Table B.76 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 70.3949 84.5419 2.5029
198 69.5164 78.9162 4.8272
199 87.0604 86.4661 3.9421
200 74.0245 74.6520 6.1083
496
Table B.77: Depot locations and number of vehicles for MS39
Depot index x-coordinate y-coordinate Number of vehicles
1 21.2953 21.7754 1
2 49.7323 68.2740 1
3 69.4499 49.0436 1
4 70.2105 53.1982 1
5 54.4113 71.3545 1
Table B.78: Customer locations and service time for
MS39
Customer index x-coordinate y-coordinate Service time (short)
1 42.0468 46.2275 4.9494
2 45.7312 44.8848 7.1078
3 63.3112 72.4928 5.1856
4 47.1559 30.7303 9.5794
5 83.9552 46.5681 4.1923
6 44.3386 67.7734 4.0512
7 38.0691 57.0178 9.0627
8 59.0753 31.8632 5.9089
9 53.9218 63.2192 7.7436
10 57.7088 4.9694 2.1239
11 15.1021 41.7902 5.0791
12 47.5000 76.1291 1.6727
13 19.4412 58.3077 6.9701
14 53.0890 63.1935 7.3329
15 62.7498 48.4508 9.2706
16 69.6597 43.6631 6.9406
17 62.5495 61.5986 7.2109
18 58.0680 88.6177 8.6835
19 62.9240 45.5267 5.2111
20 49.0556 73.9503 5.1263
21 49.3583 41.0116 8.2549
22 67.0075 42.8321 8.4229
23 68.1214 60.8456 2.7139
24 42.1528 34.9658 1.2311
25 20.0453 65.7046 1.5113
26 11.7446 21.9456 2.2864
27 22.9570 9.6542 2.5428
28 33.3321 47.3513 6.6326
29 57.4520 55.4814 1.2656
30 37.0693 71.2567 5.2510
Continued on next page
497
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
31 48.5778 51.9945 7.1060
32 56.1565 65.9072 2.0331
33 26.8965 54.0093 3.1246
34 35.8292 61.3249 3.6017
35 37.5103 33.8538 2.5548
36 36.6368 48.7265 3.9134
37 42.6792 40.0368 8.2100
38 63.1197 46.0502 3.6967
39 41.5421 88.2775 7.9806
40 61.5718 26.5974 5.9749
41 55.6721 50.5696 5.9922
42 53.1976 44.6517 7.5758
43 66.2505 56.3230 7.9626
44 85.6693 79.8780 9.1076
45 74.4555 65.2052 2.2435
46 23.5994 39.0514 8.1467
47 58.8319 26.1039 2.7047
48 29.2193 64.1332 1.2608
49 16.4867 33.4647 2.1465
50 29.8215 38.0790 2.2036
51 13.6348 57.7558 2.1548
52 31.1454 24.6259 9.4173
53 72.5716 75.9375 3.4591
54 42.0585 51.7137 9.4841
55 94.6787 46.0985 6.7434
56 56.5136 63.4637 8.8528
57 66.7333 63.4369 4.3037
58 47.5668 45.8472 3.1258
59 45.3404 68.3722 2.6859
60 36.9439 56.1219 5.9108
61 52.6803 68.3334 3.2960
62 25.2844 54.3912 3.7524
63 35.8322 46.8151 1.1399
64 32.1796 79.1458 6.2874
65 52.8056 36.9466 9.6630
66 75.2650 60.5514 8.6486
67 85.9588 83.7065 1.0715
68 20.7383 43.1109 6.7062
69 55.7791 60.5773 4.2336
70 39.0983 55.3259 2.0265
71 31.9754 44.1959 5.8674
Continued on next page
498
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
72 51.7230 49.9408 4.7478
73 42.1356 60.2964 5.6539
74 50.8520 88.8080 8.9751
75 62.8084 64.7738 2.3446
76 34.4087 45.9319 4.9121
77 47.4548 17.1146 1.5313
78 21.6607 54.1510 4.4293
79 43.6125 54.3496 7.5013
80 66.4809 36.8087 1.8561
81 20.9050 66.8222 7.0047
82 56.5142 56.5145 3.6676
83 27.4667 59.7817 6.3871
84 53.6499 41.8969 2.3667
85 42.4951 38.6024 4.9274
86 45.3579 42.2096 1.1141
87 23.2685 31.4903 3.0612
88 34.8155 41.2910 3.3731
89 46.7830 62.1140 5.6025
90 51.1946 12.4109 2.9358
91 46.8114 20.4671 4.1150
92 39.3128 50.4432 7.7304
93 72.1426 55.4749 4.7226
94 46.7589 34.1862 1.5018
95 37.0684 58.9407 4.5103
96 37.3559 70.9837 5.2704
97 48.7400 61.3957 8.4279
98 65.4834 23.9434 3.7328
99 42.9239 37.8239 8.3961
100 64.5261 35.7698 6.0911
101 53.7754 44.3541 1.4894
102 40.6112 38.8119 3.3401
103 36.3796 35.9731 6.3019
104 52.9557 81.8319 5.3176
105 48.2779 44.4505 2.7879
106 34.9168 47.4596 3.1511
107 36.7610 54.7727 8.0217
108 58.9855 21.1296 6.5558
109 58.6944 30.9728 2.2972
110 44.8100 57.8311 7.4452
111 63.7688 55.8565 4.6136
112 44.1677 30.6497 5.1615
Continued on next page
499
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
113 48.0750 68.7610 7.3655
114 70.5804 48.8877 4.6109
115 41.0013 52.3615 1.1295
116 15.9507 51.8214 1.6718
117 28.5187 40.8338 6.3196
118 54.8475 19.4786 5.0140
119 46.4035 47.8187 9.3396
120 95.8557 23.9171 1.8540
121 26.4154 47.2556 4.3788
122 45.9355 53.4558 5.9140
123 50.6708 53.2994 2.0051
124 27.1028 26.8955 9.1402
125 67.9865 56.1100 6.6995
126 62.3989 29.8256 9.1487
127 75.7143 54.1945 6.6750
128 61.4587 60.0534 1.1281
129 -9.1695 76.6401 3.8483
130 33.8824 15.8199 2.0068
131 55.1965 63.8210 6.6652
132 36.4155 47.2974 1.5464
133 54.7228 48.7448 7.0660
134 48.8960 40.6266 5.2970
135 40.8751 53.9026 3.7499
136 51.1343 45.6897 5.6470
137 58.5496 39.6873 7.3633
138 69.0516 41.0232 8.3225
139 35.1009 60.2714 3.8423
140 40.4705 58.1938 3.8017
141 37.9893 68.3437 4.1048
142 64.1316 56.0491 6.9967
143 76.2104 47.5684 8.7496
144 67.5954 31.0271 7.8560
145 72.3502 55.2464 8.8825
146 54.1546 44.8902 8.8411
147 36.6382 53.6919 2.5551
148 61.3291 64.5763 8.6520
149 78.7730 41.7859 9.6363
150 58.4343 41.9623 7.9319
151 65.4869 45.6801 8.8751
152 24.2750 53.5433 1.6067
153 59.5176 83.9490 6.8211
Continued on next page
500
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
154 47.4346 35.4518 3.9169
155 59.2221 72.3321 6.7631
156 71.2797 46.4095 8.9178
157 39.3431 64.9649 4.3627
158 75.0989 50.9951 7.9006
159 34.2768 41.0965 2.5128
160 50.6805 45.6800 5.6775
161 55.1159 65.9812 6.6471
162 67.7804 71.1131 7.4252
163 44.6142 66.0170 3.7576
164 34.4021 40.6040 3.3732
165 73.6102 28.5196 9.2440
166 56.0440 56.6811 6.5353
167 18.1054 58.7997 1.8386
168 55.3320 8.1242 6.6493
169 21.6569 50.4038 2.7283
170 63.1819 84.9260 7.9927
171 73.1194 46.8594 8.7805
172 46.9537 39.2635 4.0022
173 34.8601 33.2039 2.2187
174 70.4488 19.8173 7.8892
175 41.4883 41.8427 3.8675
176 36.3588 55.0238 3.2714
177 28.9705 33.6015 2.8007
178 25.5392 54.2244 1.6211
179 54.5963 63.1328 5.9672
180 44.4709 40.1117 4.6343
181 63.1414 58.2034 7.7510
182 49.0551 59.4247 5.3847
183 46.5052 49.2866 4.4631
184 21.3089 82.6075 1.5527
185 37.0756 28.7966 2.9232
186 51.7405 54.5844 5.8949
187 42.8642 34.5543 4.6958
188 71.2508 37.9706 9.1087
189 19.4762 57.3496 1.5066
190 46.9800 68.2149 4.9916
191 51.9096 52.8351 5.8403
192 37.9607 71.7475 2.2065
193 51.8667 34.4978 5.8685
194 77.6878 55.6360 8.7163
Continued on next page
501
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
195 32.4935 41.1518 2.7822
196 44.1520 37.3774 2.4005
197 26.3487 6.1407 1.5524
198 62.1323 62.6697 6.9497
199 29.8991 81.2475 1.1674
200 35.6968 58.3273 3.6199
201 73.7159 72.9387 9.7644
202 63.7237 50.9830 7.8818
203 37.4005 29.4930 3.1932
204 66.9424 35.4588 7.1390
205 39.0151 36.6222 2.2407
206 51.7671 68.3729 6.6683
207 80.5728 41.9940 8.7131
208 87.6194 51.5240 9.0982
209 42.6141 27.7809 4.1353
210 49.4998 46.9489 5.3768
211 67.3182 22.9022 7.1157
212 60.1252 38.2929 7.3371
213 46.1163 62.6582 5.1480
214 46.5088 78.4942 4.2785
215 36.9329 58.0907 3.5224
216 12.1337 51.6206 1.6858
217 47.3891 67.8877 5.0016
218 30.0355 62.1337 2.4914
219 46.2010 9.1855 4.5887
220 91.1383 20.1406 9.2853
221 50.5648 36.1107 5.6020
222 75.1588 35.4399 9.2273
223 31.4881 23.3295 1.8274
224 71.2595 38.6958 9.9373
225 22.1064 34.4804 1.8679
226 45.3346 68.3370 3.8183
227 54.8459 39.8337 8.0684
228 60.3350 28.7331 6.4216
229 47.9290 43.0622 5.1932
230 31.9629 38.5839 3.6832
231 29.7054 54.3693 2.1986
232 37.9640 46.1452 3.6551
233 33.0139 25.2414 2.4996
234 40.3486 59.6721 3.8539
235 34.1579 43.9341 1.9886
Continued on next page
502
Table B.78 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
236 70.7010 39.9995 8.4888
237 54.4986 35.8034 9.7443
238 54.7245 63.2315 2.9644
239 36.0169 48.1845 7.3547
240 54.6135 24.1198 1.3511
241 55.3835 86.1799 6.5467
242 34.3992 44.3051 7.0243
243 30.1804 54.5176 1.3348
244 17.7511 55.9138 1.0300
245 64.5466 28.2246 2.2822
246 33.1309 70.3524 8.7616
247 50.7790 54.1853 3.4843
248 51.3852 52.3942 5.7852
249 51.5203 72.5107 5.7000
250 39.3633 52.6516 6.1086
503
Table B.79: Depot locations and number of vehicles for MS40
Depot index x-coordinate y-coordinate Number of vehicles
1 38.9519 75.5119 1
2 79.9977 29.5210 1
3 39.9794 64.0006 1
Table B.80: Customer locations and service time for
MS40
Customer index x-coordinate y-coordinate Service time (short)
1 28.3563 21.7206 3.9973
2 1.0010 9.8747 4.7207
3 11.1355 17.5158 4.7291
4 18.0999 20.4391 9.8553
5 14.2392 11.0801 1.5197
6 26.2789 29.6993 4.5689
7 26.2663 27.5468 8.1219
8 19.2241 19.7738 6.3477
9 34.7455 13.3972 3.7861
10 18.4326 22.7059 9.1162
11 22.1201 23.6012 1.8381
12 19.4385 6.8921 3.8712
13 17.5295 35.8951 8.9827
14 25.4551 28.6294 6.9169
15 13.3820 10.3871 7.1607
16 22.3984 41.4840 5.2655
17 31.9194 23.7204 2.2712
18 31.7815 12.7217 9.5583
19 8.7827 17.2830 8.9436
20 28.3893 27.1892 4.9369
21 21.1835 13.0017 8.5146
22 28.7545 21.0538 3.9263
23 26.4343 24.1541 4.3088
24 22.3660 21.4586 8.1536
25 24.8890 26.6972 1.8938
26 30.0659 19.0666 9.5660
27 31.0502 22.9124 1.0133
28 18.7526 26.5894 3.6586
29 13.9387 6.4993 1.4361
30 21.5079 9.0149 4.9847
31 33.5000 16.1077 8.1086
32 27.8568 25.6654 9.2217
Continued on next page
504
Table B.80 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 28.2833 26.6900 5.7993
34 21.3122 18.9073 8.2367
35 18.6195 35.9369 6.0639
36 42.3086 34.4417 7.7579
37 24.1236 23.5241 1.0831
38 24.7229 52.7128 5.2911
39 22.7192 21.9558 3.2530
40 25.5810 33.1949 3.7713
41 22.3374 24.4748 9.7025
42 16.2982 10.6262 2.8792
43 29.1079 40.6653 5.6843
44 36.9982 16.1371 3.0299
45 26.5406 25.6144 6.1048
46 18.7988 41.0068 9.9835
47 25.4702 30.3561 2.1868
48 33.5025 28.0916 9.5921
49 39.8595 23.7882 2.1149
50 13.2896 27.0433 2.6761
51 25.9501 40.7514 6.8185
52 21.3893 21.1587 2.1535
53 29.5383 23.1538 1.7319
54 26.4076 21.2035 6.9330
55 20.0948 21.5663 1.2466
56 9.9401 23.5627 9.8666
57 14.8819 30.1573 5.8540
58 19.9467 25.7351 4.3645
59 22.7191 18.6607 7.3606
60 34.7979 38.7663 9.5267
61 20.0452 17.7536 4.4405
62 28.1003 22.2464 7.2362
63 32.5485 25.6675 6.4186
64 26.9305 10.9816 7.9773
65 25.7066 16.5910 6.3265
66 19.9121 14.2195 4.3856
67 32.0110 2.7975 8.6558
68 38.5718 42.7750 3.0316
69 28.9628 18.9137 8.1726
70 27.5610 32.0005 9.9719
71 26.9614 25.1433 3.5318
72 33.6170 16.7155 7.3934
73 22.2425 24.6634 6.9818
Continued on next page
505
Table B.80 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 20.7317 28.3729 4.7335
75 29.4322 15.4766 5.4844
76 22.4460 34.9842 9.5421
77 32.4319 34.9737 9.5786
78 12.8011 24.1885 7.5963
79 36.0531 30.1196 4.4621
80 18.9115 14.8450 1.3607
81 26.9879 29.7656 6.2464
82 21.1010 23.9307 6.0824
83 30.9464 38.4043 4.1966
84 13.1875 17.0244 8.9218
85 16.1059 41.7626 6.6208
86 38.6032 25.1674 6.6161
87 16.8718 28.7126 3.6617
88 19.1803 37.0794 1.6721
89 25.5193 34.1913 3.6434
90 18.3441 17.7011 3.1127
91 26.2226 17.3730 4.1131
92 34.7994 17.3765 8.6364
93 25.5724 33.9563 2.4433
94 39.3849 23.8692 2.4208
95 12.9188 21.2941 5.5779
96 22.6280 25.6876 6.4297
97 17.7163 33.6314 2.4526
98 28.0708 23.6759 6.7191
99 14.4861 27.5774 8.5955
100 10.3367 5.7050 8.0404
101 69.4368 69.6910 3.3811
102 66.1118 66.5270 3.8323
103 69.6737 84.4089 2.6488
104 68.6503 70.3624 5.0273
105 71.4825 81.2613 3.9401
106 70.9056 61.2937 3.5183
107 80.4812 59.8121 9.3859
108 86.9674 83.3113 4.5972
109 62.2081 79.9442 4.4148
110 89.6070 77.3340 6.3356
111 85.6921 83.0589 1.6166
112 75.7804 75.5633 2.8471
113 88.1675 76.1659 7.5126
114 77.0399 67.7092 6.1763
Continued on next page
506
Table B.80 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 66.4979 75.0792 2.8021
116 84.3987 65.8307 8.5913
117 93.6039 67.5775 4.8136
118 68.5479 71.0231 5.9028
119 66.6545 76.1561 5.7517
120 84.4861 88.3570 2.6660
121 74.8004 78.1461 1.7352
122 63.6347 78.3845 5.1768
123 85.3026 79.5273 1.2750
124 73.7160 85.0306 4.9149
125 68.3733 79.8368 6.0208
126 70.1536 75.5306 6.7490
127 70.8528 71.3913 1.3080
128 82.8119 79.9768 7.3891
129 65.3689 60.9707 2.5239
130 78.9102 75.3478 6.3404
131 83.3701 82.8604 6.4726
132 67.8346 73.1004 7.9512
133 77.7866 79.8068 1.5065
134 61.2211 76.4369 8.6925
135 80.8073 79.8752 4.4586
136 65.6483 70.8878 4.5966
137 81.7197 88.9272 3.9288
138 78.6130 78.3051 5.9985
139 71.5717 76.1751 3.6588
140 62.6678 65.0783 4.2951
141 86.0966 73.3904 4.1414
142 76.2725 62.9533 6.6720
143 88.9775 72.5951 6.9800
144 75.0714 64.7572 9.9289
145 60.1801 74.4670 9.4993
146 89.0839 76.2684 4.1531
147 72.5718 70.9621 2.7370
148 82.7033 88.6075 9.2762
149 68.9813 86.4075 3.5982
150 80.0986 86.7825 5.9577
151 81.9582 79.9227 9.2739
152 83.4424 81.5000 1.8104
153 79.1587 69.5230 3.3193
154 74.6599 76.0985 4.8434
155 76.2040 65.6465 6.1995
Continued on next page
507
Table B.80 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 77.5195 76.9987 9.0957
157 68.8462 84.5180 2.9640
158 79.5869 65.8261 9.7033
159 66.1294 73.2593 4.9058
160 59.1219 62.7827 8.0634
161 76.3880 80.0523 5.7271
162 76.6478 85.2569 3.9815
163 76.8395 84.5288 4.8843
164 89.7737 66.4528 7.4611
165 85.2740 69.0914 9.2459
166 90.5316 74.1487 9.0103
167 76.8363 71.7073 2.2124
168 82.5720 70.6037 2.0792
169 70.0736 53.9622 9.0411
170 73.0752 80.3056 6.8778
171 60.4353 73.0465 1.3625
172 75.5819 80.7780 5.5424
173 82.7248 77.2044 9.0501
174 66.1819 50.1788 4.4716
175 73.1460 72.4891 3.6285
176 68.9660 81.5507 3.1063
177 68.2633 83.7097 2.8085
178 82.5199 72.3565 4.4228
179 75.5606 79.3376 6.3531
180 81.1633 76.9832 3.4155
181 78.3065 82.6823 6.6020
182 82.7983 91.3634 8.2411
183 56.1900 67.4047 1.9357
184 66.4823 92.4995 7.5632
185 73.5676 76.7872 6.8373
186 77.8993 68.3414 5.2719
187 84.5703 68.2472 9.3962
188 69.6698 75.9814 1.8680
189 69.9588 76.1502 6.3920
190 72.6237 78.4243 3.1021
191 80.7935 81.8917 1.2910
192 75.8870 78.0133 6.2187
193 84.3808 66.4624 8.5798
194 68.5672 69.2487 6.0121
195 78.4261 68.6759 8.5589
196 78.2266 70.0796 2.8446
Continued on next page
508
Table B.80 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 61.2999 77.9596 6.5913
198 77.4699 77.8393 2.5662
199 89.4974 73.1038 3.6059
200 65.0185 66.6764 1.1665
509
Table B.81: Depot locations and number of vehicles for MS41
Depot index x-coordinate y-coordinate Number of vehicles
1 71.3316 71.0348 2
2 66.6381 78.9128 2
3 55.2396 73.9919 2
Table B.82: Customer locations and service time for
MS41
Customer index x-coordinate y-coordinate Service time (short)
1 52.5229 33.6356 7.3135
2 18.9956 5.8347 9.5688
3 32.3984 14.7618 7.7411
4 13.0875 27.1115 7.8105
5 17.8149 30.4936 5.8788
6 9.2119 15.5504 3.5386
7 17.7542 13.6559 3.2039
8 39.4605 43.5486 3.5769
9 29.3308 35.5805 9.6682
10 43.0507 56.2817 3.0763
11 50.4623 42.4290 5.8359
12 39.3759 13.9061 2.8451
13 46.2580 0.1800 4.9064
14 45.9164 35.6539 2.2799
15 72.6220 29.5476 4.3803
16 45.9534 42.5760 8.1420
17 8.4667 48.5662 8.3153
18 38.2628 29.9969 9.1341
19 44.4568 35.8131 5.8634
20 49.0443 21.3107 8.3608
21 46.9523 53.3549 7.3757
22 25.1349 34.1981 1.3889
23 33.7949 24.4568 2.3135
24 39.0866 25.7091 3.1000
25 36.9289 63.6379 3.2203
26 67.1499 41.7993 2.5325
27 6.5914 40.3407 3.1155
28 47.5946 38.9488 3.4791
29 53.1071 40.9055 9.5645
30 23.4900 41.2042 4.1200
31 41.5943 33.4396 3.6759
32 31.8500 61.8598 4.6398
Continued on next page
510
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
33 16.1095 29.3428 3.7201
34 35.0112 19.2760 7.8158
35 61.1356 26.4541 4.2377
36 26.6809 53.0494 2.1241
37 43.7920 46.3587 6.5546
38 14.6443 52.8660 4.1997
39 17.9723 29.7641 4.2664
40 12.6826 35.8489 1.6164
41 9.4219 3.0948 8.8045
42 17.6246 49.0933 5.1211
43 18.3393 31.5419 1.6985
44 25.9656 34.2673 9.1443
45 5.9410 50.2249 3.5353
46 24.8858 28.7771 6.5249
47 20.4180 40.5140 6.9567
48 20.1045 21.3692 2.8002
49 28.0527 24.4693 9.6399
50 52.8628 42.3610 6.9860
51 33.2534 29.8038 5.8717
52 40.3505 7.2392 8.8207
53 59.7583 24.3689 6.0134
54 44.7434 81.8252 1.1926
55 35.4898 41.5471 5.3441
56 51.4336 36.9183 8.2719
57 70.4979 26.5164 7.6241
58 24.7173 3.0092 6.1507
59 47.4729 35.5933 1.0809
60 19.7668 0.1800 7.4645
61 12.5256 17.9436 5.0448
62 22.0432 9.0813 6.9366
63 32.1045 29.7784 7.7789
64 0.6378 51.2270 8.2427
65 6.6901 41.9325 1.2624
66 32.3822 25.9389 8.0184
67 43.3427 6.2244 6.1062
68 46.4242 24.4472 1.6850
69 40.6223 13.5737 3.2646
70 30.3366 40.4914 2.2011
71 42.1669 23.5730 6.0803
72 74.8808 56.9457 5.8688
73 66.2802 31.3771 1.6203
Continued on next page
511
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
74 32.3436 8.0190 9.8959
75 56.9072 34.6539 3.2599
76 22.9903 45.2895 3.8393
77 39.1800 25.0677 3.7059
78 35.7404 43.6290 1.3784
79 46.0550 38.9884 5.7511
80 13.0844 39.7408 3.3042
81 43.7376 27.8908 4.6784
82 36.1438 31.2059 9.5276
83 38.8126 31.0955 9.2735
84 16.1898 31.1920 2.0912
85 26.7737 9.0711 6.3275
86 7.5977 33.0289 4.2369
87 21.1023 13.4927 7.4738
88 17.1683 35.4658 5.7120
89 27.5062 13.8926 3.3476
90 36.1540 56.0461 5.4377
91 47.4660 47.0163 8.7025
92 15.5156 24.3468 7.5197
93 38.2270 67.7435 2.7920
94 51.4414 52.3226 2.4156
95 49.3553 47.5566 4.3343
96 6.7592 0.1800 8.7604
97 45.5336 12.2374 7.1629
98 30.5205 21.6287 6.7078
99 56.3568 27.8718 2.2719
100 48.8217 11.4741 1.7137
101 27.5192 44.2513 8.8853
102 37.8237 24.6215 4.7839
103 41.8475 30.5771 5.3890
104 0.1800 24.1909 5.1429
105 23.1002 31.8623 5.6411
106 26.7426 56.2030 3.4479
107 14.2541 2.8255 3.0842
108 0.1800 17.3089 9.0958
109 47.3340 25.4848 9.1783
110 23.1036 42.5790 6.4328
111 52.8693 16.2819 4.2871
112 17.3627 24.5870 6.3873
113 49.2188 45.0581 7.0164
114 45.0574 12.8678 9.0511
Continued on next page
512
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
115 42.6649 50.7935 1.7860
116 16.0334 39.0363 5.8511
117 30.3614 42.8319 4.8560
118 25.5010 33.0852 6.5544
119 17.3352 16.7091 6.0299
120 25.9162 6.6745 3.0327
121 6.3138 35.8897 1.9407
122 30.7101 45.2593 1.0898
123 30.0424 45.4034 1.5324
124 19.4772 31.8992 3.9039
125 43.9556 60.8023 8.0153
126 15.8567 36.4171 4.0193
127 29.1969 26.6169 6.5761
128 42.0819 35.0870 9.9360
129 36.8871 23.0672 6.8321
130 0.1800 44.7922 5.8580
131 20.4597 59.2792 3.0903
132 26.5649 50.6681 7.6585
133 24.1113 37.4710 9.0009
134 10.7839 10.6533 8.7383
135 32.6147 22.7221 6.3735
136 30.5395 40.0507 6.8928
137 54.6599 32.0567 9.2351
138 35.2037 56.3739 4.8986
139 45.0914 44.3476 3.6078
140 31.1601 9.4384 6.6869
141 2.9089 43.8829 3.6588
142 8.7787 44.4768 6.5983
143 20.8099 62.5117 1.4278
144 26.1045 34.7554 9.9515
145 42.9392 37.7169 2.8609
146 19.4257 7.0765 6.4663
147 22.8534 25.6610 4.1287
148 37.5975 8.4408 7.4596
149 23.9658 30.8672 1.2519
150 12.8597 20.3421 1.6016
151 24.0993 11.8654 9.3436
152 21.9954 33.2586 1.7899
153 44.8527 19.3217 3.9916
154 37.0323 54.4630 5.7356
155 42.4322 70.4564 3.2198
Continued on next page
513
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
156 25.6709 35.8777 5.8861
157 68.6119 38.0377 8.0278
158 35.1517 0.6943 5.6969
159 18.0029 58.2899 9.3875
160 11.2732 22.9362 2.3240
161 34.9775 39.8483 4.7509
162 26.5560 29.9784 3.5226
163 10.8018 39.0594 6.3829
164 25.5031 31.8935 1.3283
165 6.1998 35.5115 1.5732
166 44.7070 15.5991 3.9059
167 65.7285 35.5449 1.8854
168 45.6706 8.5272 2.5304
169 27.9470 31.5239 4.3405
170 55.9941 36.3765 1.3579
171 38.1838 28.6926 7.3832
172 0.1800 38.7620 6.7721
173 30.9229 48.0833 2.5665
174 34.6450 6.7667 1.5594
175 42.7036 9.0773 4.6599
176 30.5954 23.0037 5.1676
177 52.8951 40.4701 2.8241
178 11.1934 39.0951 8.8259
179 74.3202 27.4110 6.3815
180 55.8701 43.0017 1.2071
181 29.2204 67.9795 9.0948
182 38.1336 15.3492 5.0765
183 18.7888 19.2319 1.5222
184 17.8207 2.8334 1.9564
185 34.6026 35.5602 9.9858
186 49.7611 46.5799 8.7969
187 48.7640 27.1417 6.5369
188 68.8583 51.5008 1.2425
189 27.9028 29.4740 3.9027
190 29.6164 37.3951 5.1740
191 0.1800 50.2314 1.8912
192 28.1909 43.1319 6.1389
193 35.7685 38.5948 3.9329
194 33.9622 57.1079 5.0544
195 22.5392 18.0990 6.2006
196 11.8765 25.5875 1.6736
Continued on next page
514
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
197 26.4831 38.2700 1.5161
198 70.0091 27.3826 3.7086
199 17.8492 23.9357 5.6955
200 33.3777 45.3397 6.0569
201 14.0396 24.8727 3.1740
202 52.7422 39.9177 9.2145
203 46.4406 30.2771 8.4316
204 36.0057 26.0700 5.0009
205 32.5410 40.9542 9.8386
206 57.9812 38.1850 6.2044
207 42.9628 0.4382 3.1098
208 33.2745 27.6824 8.2953
209 35.6111 15.3564 5.0615
210 58.9831 35.1983 3.2497
211 41.5806 21.3756 9.5989
212 37.8143 33.0973 2.2839
213 42.8095 54.2263 5.6131
214 31.6902 61.6959 9.7473
215 16.8796 46.6424 6.8349
216 39.4601 6.6980 6.5320
217 6.2950 57.7866 5.2269
218 21.7642 51.2512 6.2000
219 50.9657 37.5573 9.2018
220 21.7570 73.8412 4.3860
221 37.8352 25.6508 3.0589
222 29.7455 63.2281 4.8117
223 37.9576 14.8917 3.4624
224 40.3933 26.7128 5.0011
225 24.9846 13.7908 6.6476
226 0.1800 42.7102 5.8118
227 50.3525 39.3990 4.4690
228 24.0347 22.4797 8.8611
229 38.0801 9.8838 3.7031
230 49.4927 0.1800 4.6003
231 15.2933 17.4396 5.6595
232 54.2695 9.4245 1.5564
233 45.6861 44.3514 3.0823
234 35.3730 51.2905 2.0664
235 27.3535 0.1800 1.8890
236 53.4199 4.2102 9.0125
237 40.7631 25.3509 1.3005
Continued on next page
515
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
238 42.2056 49.1223 8.5513
239 78.2147 54.2200 5.5654
240 42.5773 57.8412 2.0234
241 52.9420 26.7268 5.4140
242 32.4886 22.3731 6.3950
243 63.3711 16.1041 1.8119
244 31.7484 42.5155 9.8040
245 16.7501 46.0800 6.8772
246 33.0559 7.8309 5.1502
247 4.7325 31.0029 8.7738
248 54.2933 24.4782 3.3655
249 13.5974 43.3693 8.4157
250 38.0274 52.3982 3.9608
251 48.5725 53.3252 9.4717
252 41.3791 41.4582 3.1970
253 39.5592 26.3547 9.6140
254 18.9254 25.3724 5.5974
255 32.4158 13.7611 6.0812
256 48.8400 52.7391 9.9434
257 20.6070 18.3607 7.9389
258 12.7384 0.8776 3.8242
259 21.6889 19.5498 1.5209
260 47.5740 57.5176 1.3967
261 28.7572 37.5472 8.3165
262 37.0479 27.2207 4.7087
263 4.2528 36.7383 4.4575
264 20.4561 39.8073 5.7081
265 21.6753 40.6324 9.0293
266 12.2345 30.3286 4.6533
267 52.8995 71.4070 6.4395
268 50.6649 50.9706 1.8532
269 7.2131 0.1800 4.0238
270 37.4978 17.4764 2.3036
271 17.2408 32.7918 3.2039
272 30.5709 41.6196 4.4107
273 34.0946 28.5875 3.4329
274 61.8259 32.5689 2.9404
275 39.5073 27.9181 6.7036
276 22.3924 11.3939 8.1974
277 47.1897 68.8294 2.8766
278 47.9333 30.0646 9.0663
Continued on next page
516
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
279 35.6385 72.0776 7.7114
280 70.7039 18.4963 5.8275
281 30.5539 29.0469 9.7297
282 25.6826 11.5193 6.0839
283 42.4366 19.0733 2.9592
284 11.6283 48.3673 8.7199
285 26.4746 45.9294 8.7580
286 24.3320 18.7421 3.8197
287 56.1078 35.8493 3.9429
288 45.1142 25.9934 8.5601
289 43.4595 47.1274 5.4328
290 48.6636 20.5113 1.4671
291 48.3232 59.2629 8.0022
292 33.8786 7.4941 4.8401
293 9.7357 38.1791 3.5197
294 5.3190 8.1163 4.0016
295 33.9630 21.2391 4.3025
296 61.0577 15.4065 8.1531
297 47.1833 59.1470 1.3482
298 50.7942 30.6247 7.5400
299 63.2303 38.7637 8.8542
300 25.2480 9.3015 3.5723
301 22.7728 17.3321 6.9116
302 51.6983 39.1263 3.0870
303 21.3830 31.6147 6.5976
304 70.0004 44.3439 1.6761
305 48.1769 52.6185 9.7008
306 22.7428 18.0102 6.4897
307 27.1083 17.1579 4.4534
308 42.0313 40.9350 1.2751
309 45.2150 31.3197 8.7181
310 52.8068 33.5483 6.4319
311 38.9995 18.5739 8.6306
312 16.4212 17.5236 5.5415
313 34.8858 40.7799 1.0712
314 7.7299 59.3358 9.2717
315 42.9370 27.5581 4.6963
316 42.8677 51.8028 7.5913
317 35.7780 56.1619 2.3599
318 17.9046 51.2000 8.3371
319 54.5523 58.6069 9.1864
Continued on next page
517
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
320 49.7987 39.3130 8.0015
321 21.4690 6.4293 7.8141
322 11.0949 19.6039 4.6468
323 50.0706 30.7573 7.3171
324 43.4752 9.1342 6.0891
325 33.9321 24.5966 6.2626
326 37.5892 54.5783 4.1042
327 44.9527 20.3255 7.3381
328 26.1470 36.7163 2.4478
329 59.2319 38.0214 1.0136
330 39.1108 64.0874 6.0580
331 20.5586 29.1363 5.9184
332 25.1091 44.0893 5.9574
333 58.4089 12.8109 7.2508
334 22.5024 18.7143 9.3474
335 15.6586 38.7758 9.4979
336 52.5788 42.0725 9.1294
337 38.6543 25.4639 6.4370
338 70.0588 37.9122 9.3359
339 28.8682 22.1211 2.0525
340 43.9676 42.9042 4.0672
341 33.0105 21.6275 1.3306
342 40.5376 37.5217 5.8453
343 6.8376 39.2069 7.6351
344 37.4942 57.2147 2.6310
345 46.0518 14.8424 4.8362
346 33.2378 36.8960 1.8835
347 27.3385 4.5599 3.7290
348 33.7651 35.4472 8.0211
349 0.1800 46.4052 5.8326
350 54.0311 15.5470 7.9216
351 39.0357 29.9143 6.7505
352 42.5099 53.8103 9.0383
353 44.2450 60.9298 1.5462
354 38.1135 33.3675 2.5819
355 56.9726 58.0971 4.7470
356 14.6845 30.6908 7.6581
357 32.0885 18.7677 9.0366
358 51.4020 31.6027 1.2327
359 33.0908 4.2900 2.2381
360 44.0488 19.5624 4.8168
Continued on next page
518
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
361 6.3355 22.9796 7.8811
362 39.1458 56.3071 5.7199
363 51.3902 37.0426 7.7903
364 0.1800 67.4024 2.5282
365 29.4059 40.7522 7.0545
366 12.4471 39.2273 6.5679
367 16.1634 29.6045 1.0616
368 43.2139 18.4743 7.6620
369 51.5042 36.1579 9.9256
370 29.8423 27.0644 2.1536
371 24.6796 7.3791 4.2452
372 63.3708 41.9156 2.7197
373 31.8979 30.5835 7.4296
374 39.6768 37.7000 2.6008
375 27.5346 24.6601 9.8816
376 41.7888 44.7566 1.1530
377 12.9639 23.3577 1.3582
378 33.6927 39.2631 8.2390
379 18.5715 44.4699 8.7381
380 30.1396 31.2442 6.0963
381 44.8252 17.9939 7.7870
382 65.9889 37.3107 5.6756
383 25.7993 51.2866 6.2731
384 42.2209 0.1800 2.7166
385 25.7157 35.2334 5.5310
386 34.8241 35.6856 1.4582
387 79.7098 39.1659 1.5049
388 36.3555 27.0221 4.0168
389 23.3842 38.9697 6.6781
390 50.0371 24.0985 9.0278
391 48.7469 37.5883 7.0606
392 7.9720 52.4690 7.1674
393 22.6652 31.8205 7.2617
394 25.8664 15.3463 8.1985
395 29.1056 31.6105 6.9454
396 35.0818 40.5683 5.6794
397 23.9940 28.8296 3.9856
398 40.5574 61.0213 9.4076
399 41.1793 25.9805 3.2183
400 19.2905 26.2487 5.6009
401 39.5987 60.4944 7.6629
Continued on next page
519
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
402 14.6357 38.3107 3.2875
403 47.0815 42.2552 8.6103
404 29.7692 55.5606 5.8434
405 45.3338 22.4136 9.1912
406 16.7755 30.2383 4.1564
407 46.3644 47.8249 9.4179
408 28.7289 20.0557 9.3495
409 32.1226 37.3144 6.2893
410 28.8046 13.9431 1.9159
411 44.5207 41.8219 4.3019
412 63.3787 70.5943 3.4826
413 48.2683 30.6244 3.3949
414 33.8242 26.6289 3.0388
415 20.8737 61.0181 1.0119
416 34.7341 17.6999 9.0371
417 16.7063 27.0568 5.0815
418 31.8774 32.7868 6.2058
419 49.0345 43.4499 3.8404
420 31.8750 15.1826 9.9462
421 53.2129 17.2037 9.8550
422 25.0305 38.4073 9.6809
423 40.6258 30.1810 6.9964
424 38.8341 5.3999 7.5354
425 9.9976 4.6067 4.0064
426 24.6353 4.4646 5.7050
427 50.0820 33.6635 3.4602
428 14.3702 40.8856 7.4654
429 30.7792 44.4511 8.0022
430 17.0958 15.6335 1.7296
431 17.0083 0.1800 2.9942
432 17.9758 43.2039 2.8356
433 47.0523 31.9299 6.6169
434 33.4428 33.0376 7.5268
435 39.5689 26.5651 8.5093
436 24.0801 28.1406 1.1701
437 31.2560 65.0292 2.8191
438 47.2829 30.7692 5.2218
439 11.8754 41.8465 4.4056
440 20.6915 0.1800 4.0635
441 50.3430 8.5443 1.5747
442 61.5738 20.3049 7.8520
Continued on next page
520
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
443 18.9469 35.7799 4.6240
444 40.6547 39.3610 7.0686
445 12.5520 75.1631 5.9597
446 44.2950 4.0444 1.4631
447 35.5521 4.5309 3.7675
448 16.4368 28.6470 9.6890
449 41.8161 18.8429 9.3833
450 54.4084 16.0236 4.4022
451 30.7066 49.2149 6.5590
452 18.3561 26.2220 6.0628
453 14.7006 41.1420 8.4750
454 12.6353 36.7241 9.6193
455 39.9743 6.6558 1.6796
456 38.9899 46.0977 8.9922
457 20.2737 29.0616 6.0620
458 45.9005 22.2974 2.7492
459 15.5736 30.7802 2.9931
460 58.1227 39.8891 7.3519
461 0.1800 51.7493 6.3709
462 28.7704 35.0348 6.2767
463 45.8885 4.5887 9.7164
464 33.5379 47.2388 6.2357
465 34.1512 24.2254 1.8982
466 24.8580 64.0868 2.4994
467 66.0876 43.5006 1.9188
468 25.6611 44.2358 2.3162
469 44.9666 27.6496 7.0441
470 53.5209 19.2792 6.7587
471 27.6707 21.1683 4.3519
472 57.4774 11.7231 2.4659
473 40.7318 19.6054 4.5057
474 8.5366 53.0321 8.1998
475 25.4787 23.3623 4.5981
476 30.9131 32.3405 7.7961
477 43.9654 59.2898 3.6569
478 45.2118 25.0215 6.7601
479 44.9511 29.9759 8.9661
480 9.2167 44.8556 2.8868
481 7.9041 36.6568 5.3232
482 55.7585 41.0434 2.0169
483 47.0574 27.0273 2.1913
Continued on next page
521
Table B.82 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
484 40.2031 30.3851 1.5760
485 59.1032 60.3317 1.7137
486 64.1158 67.0249 6.6426
487 20.4617 32.7607 4.7020
488 34.0317 20.4323 6.7473
489 40.5178 31.8195 8.7090
490 35.3394 23.7096 7.8722
491 36.7134 21.3575 9.7854
492 36.5692 0.4270 8.0338
493 51.4429 7.4985 9.4202
494 0.1800 32.8437 7.6524
495 33.2351 22.5485 3.2826
496 29.1595 55.3714 7.4733
497 25.5216 2.4799 7.2416
498 35.7335 17.8552 7.9599
499 42.2368 41.7127 7.7250
500 28.5843 41.1501 3.8655
522
Table B.83: Depot locations and number of vehicles for MS42
Depot index x-coordinate y-coordinate Number of vehicles
1 19.8222 32.6840 2
2 19.5072 88.0338 3
Table B.84: Customer locations and service time for
MS42
Customer index x-coordinate y-coordinate Service time (short)
1 9.0190 22.3647 5.5939
2 25.6813 16.4739 7.9576
3 46.6143 30.2990 6.1553
4 8.3328 6.2406 9.5847
5 6.3837 25.8043 2.5442
6 6.8673 39.6886 9.1651
7 6.7582 15.5750 7.7700
8 43.9370 17.5988 3.5756
9 40.0121 2.6705 6.6467
10 0.0121 49.3136 5.1655
11 32.8627 14.0979 2.1650
12 62.3673 94.8101 5.9445
13 5.5398 94.5378 9.7256
14 20.0722 41.4347 4.9793
15 32.4169 73.9770 6.3187
16 0.3770 16.1510 1.9987
17 24.6303 39.9337 2.7987
18 41.2569 97.0691 2.4667
19 4.8959 31.3015 1.3319
20 70.0663 87.1594 3.4545
21 94.2987 51.8894 3.0712
22 71.6347 23.4293 4.2269
23 25.6035 40.8361 2.2091
24 7.7772 78.7899 9.9874
25 55.7437 3.9496 5.6217
26 5.6136 15.6314 4.4906
27 91.6510 98.4412 3.2487
28 38.4723 16.1887 4.2828
29 36.0315 43.4092 4.5915
30 2.9792 81.2428 9.3367
31 0.8163 99.0785 5.4593
32 6.5159 42.6622 6.4827
33 73.7143 1.1758 1.0433
Continued on next page
523
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 83.0043 0.1304 6.2896
35 48.9487 38.2037 7.9972
36 52.5889 32.1653 6.9146
37 5.2848 92.5376 5.7548
38 33.1838 55.6673 8.4320
39 65.7118 43.8928 9.6619
40 16.3089 27.3857 3.8236
41 97.7012 6.7545 8.1738
42 0.8100 92.5432 3.5666
43 10.3003 29.1820 1.1341
44 26.1539 0.0916 1.8473
45 0.3673 48.4854 3.9585
46 52.6623 27.0105 3.7501
47 30.9754 0.3485 1.1622
48 28.0222 79.2164 2.4599
49 68.8871 10.9034 4.9959
50 73.7467 5.2763 7.9009
51 62.2567 1.2984 7.1313
52 10.1018 9.6673 7.4308
53 20.4492 5.2181 5.1380
54 56.5847 42.5100 9.2734
55 1.2070 0.4377 9.9005
56 1.2043 7.5862 9.3934
57 7.2837 7.9423 5.1537
58 27.5244 77.4517 9.1443
59 94.6050 19.7429 4.4781
60 50.4681 57.1406 6.4271
61 9.7257 36.3967 6.0429
62 8.4947 61.3506 8.6126
63 72.3108 1.2980 3.5632
64 83.1101 95.7587 6.9699
65 40.8674 72.0116 6.4203
66 6.5214 0.2565 6.9082
67 0.7862 21.7344 3.7894
68 70.2672 10.6050 3.9848
69 34.1896 39.7158 2.6938
70 89.8910 5.3038 1.9062
71 0.3725 33.6267 3.5791
72 34.1805 36.3798 4.1934
73 8.1287 35.9855 5.8219
74 68.5141 20.1088 9.9175
Continued on next page
524
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 3.6476 0.1255 1.2536
76 19.5833 26.4006 7.3858
77 15.4773 16.6244 9.1464
78 68.3225 1.1674 8.7925
79 45.8154 21.1486 2.0725
80 4.3099 20.3295 9.5975
81 10.1191 30.3756 4.9681
82 1.7905 64.8676 8.8818
83 45.0862 49.1191 8.7846
84 32.6031 76.0795 4.1964
85 2.8821 0.2724 6.6803
86 2.1802 4.8260 8.7809
87 22.6652 21.1271 1.1889
88 82.4650 91.8787 1.6914
89 30.4897 62.4172 4.3904
90 0.1085 20.4191 2.3427
91 0.2901 11.1174 1.3069
92 64.8127 0.3492 8.0402
93 20.3739 54.8941 3.9452
94 14.6418 25.6841 8.3573
95 62.3537 3.9970 2.5626
96 13.2705 18.2494 7.0851
97 28.3396 2.8456 8.8804
98 50.6455 56.5045 7.8144
99 75.9471 13.5682 3.0666
100 10.8037 88.7021 4.2305
101 42.2653 0.0295 4.2685
102 95.0306 68.7334 3.4070
103 0.5771 39.2616 4.0357
104 34.4592 29.0248 1.7826
105 17.1302 42.3160 5.0640
106 9.5565 52.7990 5.0920
107 6.9608 0.8928 1.2613
108 57.5726 77.0136 6.7339
109 99.0455 0.0206 1.5351
110 3.4809 8.6614 2.5228
111 61.0188 3.2369 7.1621
112 3.8337 85.8021 5.9911
113 98.4776 0.4649 1.0543
114 64.3624 33.7669 3.5928
115 17.9968 40.5962 4.3895
Continued on next page
525
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 53.1243 42.4152 2.3184
117 24.8356 74.7571 1.6708
118 65.4465 0.3131 5.1467
119 12.7099 66.7252 4.3335
120 0.5365 27.9759 8.4210
121 34.9271 48.2123 5.8378
122 82.8442 4.5116 8.3576
123 3.7545 29.5153 5.1434
124 18.6942 49.3535 1.1263
125 56.1240 91.4767 1.0448
126 0.1535 19.7618 2.4960
127 89.5531 0.7293 4.2934
128 58.3197 0.3288 7.4639
129 31.2280 39.6208 2.4348
130 3.3798 63.3901 3.5089
131 24.7953 47.7745 6.8044
132 26.8164 11.9238 3.5848
133 98.8519 89.6462 3.8974
134 73.0771 27.0598 2.3988
135 92.6221 90.9759 4.4890
136 46.0961 0.5416 9.0616
137 16.2813 4.2862 8.9899
138 87.4186 60.0668 4.5425
139 22.9905 83.5739 7.0791
140 5.3727 61.2386 3.2699
141 15.7046 8.7340 9.5499
142 49.7134 2.3057 6.6221
143 31.1988 71.8952 2.8625
144 57.2490 61.5997 1.9869
145 99.0983 7.3350 6.0926
146 92.6274 5.1898 3.4690
147 28.6297 10.3056 1.6405
148 92.9046 68.8173 2.4260
149 1.3369 67.5984 1.4457
150 0.2647 32.5679 7.1280
151 9.2628 32.6989 8.0358
152 33.6623 8.1806 8.2663
153 28.1923 48.8788 3.3855
154 81.2176 63.4027 9.0631
155 29.2195 19.5001 6.4719
156 18.6607 19.9108 1.1296
Continued on next page
526
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 29.4487 21.6841 4.0963
158 50.7535 7.7863 5.8030
159 0.0278 45.6132 6.6499
160 64.1474 81.6610 5.0206
161 2.0309 82.5419 8.3000
162 22.8938 55.8303 2.3035
163 6.5964 6.7866 9.7735
164 13.6229 47.5600 8.5038
165 43.7933 1.7379 4.0609
166 2.8767 1.5252 6.5462
167 7.7721 3.6444 3.7338
168 3.9292 2.1238 1.8030
169 3.8053 34.2276 5.6937
170 10.6824 0.5382 8.4276
171 77.4995 67.6220 7.8753
172 22.1937 52.2589 9.5288
173 16.3191 85.7213 4.0019
174 3.2124 24.2693 4.5076
175 93.8816 42.8872 2.3537
176 16.6020 79.2320 4.0033
177 71.3159 29.0010 5.9831
178 37.8625 7.9640 5.9526
179 14.1836 95.2493 2.4438
180 76.9448 0.1327 2.0538
181 61.5993 10.6436 4.5870
182 21.6182 94.6756 8.4824
183 66.2558 13.3249 2.6650
184 80.7202 9.5573 5.5071
185 18.4246 1.4620 2.1368
186 11.1776 83.8627 8.7817
187 35.5988 1.8354 7.8998
188 81.3587 11.0302 6.0792
189 49.2897 80.5470 4.5061
190 14.2472 24.9649 5.4112
191 54.0160 37.8580 8.9821
192 91.0312 34.0044 9.1454
193 29.4646 48.7559 5.4855
194 29.1714 0.0860 5.7630
195 9.6789 27.8660 9.1873
196 0.5074 0.1029 6.2074
197 3.3117 68.4164 7.9821
Continued on next page
527
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 0.8647 11.5591 6.9526
199 21.4822 71.6919 5.2269
200 0.0087 6.0550 2.9779
201 83.7272 33.8132 6.4233
202 41.3117 87.9238 2.6583
203 0.0002 0.2284 2.7776
204 0.0923 0.2914 8.7579
205 4.3460 0.0425 2.1308
206 20.6994 46.4413 6.8102
207 1.6197 35.8356 4.9359
208 0.0075 1.3003 6.5134
209 52.8645 63.4007 7.6373
210 12.5398 38.1739 3.7295
211 60.9096 0.4930 1.3867
212 19.0669 0.4800 8.5196
213 19.0580 1.8498 4.3238
214 0.2422 62.2350 6.9521
215 0.2463 0.8537 9.0615
216 0.8299 5.6582 3.4669
217 35.2880 5.9364 9.9811
218 5.8122 1.0988 8.5092
219 70.7902 73.6769 8.1221
220 73.4814 48.7483 6.9095
221 92.8548 53.8378 5.8931
222 23.9023 42.3190 4.4801
223 4.8537 26.6535 8.4001
224 5.1170 10.6529 6.3580
225 28.8141 43.7948 8.0348
226 58.0811 1.3822 9.8891
227 12.0803 2.1850 8.0943
228 21.2735 0.0391 8.6763
229 40.8735 92.9859 5.3705
230 84.1505 94.1624 8.8638
231 2.6106 1.5341 4.0046
232 51.2134 21.8472 2.8479
233 33.3782 43.1247 5.4492
234 18.7748 8.4208 1.2809
235 78.1885 56.9326 8.4482
236 15.4490 31.1496 3.3783
237 3.2032 18.3007 7.0975
238 40.1111 7.1393 8.1448
Continued on next page
528
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 38.9377 56.8118 7.1366
240 10.7546 80.7080 6.8568
241 64.4753 53.0631 3.1361
242 99.8956 16.5511 5.2966
243 96.2318 88.0437 9.4278
244 1.6138 6.5243 3.1699
245 5.3935 28.4263 2.8820
246 0.0558 91.1557 3.4522
247 36.8974 7.1689 7.9824
248 1.2279 6.2542 3.9827
249 16.6023 86.0577 6.4277
250 78.1592 0.4704 2.6561
251 30.0450 8.9641 1.7871
252 13.6163 34.9971 3.7802
253 4.3408 4.1331 3.0779
254 19.4431 40.4347 9.1827
255 91.4311 63.7395 9.4320
256 1.5382 25.1704 1.2869
257 22.1618 42.3556 6.3428
258 73.4271 63.3544 1.3944
259 0.1883 5.4463 4.8241
260 47.8345 36.1007 5.6942
261 95.8413 1.2648 8.5631
262 8.0241 26.6014 6.6253
263 1.7897 70.1977 3.2968
264 46.9608 84.7854 9.1422
265 82.7108 24.8231 7.9057
266 37.3161 7.7068 6.0640
267 80.9969 42.5782 9.0744
268 3.7417 84.1437 4.3127
269 56.9156 25.9936 4.0396
270 11.9896 94.9049 6.5697
271 17.5247 3.8919 1.7821
272 2.4249 1.2362 4.3795
273 67.0762 8.8420 2.6864
274 39.0529 15.7148 8.2947
275 54.5471 17.7035 7.5092
276 64.8206 9.7017 7.0721
277 0.4519 48.1418 9.2258
278 90.4002 0.8440 8.3886
279 24.7583 16.1675 5.9385
Continued on next page
529
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 57.0245 8.7132 1.1399
281 55.1165 9.3940 1.8522
282 69.0776 1.1143 5.6328
283 2.4493 35.2631 9.5723
284 20.9131 7.9935 8.5876
285 38.2048 2.4094 9.4151
286 86.8966 0.0000 9.7607
287 69.7372 8.0426 4.3527
288 80.1783 30.3393 3.8881
289 33.9328 75.8471 8.0492
290 33.9594 0.1785 2.9100
291 73.0898 81.8522 9.6324
292 0.1216 1.7154 9.3721
293 78.3969 69.5104 4.2916
294 16.6244 64.0750 4.1042
295 0.1324 84.2504 7.2341
296 55.6737 1.8852 7.4494
297 2.3972 25.4755 8.2031
298 2.0710 16.3991 6.3430
299 36.7186 3.0127 1.8746
300 6.4760 33.0836 6.0356
301 10.5076 36.7500 1.3878
302 16.1436 4.5987 7.8187
303 16.5139 27.0330 6.9368
304 14.9144 97.8489 6.3951
305 37.1858 24.0017 3.0430
306 2.7853 48.2849 7.4234
307 3.5379 16.9268 7.5205
308 0.8955 0.1209 4.0980
309 10.4449 8.5750 1.2948
310 59.2279 64.2309 8.5925
311 5.4811 12.0064 7.9327
312 54.8141 0.6942 5.5868
313 47.9997 26.1230 7.3627
314 67.9105 13.4567 8.1206
315 68.5547 54.6830 3.9760
316 8.6065 27.5352 9.2231
317 9.5709 64.7254 6.1903
318 27.3560 66.7344 3.5912
319 10.5819 3.5899 3.4018
320 69.1962 1.5300 9.0116
Continued on next page
530
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
321 65.6578 67.4035 4.2949
322 31.0247 40.6913 2.3501
323 6.9150 0.0260 9.5169
324 46.3170 80.2735 6.8575
325 5.4594 26.5611 9.8399
326 20.8324 29.6504 2.7445
327 14.7892 36.7772 8.4587
328 29.0092 57.8263 5.4442
329 98.3476 73.1618 6.3170
330 57.0358 14.6588 1.4040
331 96.1292 0.7165 6.0801
332 5.5123 53.8570 6.7019
333 27.9375 11.0217 5.4829
334 0.2646 70.5179 1.5366
335 57.2860 13.8178 5.6365
336 36.2380 68.5941 1.4788
337 73.4738 3.1159 8.5927
338 97.6692 1.6775 6.3521
339 86.3941 77.4195 7.2192
340 16.7702 0.1943 6.8250
341 0.0000 47.1584 6.6110
342 29.2549 53.8423 9.5847
343 4.3152 19.1120 2.5925
344 4.8085 14.4278 5.2741
345 10.6150 95.9729 8.5816
346 0.9206 15.9196 5.4727
347 55.8807 19.3765 7.8616
348 56.0266 2.4589 2.6189
349 29.5174 10.6298 7.2246
350 11.4333 9.8635 9.2298
351 69.2779 80.0131 2.4639
352 30.5336 6.1021 4.8529
353 91.6889 9.6521 1.3767
354 79.7151 16.7174 3.0317
355 12.7095 50.1279 6.9954
356 29.8555 2.0632 8.8421
357 12.0188 75.9202 4.1026
358 38.7883 0.6915 1.2453
359 63.4611 21.3202 9.1475
360 55.6329 0.0923 5.2396
361 1.5759 56.7311 9.1942
Continued on next page
531
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
362 67.6332 49.0060 3.9518
363 0.0633 4.6016 7.2199
364 17.1751 46.2270 1.1570
365 53.4957 31.0575 5.6111
366 61.0545 72.3655 3.9863
367 13.4899 31.1995 4.0250
368 55.4828 81.3196 9.5801
369 79.6141 17.5995 7.7545
370 5.8856 12.8256 4.0053
371 1.6795 23.9109 6.6955
372 5.0656 6.5517 4.7399
373 12.2510 86.3356 6.1885
374 8.2418 21.7862 9.6355
375 86.0234 6.4520 6.5426
376 0.2633 18.5949 2.3552
377 35.1254 49.3548 8.5444
378 2.6536 16.1869 7.5355
379 70.2924 3.3066 1.9796
380 2.8077 73.3166 2.4522
381 25.2205 34.1291 3.6731
382 99.8659 13.9561 4.8122
383 12.6314 4.9148 5.7557
384 0.2216 4.7958 3.4759
385 4.5651 27.2727 8.4516
386 15.8276 18.7855 8.1351
387 11.1334 54.9532 3.4637
388 5.2717 0.4963 6.5412
389 87.6321 71.7974 1.9140
390 46.6747 46.2237 7.0297
391 92.5663 1.8674 4.1266
392 19.1821 73.6854 7.0255
393 88.4233 3.9934 3.6577
394 0.0034 36.8862 7.1239
395 37.2475 29.4898 4.5440
396 64.1722 2.6349 4.5264
397 5.4280 0.0032 2.8627
398 86.9498 59.5189 7.5207
399 58.2570 58.4900 8.3737
400 68.3019 17.7299 9.3382
401 32.8860 0.3228 5.6271
402 62.8186 34.3100 2.7383
Continued on next page
532
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
403 10.8268 3.0330 6.4261
404 4.9935 53.0873 2.7836
405 9.7585 28.5467 4.6935
406 34.1668 6.4042 8.6777
407 68.8757 84.0993 4.8617
408 8.4368 57.4859 9.3309
409 16.2050 78.6824 4.3577
410 74.3143 0.4733 7.2842
411 37.7905 3.3683 6.2976
412 98.2453 54.3276 1.9078
413 4.1493 48.5412 4.7116
414 68.4275 60.3718 9.3224
415 45.6789 25.1907 1.5000
416 6.1976 18.1048 4.4564
417 22.6372 37.3611 3.1658
418 15.9261 73.2346 3.0503
419 35.9326 44.9969 4.2141
420 64.0837 27.4149 9.3169
421 1.1039 8.9291 5.5225
422 67.4767 49.5572 8.2291
423 70.7426 14.5627 4.1524
424 12.5675 32.2266 5.1281
425 18.4960 78.8297 9.5599
426 32.7458 71.0564 2.1969
427 49.1155 80.7839 1.6328
428 55.1261 88.1727 7.3547
429 57.4388 66.4934 9.3853
430 15.1421 0.0002 1.9801
431 18.4301 0.0010 6.8653
432 91.4595 0.7651 2.3146
433 32.8296 6.7979 7.2457
434 72.2028 0.0520 6.6305
435 7.6367 17.9848 1.3935
436 38.7287 11.6325 8.1813
437 34.6169 29.3064 9.8759
438 92.8271 85.7789 4.9307
439 0.7379 8.9102 4.1027
440 25.0499 11.4301 1.4393
441 27.2056 73.8706 3.0268
442 0.8130 11.5925 6.2291
443 81.8421 1.9077 6.4124
Continued on next page
533
Table B.84 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
444 78.2144 25.7860 3.2727
445 19.2712 73.3860 6.8891
446 61.1090 14.7697 1.5409
447 2.2042 48.3986 9.4646
448 38.4172 39.4264 1.8328
449 6.7925 20.2849 4.0058
450 19.8609 22.4314 6.8594
534
Table B.85: Depot locations and number of vehicles for MS43
Depot index x-coordinate y-coordinate Number of vehicles
1 74.0844 94.6916 2
2 73.7633 51.0100 2
Table B.86: Customer locations and service time for
MS43
Customer index x-coordinate y-coordinate Service time (short)
1 28.3119 10.2175 5.5352
2 1.9369 38.5861 5.7783
3 28.4609 13.5457 4.4121
4 25.1899 57.2641 7.9202
5 26.2727 18.3687 3.5426
6 59.3718 0.0334 6.8435
7 83.6215 2.2595 9.2997
8 86.9774 51.3452 3.9760
9 1.2457 10.0833 8.3210
10 58.8032 41.2004 8.0887
11 1.9156 0.0171 2.1189
12 8.3097 83.9081 2.4165
13 1.6177 56.2041 4.7350
14 0.3844 3.5590 7.1860
15 74.0135 83.8281 6.9193
16 36.7357 21.9723 7.1198
17 0.0378 3.9751 1.0845
18 12.6171 6.8213 2.1575
19 1.0731 73.6742 7.8752
20 26.8085 31.5963 8.5772
21 97.2012 42.2006 7.7225
22 14.2219 27.1965 9.5007
23 59.1214 17.0236 9.2774
24 22.3319 72.9648 3.0077
25 7.5629 0.8962 5.5879
26 15.4122 12.9460 8.0897
27 16.9442 70.0670 5.7021
28 32.0996 18.8434 6.5565
29 57.1275 0.4676 6.0242
30 32.6086 4.7045 7.5789
31 97.9749 9.8793 1.5706
32 15.3021 28.4922 5.4351
33 0.1766 54.7129 3.0693
Continued on next page
535
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
34 81.8217 18.5530 4.0365
35 93.0086 56.4346 5.9647
36 1.2942 46.3350 7.6932
37 56.7097 0.7956 4.7107
38 98.2249 1.3174 5.5686
39 3.4255 4.2194 2.1608
40 73.8741 0.5504 2.9335
41 1.4432 67.4304 3.6355
42 81.8343 23.2767 5.0497
43 41.9178 13.9125 3.1625
44 16.5307 0.7537 3.3694
45 17.2074 11.2917 9.0242
46 11.0435 37.3085 6.2753
47 12.3885 6.7596 9.4481
48 32.1071 3.3257 6.5627
49 74.0015 15.9724 3.2565
50 6.1539 83.7230 1.9228
51 57.4887 0.6028 5.9173
52 12.2179 89.5677 4.9838
53 2.0342 22.3705 7.2236
54 83.8377 77.6420 7.8350
55 0.0779 38.4223 4.5948
56 93.8070 3.5032 6.1067
57 2.7092 57.1391 2.8503
58 2.6990 1.3358 9.4918
59 90.2771 8.2572 5.6153
60 20.6219 38.6699 3.4862
61 0.3230 56.4122 3.0623
62 46.0399 55.8228 9.5764
63 3.7455 5.4176 7.2048
64 15.8883 90.2762 7.3709
65 4.4260 9.9043 6.9123
66 4.0327 14.4189 8.0107
67 90.3327 6.4169 6.2242
68 51.3804 0.0517 5.5291
69 12.0092 37.9563 8.9086
70 26.0452 54.7296 4.5365
71 0.0737 1.5014 3.1837
72 6.3257 3.7599 3.5346
73 18.6761 29.0390 9.1429
74 49.1451 82.6351 7.3241
Continued on next page
536
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
75 55.3373 18.9862 8.6775
76 1.2868 66.0347 4.4082
77 30.6029 21.9315 6.6972
78 3.3861 41.5982 1.2840
79 81.2996 46.9522 9.2803
80 1.9714 7.4670 5.2277
81 94.5505 23.4476 5.6791
82 1.0169 4.3830 7.8968
83 1.0013 63.2832 4.0259
84 22.6475 10.3616 6.6339
85 77.4049 89.7784 3.9421
86 67.6023 3.9532 3.8000
87 8.6373 10.3318 6.8147
88 2.8440 0.2915 4.9032
89 93.1546 82.5267 1.9260
90 5.8642 0.8384 3.1254
91 0.1839 24.0146 9.7460
92 43.1819 14.8299 7.2901
93 13.0868 46.7759 6.9351
94 43.1641 85.1029 3.9349
95 61.3917 2.2316 1.1784
96 4.5710 73.1834 6.1343
97 7.6679 39.6288 1.3270
98 52.0073 14.2588 3.3827
99 17.4364 0.0006 2.7159
100 33.5234 23.2957 5.0437
101 82.4339 0.0090 7.9179
102 95.2523 59.8249 6.6514
103 25.8933 36.2398 3.8323
104 52.0898 9.2071 3.6284
105 43.5921 87.4897 1.7041
106 50.7871 6.3675 2.5475
107 68.7401 33.5936 7.4915
108 36.0885 3.5601 1.8050
109 9.1416 38.4890 9.2603
110 63.4131 46.3669 4.8671
111 11.1338 0.0195 1.7175
112 31.0175 7.9422 6.1493
113 32.1154 34.4354 8.4860
114 68.0230 81.2467 4.1263
115 65.0923 7.0459 8.0190
Continued on next page
537
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
116 14.7133 13.1547 7.3751
117 53.4345 85.7769 6.3185
118 19.3884 77.3506 4.3929
119 0.3049 0.0339 4.5444
120 8.1526 25.3211 4.8548
121 10.2900 95.5675 4.8072
122 0.1650 89.5235 2.9703
123 5.0475 73.8098 5.4709
124 15.3878 1.1348 1.3588
125 0.2704 28.5348 6.0833
126 88.4274 19.2847 1.4423
127 53.4782 25.5574 8.8505
128 0.0177 86.9024 8.7402
129 5.1890 1.0476 4.0443
130 27.5253 50.6139 9.7663
131 10.1825 53.4293 9.5930
132 33.9965 16.4678 9.8976
133 38.4215 27.4703 2.4195
134 61.8943 39.9031 1.0263
135 38.0766 11.8604 3.2336
136 94.1545 0.3819 4.1166
137 27.8445 14.4077 3.1000
138 44.4392 51.4318 7.8030
139 0.0583 63.1737 3.0333
140 19.7630 31.4571 5.0360
141 2.3623 94.6242 3.3350
142 35.0389 1.5330 4.1122
143 28.9424 15.2028 9.1266
144 3.0169 63.4265 1.1143
145 0.0077 23.0480 2.1900
146 22.6626 89.5248 4.4926
147 0.5560 1.8992 8.5656
148 6.8110 31.0322 2.9194
149 18.7117 20.4296 9.4171
150 0.0975 18.7610 9.7282
151 3.0800 10.2147 4.3773
152 0.1631 39.5165 9.8638
153 12.5071 84.9662 2.0988
154 38.4929 29.5555 7.8486
155 27.3974 90.6601 6.2143
156 0.7763 6.8509 6.5904
Continued on next page
538
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
157 97.0513 92.5441 5.4091
158 71.1165 0.2094 2.9841
159 27.9241 6.6372 2.2972
160 20.8857 0.3913 6.7166
161 88.4181 23.6815 8.2217
162 11.6943 57.6226 7.0268
163 1.2180 54.7651 5.2444
164 79.2754 5.8093 9.5003
165 31.6099 0.0044 6.3233
166 51.8069 41.3827 3.0407
167 0.0218 6.1079 7.1546
168 15.3070 79.2014 3.8858
169 55.6890 16.2373 7.7403
170 75.2357 32.4222 9.9833
171 20.7021 7.2513 3.4276
172 2.9651 54.5861 9.3868
173 2.6567 81.9373 7.2675
174 2.7773 30.1441 1.8573
175 63.4069 12.9546 3.2128
176 20.7555 75.3357 9.4119
177 1.5639 29.9403 5.3181
178 77.2641 12.0965 8.9427
179 2.0635 2.9930 8.0137
180 1.0045 47.8758 1.1646
181 61.1735 35.7169 7.9369
182 85.1968 1.3402 7.1722
183 27.6450 8.9653 8.8090
184 2.7216 57.4758 6.2246
185 28.1543 5.7681 6.6349
186 34.3666 50.2786 2.0003
187 24.7261 52.2095 2.9232
188 76.4855 98.7822 1.3273
189 75.2929 39.0986 5.0009
190 1.6777 31.7045 3.9392
191 15.7649 48.4001 3.5856
192 53.9782 50.2879 5.4681
193 1.8278 57.3782 2.6353
194 88.7158 0.4009 9.4041
195 29.4031 1.9547 9.4616
196 7.7167 36.3334 6.3232
197 43.6922 27.1004 1.0073
Continued on next page
539
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
198 35.8538 18.9228 9.1271
199 22.3748 26.0488 7.1460
200 1.1186 53.3175 1.6647
201 4.9124 0.0105 9.9675
202 86.6077 66.6385 3.8301
203 52.0152 1.9139 8.2830
204 38.5182 93.5800 5.1531
205 1.8314 44.6280 6.2843
206 33.6446 6.3128 5.2984
207 57.7786 12.6475 5.9721
208 16.1882 69.0166 2.5778
209 27.1020 0.2284 6.2852
210 1.0293 20.8602 2.3932
211 0.4263 56.0382 5.0091
212 3.3165 17.7601 5.8386
213 8.4734 0.7144 5.1571
214 6.5936 1.0900 8.5070
215 1.0058 26.7799 9.9656
216 87.3777 31.0539 9.7502
217 44.1014 47.3681 7.7134
218 99.1349 89.2432 2.7996
219 2.9551 6.0618 1.3270
220 24.2620 75.3515 2.6974
221 40.1750 41.4836 6.1979
222 59.8086 36.4972 6.6545
223 21.6382 1.3105 4.2830
224 50.4832 95.7972 6.7290
225 86.7933 2.4311 9.0216
226 83.7279 50.6843 3.2817
227 86.7991 56.1986 3.5772
228 34.8317 26.1755 2.1288
229 76.8460 7.3421 5.7572
230 31.0231 63.5821 8.3869
231 1.0213 61.4223 3.6980
232 41.7783 0.0560 8.0891
233 77.4087 16.5457 4.9331
234 18.5665 48.3854 5.9549
235 1.5617 0.1043 9.8750
236 42.4355 1.0822 7.2080
237 91.7915 65.6059 9.7312
238 73.5581 99.6405 1.8637
Continued on next page
540
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
239 85.2681 8.3080 9.0828
240 6.7326 1.7496 1.5260
241 29.5365 77.7381 2.1099
242 11.0059 92.3477 6.6765
243 9.0453 16.1448 4.3309
244 18.3735 15.6568 3.8762
245 13.7869 23.3838 8.1612
246 1.4942 98.5042 3.7153
247 11.4006 9.6762 6.4672
248 1.5522 0.2914 5.1578
249 28.3538 1.5993 3.6333
250 73.7304 78.6279 8.4918
251 86.8373 41.6581 6.1347
252 8.1657 57.4660 1.6346
253 47.8883 19.3307 3.3968
254 10.8133 14.9980 2.5379
255 12.0811 48.8868 6.0428
256 21.9915 4.0747 2.8188
257 8.1164 4.1762 5.4313
258 24.5213 4.7921 7.5643
259 26.2145 42.1073 9.5950
260 25.2166 89.4353 7.8613
261 0.4099 8.4853 1.7206
262 37.2977 0.0050 9.4442
263 77.9433 70.1446 9.7703
264 57.6956 78.5765 6.4640
265 9.9283 0.7591 9.6175
266 2.5839 26.8679 3.9759
267 0.0891 2.1961 9.1109
268 61.5959 3.6133 1.0033
269 5.7435 66.1360 5.3495
270 17.2970 56.6708 2.3273
271 35.6467 89.4559 3.8349
272 24.0060 15.2911 2.5424
273 25.4375 4.9625 6.3362
274 12.1544 23.9058 6.9185
275 6.5687 94.5270 4.1407
276 48.7269 0.0092 1.4832
277 82.8806 24.9061 1.4245
278 3.0288 44.6227 1.5027
279 37.2604 68.2469 1.6436
Continued on next page
541
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
280 5.0488 14.0148 1.1411
281 67.3435 18.0510 9.7631
282 79.3237 6.2008 7.6132
283 0.8995 71.6530 7.7715
284 1.5289 41.3723 1.2998
285 0.0000 73.2820 2.0585
286 1.8427 2.2318 3.3517
287 92.7605 43.8416 9.0402
288 20.7314 52.5340 9.7486
289 0.0006 98.8014 9.9467
290 23.9113 3.9239 4.1211
291 1.5999 25.2598 3.6307
292 86.4488 21.3589 2.6852
293 0.0155 1.6664 7.6883
294 0.5973 7.6816 7.4622
295 18.9869 11.0167 2.7001
296 32.3235 67.4324 4.9054
297 43.8450 20.2054 1.4103
298 7.7995 0.1610 6.8993
299 97.2875 16.3198 8.0294
300 39.1801 3.6645 8.7661
301 0.5978 0.0239 8.0682
302 20.5681 1.3013 4.9014
303 27.6795 61.8052 4.1304
304 25.3475 93.1939 1.4985
305 47.7521 30.1265 8.3750
306 0.2417 97.2601 1.9544
307 0.0324 27.6980 1.0547
308 23.6621 0.2382 3.4754
309 0.0055 56.4073 9.4849
310 29.6106 37.6477 7.0683
311 32.9429 32.3268 4.4709
312 61.9031 2.8599 8.7125
313 65.0846 3.0749 7.0734
314 2.7971 29.9211 6.4729
315 7.4727 38.3706 4.9548
316 22.1139 0.5495 9.6516
317 2.9213 6.7162 8.4062
318 23.8267 6.8836 1.0945
319 20.0738 0.2818 2.2746
320 61.8921 24.0002 5.3453
Continued on next page
542
Table B.86 –Continued from previous page
Customer index x-coordinate y-coordinate Service time (short)
321 16.9892 4.3314 6.2256
322 73.4855 30.0114 3.6369
323 89.8280 2.2741 4.9498
324 10.0294 37.1575 4.5844
325 15.3226 6.8447 2.2357
326 60.8937 0.0555 9.5749
327 35.2504 22.7244 4.2404
328 13.6968 32.4997 8.5328
329 19.7751 62.8598 1.3720
330 76.1118 45.7786 4.8145
331 69.0231 79.0552 1.6807
332 99.8002 39.0362 3.8243
333 33.8535 44.9029 9.5138
334 26.1647 43.2826 8.6905
335 70.5820 3.3446 2.5618
336 11.0997 21.9319 5.8230
337 96.4480 22.9324 3.6540
338 77.4971 5.0936 9.1258
339 0.2292 77.3938 1.7325
340 0.0583 14.0288 8.0873
341 93.9127 42.6868 2.5697
342 25.6156 44.2731 7.4799
343 1.8845 18.0951 3.0881
344 57.3236 1.8513 2.8642
345 2.7466 64.2301 2.9452
346 3.4748 10.7288 9.7900
347 13.7661 0.9637 4.4366
348 99.5529 64.1349 6.7176
349 38.4742 49.2405 1.4191
350 0.9138 25.3492 3.0886
543
Appendix C: Min-Max Single-Depot Vehicle Routing Problem test
instances
In this appendix, we present the problem data for the Min-Max Single-Depot
Vehicle Routing Problem used in Chapter 4. These date are modified from [25].
There are 21 instances. Each instance has customers located on concentric circles.
The instance differ in the number of customers per circle (A) and the number of
circles (B). Table C.1 gives the specification of each instance. The number n gives
the number of customers, i.e., n = A × B. The number m gives the number of
vehicles. All customer require service time equal to 100.
Table C.2: Min-Max Single-Depot Split-Delivery VRP
instance SD1
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 0.0000 100.0000 100
3 -100.0000 0.0000 100
4 0.0000 -100.0000 100
5 200.0000 0.0000 100
6 0.0000 200.0000 100
7 -200.0000 0.0000 100
8 0.0000 -200.0000 100
Depot 0 0 N.A.
544
Table C.1: SD instance specifications
Problem A B n m Problem A B n m
SD1 4 2 8 6 SD12 8 10 80 12
SD2 4 4 16 6 SD13 8 12 96 12
SD3 8 2 16 12 SD14 12 10 120 18
SD4 12 2 24 18 SD15 12 12 144 18
SD5 8 4 32 12 SD16 72 2 144 108
SD6 16 2 32 24 SD17 8 20 160 12
SD7 4 10 40 6 SD18 16 10 160 24
SD8 4 12 48 6 SD19 16 12 192 24
SD9 12 4 48 18 SD20 12 20 240 18
SD10 16 4 64 24 SD21 72 4 288 108
SD11 4 20 80 6
A: number of customers per circle
B: number of concentric circles
n: total number of customers
m: number of routes
l: number of longest routes
Table C.3: Min-Max Single-Depot Split-Delivery VRP
instance SD2
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 0.0000 100.0000 100
3 -100.0000 0.0000 100
4 0.0000 -100.0000 100
5 200.0000 0.0000 100
6 0.0000 200.0000 100
7 -200.0000 0.0000 100
8 0.0000 -200.0000 100
9 300.0000 0.0000 100
10 0.0000 300.0000 100
11 -300.0000 0.0000 100
12 0.0000 -300.0000 100
13 400.0000 0.0000 100
14 0.0000 400.0000 100
15 -400.0000 0.0000 100
16 0.0000 -400.0000 100
Depot 0 0 N.A.
Table C.4: Min-Max Single-Depot Split-Delivery VRP
instance SD3
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 70.7107 70.7107 100
3 0.0000 100.0000 100
4 -70.7107 70.7107 100
5 -100.0000 0.0000 100
6 -70.7107 -70.7107 100
7 0.0000 -100.0000 100
8 70.7107 -70.7107 100
9 200.0000 0.0000 100
10 141.4210 141.4210 100
11 0.0000 200.0000 100
12 -141.4210 141.4210 100
13 -200.0000 0.0000 100
14 -141.4210 -141.4210 100
15 0.0000 -200.0000 100
Continued on next page
545
Table C.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
16 141.4210 -141.4210 100
Depot 0 0 N.A.
Table C.5: Min-Max Single-Depot Split-Delivery VRP
instance SD4
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 86.6025 50.0000 100
3 50.0000 86.6025 100
4 0.0000 100.0000 100
5 -50.0000 86.6025 100
6 -86.6025 50.0000 100
7 -100.0000 0.0000 100
8 -86.6025 -50.0000 100
9 -50.0000 -86.6025 100
10 0.0000 -100.0000 100
11 50.0000 -86.6025 100
12 86.6025 -50.0000 100
13 200.0000 0.0000 100
14 173.2050 100.0000 100
15 100.0000 173.2050 100
16 0.0000 200.0000 100
17 -100.0000 173.2050 100
18 -173.2050 100.0000 100
19 -200.0000 0.0000 100
20 -173.2050 -100.0000 100
21 -100.0000 -173.2050 100
22 0.0000 -200.0000 100
23 100.0000 -173.2050 100
24 173.2050 -100.0000 100
Depot 0 0 N.A.
546
Table C.6: Min-Max Single-Depot Split-Delivery VRP
instance SD5
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 70.7107 70.7107 100
3 0.0000 100.0000 100
4 -70.7107 70.7107 100
5 -100.0000 0.0000 100
6 -70.7107 -70.7107 100
7 0.0000 -100.0000 100
8 70.7107 -70.7107 100
9 200.0000 0.0000 100
10 141.4210 141.4210 100
11 0.0000 200.0000 100
12 -141.4210 141.4210 100
13 -200.0000 0.0000 100
14 -141.4210 -141.4210 100
15 0.0000 -200.0000 100
16 141.4210 -141.4210 100
17 300.0000 0.0000 100
18 212.1320 212.1320 100
19 0.0000 300.0000 100
20 -212.1320 212.1320 100
21 -300.0000 0.0000 100
22 -212.1320 -212.1320 100
23 0.0000 -300.0000 100
24 212.1320 -212.1320 100
25 400.0000 0.0000 100
26 282.8430 282.8430 100
27 0.0000 400.0000 100
28 -282.8430 282.8430 100
29 -400.0000 0.0000 100
30 -282.8430 -282.8430 100
31 0.0000 -400.0000 100
32 282.8430 -282.8430 100
Depot 0 0 N.A.
547
Table C.7: Min-Max Single-Depot Split-Delivery VRP
instance SD6
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 92.3880 38.2683 100
3 70.7107 70.7107 100
4 38.2683 92.3880 100
5 0.0000 100.0000 100
6 -38.2683 92.3880 100
7 -70.7107 70.7107 100
8 -92.3880 38.2683 100
9 -100.0000 0.0000 100
10 -92.3880 -38.2683 100
11 -70.7107 -70.7107 100
12 -38.2683 -92.3880 100
13 0.0000 -100.0000 100
14 38.2683 -92.3880 100
15 70.7107 -70.7107 100
16 92.3880 -38.2683 100
17 200.0000 0.0000 100
18 184.7760 76.5367 100
19 141.4210 141.4210 100
20 76.5367 184.7760 100
21 0.0000 200.0000 100
22 -76.5367 184.7760 100
23 -141.4210 141.4210 100
24 -184.7760 76.5367 100
25 -200.0000 0.0000 100
26 -184.7760 -76.5367 100
27 -141.4210 -141.4210 100
28 -76.5367 -184.7760 100
29 0.0000 -200.0000 100
30 76.5367 -184.7760 100
31 141.4210 -141.4210 100
32 184.7760 -76.5367 100
Depot 0 0 N.A.
548
Table C.8: Min-Max Single-Depot Split-Delivery VRP
instance SD7
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 0.0000 100.0000 100
3 -100.0000 0.0000 100
4 0.0000 -100.0000 100
5 200.0000 0.0000 100
6 0.0000 200.0000 100
7 -200.0000 0.0000 100
8 0.0000 -200.0000 100
9 300.0000 0.0000 100
10 0.0000 300.0000 100
11 -300.0000 0.0000 100
12 0.0000 -300.0000 100
13 400.0000 0.0000 100
14 0.0000 400.0000 100
15 -400.0000 0.0000 100
16 0.0000 -400.0000 100
17 500.0000 0.0000 100
18 0.0000 500.0000 100
19 -500.0000 0.0000 100
20 0.0000 -500.0000 100
21 600.0000 0.0000 100
22 0.0000 600.0000 100
23 -600.0000 0.0000 100
24 0.0000 -600.0000 100
25 700.0000 0.0000 100
26 0.0000 700.0000 100
27 -700.0000 0.0000 100
28 0.0000 -700.0000 100
29 800.0000 0.0000 100
30 0.0000 800.0000 100
31 -800.0000 0.0000 100
32 0.0000 -800.0000 100
33 900.0000 0.0000 100
34 0.0000 900.0000 100
35 -900.0000 0.0000 100
36 0.0000 -900.0000 100
37 1000.0000 0.0000 100
38 0.0000 1000.0000 100
39 -1000.0000 0.0000 100
40 0.0000 -1000.0000 100
Continued on next page
549
Table C.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
Depot 0 0 N.A.
Table C.9: Min-Max Single-Depot Split-Delivery VRP
instance SD8
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 0.0000 100.0000 100
3 -100.0000 0.0000 100
4 0.0000 -100.0000 100
5 200.0000 0.0000 100
6 0.0000 200.0000 100
7 -200.0000 0.0000 100
8 0.0000 -200.0000 100
9 300.0000 0.0000 100
10 0.0000 300.0000 100
11 -300.0000 0.0000 100
12 0.0000 -300.0000 100
13 400.0000 0.0000 100
14 0.0000 400.0000 100
15 -400.0000 0.0000 100
16 0.0000 -400.0000 100
17 500.0000 0.0000 100
18 0.0000 500.0000 100
19 -500.0000 0.0000 100
20 0.0000 -500.0000 100
21 600.0000 0.0000 100
22 0.0000 600.0000 100
23 -600.0000 0.0000 100
24 0.0000 -600.0000 100
25 700.0000 0.0000 100
26 0.0000 700.0000 100
27 -700.0000 0.0000 100
28 0.0000 -700.0000 100
29 800.0000 0.0000 100
30 0.0000 800.0000 100
31 -800.0000 0.0000 100
32 0.0000 -800.0000 100
Continued on next page
550
Table C.9 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
33 900.0000 0.0000 100
34 0.0000 900.0000 100
35 -900.0000 0.0000 100
36 0.0000 -900.0000 100
37 1000.0000 0.0000 100
38 0.0000 1000.0000 100
39 -1000.0000 0.0000 100
40 0.0000 -1000.0000 100
41 1100.0000 0.0000 100
42 0.0000 1100.0000 100
43 -1100.0000 0.0000 100
44 0.0000 -1100.0000 100
45 1200.0000 0.0000 100
46 0.0000 1200.0000 100
47 -1200.0000 0.0000 100
48 0.0000 -1200.0000 100
Depot 0 0 N.A.
Table C.10: Min-Max Single-Depot Split-Delivery VRP
instance SD9
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 86.6025 50.0000 100
3 50.0000 86.6025 100
4 0.0000 100.0000 100
5 -50.0000 86.6025 100
6 -86.6025 50.0000 100
7 -100.0000 0.0000 100
8 -86.6025 -50.0000 100
9 -50.0000 -86.6025 100
10 0.0000 -100.0000 100
11 50.0000 -86.6025 100
12 86.6025 -50.0000 100
13 200.0000 0.0000 100
14 173.2050 100.0000 100
15 100.0000 173.2050 100
16 0.0000 200.0000 100
Continued on next page
551
Table C.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
17 -100.0000 173.2050 100
18 -173.2050 100.0000 100
19 -200.0000 0.0000 100
20 -173.2050 -100.0000 100
21 -100.0000 -173.2050 100
22 0.0000 -200.0000 100
23 100.0000 -173.2050 100
24 173.2050 -100.0000 100
25 300.0000 0.0000 100
26 259.8080 150.0000 100
27 150.0000 259.8080 100
28 0.0000 300.0000 100
29 -150.0000 259.8080 100
30 -259.8080 150.0000 100
31 -300.0000 0.0000 100
32 -259.8080 -150.0000 100
33 -150.0000 -259.8080 100
34 0.0000 -300.0000 100
35 150.0000 -259.8080 100
36 259.8080 -150.0000 100
37 400.0000 0.0000 100
38 346.4100 200.0000 100
39 200.0000 346.4100 100
40 0.0000 400.0000 100
41 -200.0000 346.4100 100
42 -346.4100 200.0000 100
43 -400.0000 0.0000 100
44 -346.4100 -200.0000 100
45 -200.0000 -346.4100 100
46 0.0000 -400.0000 100
47 200.0000 -346.4100 100
48 346.4100 -200.0000 100
Depot 0 0 N.A.
552
Table C.11: Min-Max Single-Depot Split-Delivery VRP
instance SD10
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 92.3880 38.2683 100
3 70.7107 70.7107 100
4 38.2683 92.3880 100
5 0.0000 100.0000 100
6 -38.2683 92.3880 100
7 -70.7107 70.7107 100
8 -92.3880 38.2683 100
9 -100.0000 0.0000 100
10 -92.3880 -38.2683 100
11 -70.7107 -70.7107 100
12 -38.2683 -92.3880 100
13 0.0000 -100.0000 100
14 38.2683 -92.3880 100
15 70.7107 -70.7107 100
16 92.3880 -38.2683 100
17 200.0000 0.0000 100
18 184.7760 76.5367 100
19 141.4210 141.4210 100
20 76.5367 184.7760 100
21 0.0000 200.0000 100
22 -76.5367 184.7760 100
23 -141.4210 141.4210 100
24 -184.7760 76.5367 100
25 -200.0000 0.0000 100
26 -184.7760 -76.5367 100
27 -141.4210 -141.4210 100
28 -76.5367 -184.7760 100
29 0.0000 -200.0000 100
30 76.5367 -184.7760 100
31 141.4210 -141.4210 100
32 184.7760 -76.5367 100
33 300.0000 0.0000 100
34 277.1640 114.8050 100
35 212.1320 212.1320 100
36 114.8050 277.1640 100
37 0.0000 300.0000 100
38 -114.8050 277.1640 100
39 -212.1320 212.1320 100
40 -277.1640 114.8050 100
Continued on next page
553
Table C.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
41 -300.0000 0.0000 100
42 -277.1640 -114.8050 100
43 -212.1320 -212.1320 100
44 -114.8050 -277.1640 100
45 0.0000 -300.0000 100
46 114.8050 -277.1640 100
47 212.1320 -212.1320 100
48 277.1640 -114.8050 100
49 400.0000 0.0000 100
50 369.5520 153.0730 100
51 282.8430 282.8430 100
52 153.0730 369.5520 100
53 0.0000 400.0000 100
54 -153.0730 369.5520 100
55 -282.8430 282.8430 100
56 -369.5520 153.0730 100
57 -400.0000 0.0000 100
58 -369.5520 -153.0730 100
59 -282.8430 -282.8430 100
60 -153.0730 -369.5520 100
61 0.0000 -400.0000 100
62 153.0730 -369.5520 100
63 282.8430 -282.8430 100
64 369.5520 -153.0730 100
Depot 0 0 N.A.
Table C.12: Min-Max Single-Depot Split-Delivery VRP
instance SD11
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 0.0000 100.0000 100
3 -100.0000 0.0000 100
4 0.0000 -100.0000 100
5 200.0000 0.0000 100
6 0.0000 200.0000 100
7 -200.0000 0.0000 100
8 0.0000 -200.0000 100
Continued on next page
554
Table C.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
9 300.0000 0.0000 100
10 0.0000 300.0000 100
11 -300.0000 0.0000 100
12 0.0000 -300.0000 100
13 400.0000 0.0000 100
14 0.0000 400.0000 100
15 -400.0000 0.0000 100
16 0.0000 -400.0000 100
17 500.0000 0.0000 100
18 0.0000 500.0000 100
19 -500.0000 0.0000 100
20 0.0000 -500.0000 100
21 600.0000 0.0000 100
22 0.0000 600.0000 100
23 -600.0000 0.0000 100
24 0.0000 -600.0000 100
25 700.0000 0.0000 100
26 0.0000 700.0000 100
27 -700.0000 0.0000 100
28 0.0000 -700.0000 100
29 800.0000 0.0000 100
30 0.0000 800.0000 100
31 -800.0000 0.0000 100
32 0.0000 -800.0000 100
33 900.0000 0.0000 100
34 0.0000 900.0000 100
35 -900.0000 0.0000 100
36 0.0000 -900.0000 100
37 1000.0000 0.0000 100
38 0.0000 1000.0000 100
39 -1000.0000 0.0000 100
40 0.0000 -1000.0000 100
41 1100.0000 0.0000 100
42 0.0000 1100.0000 100
43 -1100.0000 0.0000 100
44 0.0000 -1100.0000 100
45 1200.0000 0.0000 100
46 0.0000 1200.0000 100
47 -1200.0000 0.0000 100
48 0.0000 -1200.0000 100
49 1300.0000 0.0000 100
Continued on next page
555
Table C.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
50 0.0000 1300.0000 100
51 -1300.0000 0.0000 100
52 0.0000 -1300.0000 100
53 1400.0000 0.0000 100
54 0.0000 1400.0000 100
55 -1400.0000 0.0000 100
56 0.0000 -1400.0000 100
57 1500.0000 0.0000 100
58 0.0000 1500.0000 100
59 -1500.0000 0.0000 100
60 0.0000 -1500.0000 100
61 1600.0000 0.0000 100
62 0.0000 1600.0000 100
63 -1600.0000 0.0000 100
64 0.0000 -1600.0000 100
65 1700.0000 0.0000 100
66 0.0000 1700.0000 100
67 -1700.0000 0.0000 100
68 0.0000 -1700.0000 100
69 1800.0000 0.0000 100
70 0.0000 1800.0000 100
71 -1800.0000 0.0000 100
72 0.0000 -1800.0000 100
73 1900.0000 0.0000 100
74 0.0000 1900.0000 100
75 -1900.0000 0.0000 100
76 0.0000 -1900.0000 100
77 2000.0000 0.0000 100
78 0.0000 2000.0000 100
79 -2000.0000 0.0000 100
80 0.0000 -2000.0000 100
Depot 0 0 N.A.
Table C.13: Min-Max Single-Depot Split-Delivery VRP
instance SD12
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
Continued on next page
556
Table C.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
2 70.7107 70.7107 100
3 0.0000 100.0000 100
4 -70.7107 70.7107 100
5 -100.0000 0.0000 100
6 -70.7107 -70.7107 100
7 0.0000 -100.0000 100
8 70.7107 -70.7107 100
9 200.0000 0.0000 100
10 141.4210 141.4210 100
11 0.0000 200.0000 100
12 -141.4210 141.4210 100
13 -200.0000 0.0000 100
14 -141.4210 -141.4210 100
15 0.0000 -200.0000 100
16 141.4210 -141.4210 100
17 300.0000 0.0000 100
18 212.1320 212.1320 100
19 0.0000 300.0000 100
20 -212.1320 212.1320 100
21 -300.0000 0.0000 100
22 -212.1320 -212.1320 100
23 0.0000 -300.0000 100
24 212.1320 -212.1320 100
25 400.0000 0.0000 100
26 282.8430 282.8430 100
27 0.0000 400.0000 100
28 -282.8430 282.8430 100
29 -400.0000 0.0000 100
30 -282.8430 -282.8430 100
31 0.0000 -400.0000 100
32 282.8430 -282.8430 100
33 500.0000 0.0000 100
34 353.5530 353.5530 100
35 0.0000 500.0000 100
36 -353.5530 353.5530 100
37 -500.0000 0.0000 100
38 -353.5530 -353.5530 100
39 0.0000 -500.0000 100
40 353.5530 -353.5530 100
41 600.0000 0.0000 100
42 424.2640 424.2640 100
Continued on next page
557
Table C.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
43 0.0000 600.0000 100
44 -424.2640 424.2640 100
45 -600.0000 0.0000 100
46 -424.2640 -424.2640 100
47 0.0000 -600.0000 100
48 424.2640 -424.2640 100
49 700.0000 0.0000 100
50 494.9750 494.9750 100
51 0.0000 700.0000 100
52 -494.9750 494.9750 100
53 -700.0000 0.0000 100
54 -494.9750 -494.9750 100
55 0.0000 -700.0000 100
56 494.9750 -494.9750 100
57 800.0000 0.0000 100
58 565.6850 565.6850 100
59 0.0000 800.0000 100
60 -565.6850 565.6850 100
61 -800.0000 0.0000 100
62 -565.6850 -565.6850 100
63 0.0000 -800.0000 100
64 565.6850 -565.6850 100
65 900.0000 0.0000 100
66 636.3960 636.3960 100
67 0.0000 900.0000 100
68 -636.3960 636.3960 100
69 -900.0000 0.0000 100
70 -636.3960 -636.3960 100
71 0.0000 -900.0000 100
72 636.3960 -636.3960 100
73 1000.0000 0.0000 100
74 707.1070 707.1070 100
75 0.0000 1000.0000 100
76 -707.1070 707.1070 100
77 -1000.0000 0.0000 100
78 -707.1070 -707.1070 100
79 0.0000 -1000.0000 100
80 707.1070 -707.1070 100
Depot 0 0 N.A.
558
Table C.14: Min-Max Single-Depot Split-Delivery VRP
instance SD13
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 70.7107 70.7107 100
3 0.0000 100.0000 100
4 -70.7107 70.7107 100
5 -100.0000 0.0000 100
6 -70.7107 -70.7107 100
7 0.0000 -100.0000 100
8 70.7107 -70.7107 100
9 200.0000 0.0000 100
10 141.4210 141.4210 100
11 0.0000 200.0000 100
12 -141.4210 141.4210 100
13 -200.0000 0.0000 100
14 -141.4210 -141.4210 100
15 0.0000 -200.0000 100
16 141.4210 -141.4210 100
17 300.0000 0.0000 100
18 212.1320 212.1320 100
19 0.0000 300.0000 100
20 -212.1320 212.1320 100
21 -300.0000 0.0000 100
22 -212.1320 -212.1320 100
23 0.0000 -300.0000 100
24 212.1320 -212.1320 100
25 400.0000 0.0000 100
26 282.8430 282.8430 100
27 0.0000 400.0000 100
28 -282.8430 282.8430 100
29 -400.0000 0.0000 100
30 -282.8430 -282.8430 100
31 0.0000 -400.0000 100
32 282.8430 -282.8430 100
33 500.0000 0.0000 100
34 353.5530 353.5530 100
35 0.0000 500.0000 100
36 -353.5530 353.5530 100
37 -500.0000 0.0000 100
38 -353.5530 -353.5530 100
39 0.0000 -500.0000 100
40 353.5530 -353.5530 100
Continued on next page
559
Table C.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
41 600.0000 0.0000 100
42 424.2640 424.2640 100
43 0.0000 600.0000 100
44 -424.2640 424.2640 100
45 -600.0000 0.0000 100
46 -424.2640 -424.2640 100
47 0.0000 -600.0000 100
48 424.2640 -424.2640 100
49 700.0000 0.0000 100
50 494.9750 494.9750 100
51 0.0000 700.0000 100
52 -494.9750 494.9750 100
53 -700.0000 0.0000 100
54 -494.9750 -494.9750 100
55 0.0000 -700.0000 100
56 494.9750 -494.9750 100
57 800.0000 0.0000 100
58 565.6850 565.6850 100
59 0.0000 800.0000 100
60 -565.6850 565.6850 100
61 -800.0000 0.0000 100
62 -565.6850 -565.6850 100
63 0.0000 -800.0000 100
64 565.6850 -565.6850 100
65 900.0000 0.0000 100
66 636.3960 636.3960 100
67 0.0000 900.0000 100
68 -636.3960 636.3960 100
69 -900.0000 0.0000 100
70 -636.3960 -636.3960 100
71 0.0000 -900.0000 100
72 636.3960 -636.3960 100
73 1000.0000 0.0000 100
74 707.1070 707.1070 100
75 0.0000 1000.0000 100
76 -707.1070 707.1070 100
77 -1000.0000 0.0000 100
78 -707.1070 -707.1070 100
79 0.0000 -1000.0000 100
80 707.1070 -707.1070 100
81 1100.0000 0.0000 100
Continued on next page
560
Table C.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
82 777.8170 777.8170 100
83 0.0000 1100.0000 100
84 -777.8170 777.8170 100
85 -1100.0000 0.0000 100
86 -777.8170 -777.8170 100
87 0.0000 -1100.0000 100
88 777.8170 -777.8170 100
89 1200.0000 0.0000 100
90 848.5280 848.5280 100
91 0.0000 1200.0000 100
92 -848.5280 848.5280 100
93 -1200.0000 0.0000 100
94 -848.5280 -848.5280 100
95 0.0000 -1200.0000 100
96 848.5280 -848.5280 100
Depot 0 0 N.A.
Table C.15: Min-Max Single-Depot Split-Delivery VRP
instance SD14
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 86.6025 50.0000 100
3 50.0000 86.6025 100
4 0.0000 100.0000 100
5 -50.0000 86.6025 100
6 -86.6025 50.0000 100
7 -100.0000 0.0000 100
8 -86.6025 -50.0000 100
9 -50.0000 -86.6025 100
10 0.0000 -100.0000 100
11 50.0000 -86.6025 100
12 86.6025 -50.0000 100
13 200.0000 0.0000 100
14 173.2050 100.0000 100
15 100.0000 173.2050 100
16 0.0000 200.0000 100
17 -100.0000 173.2050 100
Continued on next page
561
Table C.15 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
18 -173.2050 100.0000 100
19 -200.0000 0.0000 100
20 -173.2050 -100.0000 100
21 -100.0000 -173.2050 100
22 0.0000 -200.0000 100
23 100.0000 -173.2050 100
24 173.2050 -100.0000 100
25 300.0000 0.0000 100
26 259.8080 150.0000 100
27 150.0000 259.8080 100
28 0.0000 300.0000 100
29 -150.0000 259.8080 100
30 -259.8080 150.0000 100
31 -300.0000 0.0000 100
32 -259.8080 -150.0000 100
33 -150.0000 -259.8080 100
34 0.0000 -300.0000 100
35 150.0000 -259.8080 100
36 259.8080 -150.0000 100
37 400.0000 0.0000 100
38 346.4100 200.0000 100
39 200.0000 346.4100 100
40 0.0000 400.0000 100
41 -200.0000 346.4100 100
42 -346.4100 200.0000 100
43 -400.0000 0.0000 100
44 -346.4100 -200.0000 100
45 -200.0000 -346.4100 100
46 0.0000 -400.0000 100
47 200.0000 -346.4100 100
48 346.4100 -200.0000 100
49 500.0000 0.0000 100
50 433.0130 250.0000 100
51 250.0000 433.0130 100
52 0.0000 500.0000 100
53 -250.0000 433.0130 100
54 -433.0130 250.0000 100
55 -500.0000 0.0000 100
56 -433.0130 -250.0000 100
57 -250.0000 -433.0130 100
58 0.0000 -500.0000 100
Continued on next page
562
Table C.15 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
59 250.0000 -433.0130 100
60 433.0130 -250.0000 100
61 600.0000 0.0000 100
62 519.6150 300.0000 100
63 300.0000 519.6150 100
64 0.0000 600.0000 100
65 -300.0000 519.6150 100
66 -519.6150 300.0000 100
67 -600.0000 0.0000 100
68 -519.6150 -300.0000 100
69 -300.0000 -519.6150 100
70 0.0000 -600.0000 100
71 300.0000 -519.6150 100
72 519.6150 -300.0000 100
73 700.0000 0.0000 100
74 606.2180 350.0000 100
75 350.0000 606.2180 100
76 0.0000 700.0000 100
77 -350.0000 606.2180 100
78 -606.2180 350.0000 100
79 -700.0000 0.0000 100
80 -606.2180 -350.0000 100
81 -350.0000 -606.2180 100
82 0.0000 -700.0000 100
83 350.0000 -606.2180 100
84 606.2180 -350.0000 100
85 800.0000 0.0000 100
86 692.8200 400.0000 100
87 400.0000 692.8200 100
88 0.0000 800.0000 100
89 -400.0000 692.8200 100
90 -692.8200 400.0000 100
91 -800.0000 0.0000 100
92 -692.8200 -400.0000 100
93 -400.0000 -692.8200 100
94 0.0000 -800.0000 100
95 400.0000 -692.8200 100
96 692.8200 -400.0000 100
97 900.0000 0.0000 100
98 779.4230 450.0000 100
99 450.0000 779.4230 100
Continued on next page
563
Table C.15 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
100 0.0000 900.0000 100
101 -450.0000 779.4230 100
102 -779.4230 450.0000 100
103 -900.0000 0.0000 100
104 -779.4230 -450.0000 100
105 -450.0000 -779.4230 100
106 0.0000 -900.0000 100
107 450.0000 -779.4230 100
108 779.4230 -450.0000 100
109 1000.0000 0.0000 100
110 866.0250 500.0000 100
111 500.0000 866.0250 100
112 0.0000 1000.0000 100
113 -500.0000 866.0250 100
114 -866.0250 500.0000 100
115 -1000.0000 0.0000 100
116 -866.0250 -500.0000 100
117 -500.0000 -866.0250 100
118 0.0000 -1000.0000 100
119 500.0000 -866.0250 100
120 866.0250 -500.0000 100
Depot 0 0 N.A.
Table C.16: Min-Max Single-Depot Split-Delivery VRP
instance SD15
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 86.6025 50.0000 100
3 50.0000 86.6025 100
4 0.0000 100.0000 100
5 -50.0000 86.6025 100
6 -86.6025 50.0000 100
7 -100.0000 0.0000 100
8 -86.6025 -50.0000 100
9 -50.0000 -86.6025 100
10 0.0000 -100.0000 100
11 50.0000 -86.6025 100
Continued on next page
564
Table C.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
12 86.6025 -50.0000 100
13 200.0000 0.0000 100
14 173.2050 100.0000 100
15 100.0000 173.2050 100
16 0.0000 200.0000 100
17 -100.0000 173.2050 100
18 -173.2050 100.0000 100
19 -200.0000 0.0000 100
20 -173.2050 -100.0000 100
21 -100.0000 -173.2050 100
22 0.0000 -200.0000 100
23 100.0000 -173.2050 100
24 173.2050 -100.0000 100
25 300.0000 0.0000 100
26 259.8080 150.0000 100
27 150.0000 259.8080 100
28 0.0000 300.0000 100
29 -150.0000 259.8080 100
30 -259.8080 150.0000 100
31 -300.0000 0.0000 100
32 -259.8080 -150.0000 100
33 -150.0000 -259.8080 100
34 0.0000 -300.0000 100
35 150.0000 -259.8080 100
36 259.8080 -150.0000 100
37 400.0000 0.0000 100
38 346.4100 200.0000 100
39 200.0000 346.4100 100
40 0.0000 400.0000 100
41 -200.0000 346.4100 100
42 -346.4100 200.0000 100
43 -400.0000 0.0000 100
44 -346.4100 -200.0000 100
45 -200.0000 -346.4100 100
46 0.0000 -400.0000 100
47 200.0000 -346.4100 100
48 346.4100 -200.0000 100
49 500.0000 0.0000 100
50 433.0130 250.0000 100
51 250.0000 433.0130 100
52 0.0000 500.0000 100
Continued on next page
565
Table C.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
53 -250.0000 433.0130 100
54 -433.0130 250.0000 100
55 -500.0000 0.0000 100
56 -433.0130 -250.0000 100
57 -250.0000 -433.0130 100
58 0.0000 -500.0000 100
59 250.0000 -433.0130 100
60 433.0130 -250.0000 100
61 600.0000 0.0000 100
62 519.6150 300.0000 100
63 300.0000 519.6150 100
64 0.0000 600.0000 100
65 -300.0000 519.6150 100
66 -519.6150 300.0000 100
67 -600.0000 0.0000 100
68 -519.6150 -300.0000 100
69 -300.0000 -519.6150 100
70 0.0000 -600.0000 100
71 300.0000 -519.6150 100
72 519.6150 -300.0000 100
73 700.0000 0.0000 100
74 606.2180 350.0000 100
75 350.0000 606.2180 100
76 0.0000 700.0000 100
77 -350.0000 606.2180 100
78 -606.2180 350.0000 100
79 -700.0000 0.0000 100
80 -606.2180 -350.0000 100
81 -350.0000 -606.2180 100
82 0.0000 -700.0000 100
83 350.0000 -606.2180 100
84 606.2180 -350.0000 100
85 800.0000 0.0000 100
86 692.8200 400.0000 100
87 400.0000 692.8200 100
88 0.0000 800.0000 100
89 -400.0000 692.8200 100
90 -692.8200 400.0000 100
91 -800.0000 0.0000 100
92 -692.8200 -400.0000 100
93 -400.0000 -692.8200 100
Continued on next page
566
Table C.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
94 0.0000 -800.0000 100
95 400.0000 -692.8200 100
96 692.8200 -400.0000 100
97 900.0000 0.0000 100
98 779.4230 450.0000 100
99 450.0000 779.4230 100
100 0.0000 900.0000 100
101 -450.0000 779.4230 100
102 -779.4230 450.0000 100
103 -900.0000 0.0000 100
104 -779.4230 -450.0000 100
105 -450.0000 -779.4230 100
106 0.0000 -900.0000 100
107 450.0000 -779.4230 100
108 779.4230 -450.0000 100
109 1000.0000 0.0000 100
110 866.0250 500.0000 100
111 500.0000 866.0250 100
112 0.0000 1000.0000 100
113 -500.0000 866.0250 100
114 -866.0250 500.0000 100
115 -1000.0000 0.0000 100
116 -866.0250 -500.0000 100
117 -500.0000 -866.0250 100
118 0.0000 -1000.0000 100
119 500.0000 -866.0250 100
120 866.0250 -500.0000 100
121 1100.0000 0.0000 100
122 952.6280 550.0000 100
123 550.0000 952.6280 100
124 0.0000 1100.0000 100
125 -550.0000 952.6280 100
126 -952.6280 550.0000 100
127 -1100.0000 0.0000 100
128 -952.6280 -550.0000 100
129 -550.0000 -952.6280 100
130 0.0000 -1100.0000 100
131 550.0000 -952.6280 100
132 952.6280 -550.0000 100
133 1200.0000 0.0000 100
134 1039.2300 600.0000 100
Continued on next page
567
Table C.16 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
135 600.0000 1039.2300 100
136 0.0000 1200.0000 100
137 -600.0000 1039.2300 100
138 -1039.2300 600.0000 100
139 -1200.0000 0.0000 100
140 -1039.2300 -600.0000 100
141 -600.0000 -1039.2300 100
142 0.0000 -1200.0000 100
143 600.0000 -1039.2300 100
144 1039.2300 -600.0000 100
Depot 0 0 N.A.
Table C.17: Min-Max Single-Depot Split-Delivery VRP
instance SD16
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 99.6195 8.7156 100
3 98.4808 17.3648 100
4 96.5926 25.8819 100
5 93.9693 34.2020 100
6 90.6308 42.2618 100
7 86.6025 50.0000 100
8 81.9152 57.3576 100
9 76.6044 64.2788 100
10 70.7107 70.7107 100
11 64.2788 76.6044 100
12 57.3576 81.9152 100
13 50.0000 86.6025 100
14 42.2618 90.6308 100
15 34.2020 93.9693 100
16 25.8819 96.5926 100
17 17.3648 98.4808 100
18 8.7156 99.6195 100
19 0.0000 100.0000 100
20 -8.7156 99.6195 100
21 -17.3648 98.4808 100
22 -25.8819 96.5926 100
Continued on next page
568
Table C.17 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
23 -34.2020 93.9693 100
24 -42.2618 90.6308 100
25 -50.0000 86.6025 100
26 -57.3576 81.9152 100
27 -64.2788 76.6044 100
28 -70.7107 70.7107 100
29 -76.6044 64.2788 100
30 -81.9152 57.3576 100
31 -86.6025 50.0000 100
32 -90.6308 42.2618 100
33 -93.9693 34.2020 100
34 -96.5926 25.8819 100
35 -98.4808 17.3648 100
36 -99.6195 8.7156 100
37 -100.0000 0.0000 100
38 -99.6195 -8.7156 100
39 -98.4808 -17.3648 100
40 -96.5926 -25.8819 100
41 -93.9693 -34.2020 100
42 -90.6308 -42.2618 100
43 -86.6025 -50.0000 100
44 -81.9152 -57.3576 100
45 -76.6044 -64.2788 100
46 -70.7107 -70.7107 100
47 -64.2788 -76.6044 100
48 -57.3576 -81.9152 100
49 -50.0000 -86.6025 100
50 -42.2618 -90.6308 100
51 -34.2020 -93.9693 100
52 -25.8819 -96.5926 100
53 -17.3648 -98.4808 100
54 -8.7156 -99.6195 100
55 0.0000 -100.0000 100
56 8.7156 -99.6195 100
57 17.3648 -98.4808 100
58 25.8819 -96.5926 100
59 34.2020 -93.9693 100
60 42.2618 -90.6308 100
61 50.0000 -86.6025 100
62 57.3576 -81.9152 100
63 64.2788 -76.6044 100
Continued on next page
569
Table C.17 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
64 70.7107 -70.7107 100
65 76.6044 -64.2788 100
66 81.9152 -57.3576 100
67 86.6025 -50.0000 100
68 90.6308 -42.2618 100
69 93.9693 -34.2020 100
70 96.5926 -25.8819 100
71 98.4808 -17.3648 100
72 99.6195 -8.7156 100
73 200.0000 0.0000 100
74 199.2390 17.4311 100
75 196.9620 34.7296 100
76 193.1850 51.7638 100
77 187.9390 68.4040 100
78 181.2620 84.5237 100
79 173.2050 100.0000 100
80 163.8300 114.7150 100
81 153.2090 128.5580 100
82 141.4210 141.4210 100
83 128.5580 153.2090 100
84 114.7150 163.8300 100
85 100.0000 173.2050 100
86 84.5237 181.2620 100
87 68.4040 187.9390 100
88 51.7638 193.1850 100
89 34.7296 196.9620 100
90 17.4311 199.2390 100
91 0.0000 200.0000 100
92 -17.4311 199.2390 100
93 -34.7296 196.9620 100
94 -51.7638 193.1850 100
95 -68.4040 187.9390 100
96 -84.5237 181.2620 100
97 -100.0000 173.2050 100
98 -114.7150 163.8300 100
99 -128.5580 153.2090 100
100 -141.4210 141.4210 100
101 -153.2090 128.5580 100
102 -163.8300 114.7150 100
103 -173.2050 100.0000 100
104 -181.2620 84.5237 100
Continued on next page
570
Table C.17 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
105 -187.9390 68.4040 100
106 -193.1850 51.7638 100
107 -196.9620 34.7296 100
108 -199.2390 17.4311 100
109 -200.0000 0.0000 100
110 -199.2390 -17.4311 100
111 -196.9620 -34.7296 100
112 -193.1850 -51.7638 100
113 -187.9390 -68.4040 100
114 -181.2620 -84.5237 100
115 -173.2050 -100.0000 100
116 -163.8300 -114.7150 100
117 -153.2090 -128.5580 100
118 -141.4210 -141.4210 100
119 -128.5580 -153.2090 100
120 -114.7150 -163.8300 100
121 -100.0000 -173.2050 100
122 -84.5237 -181.2620 100
123 -68.4040 -187.9390 100
124 -51.7638 -193.1850 100
125 -34.7296 -196.9620 100
126 -17.4311 -199.2390 100
127 0.0000 -200.0000 100
128 17.4311 -199.2390 100
129 34.7296 -196.9620 100
130 51.7638 -193.1850 100
131 68.4040 -187.9390 100
132 84.5237 -181.2620 100
133 100.0000 -173.2050 100
134 114.7150 -163.8300 100
135 128.5580 -153.2090 100
136 141.4210 -141.4210 100
137 153.2090 -128.5580 100
138 163.8300 -114.7150 100
139 173.2050 -100.0000 100
140 181.2620 -84.5237 100
141 187.9390 -68.4040 100
142 193.1850 -51.7638 100
143 196.9620 -34.7296 100
144 199.2390 -17.4311 100
Depot 0 0 N.A.
571
Table C.18: Min-Max Single-Depot Split-Delivery VRP
instance SD17
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 70.7107 70.7107 100
3 0.0000 100.0000 100
4 -70.7107 70.7107 100
5 -100.0000 0.0000 100
6 -70.7107 -70.7107 100
7 0.0000 -100.0000 100
8 70.7107 -70.7107 100
9 200.0000 0.0000 100
10 141.4210 141.4210 100
11 0.0000 200.0000 100
12 -141.4210 141.4210 100
13 -200.0000 0.0000 100
14 -141.4210 -141.4210 100
15 0.0000 -200.0000 100
16 141.4210 -141.4210 100
17 300.0000 0.0000 100
18 212.1320 212.1320 100
19 0.0000 300.0000 100
20 -212.1320 212.1320 100
21 -300.0000 0.0000 100
22 -212.1320 -212.1320 100
23 0.0000 -300.0000 100
24 212.1320 -212.1320 100
25 400.0000 0.0000 100
26 282.8430 282.8430 100
27 0.0000 400.0000 100
28 -282.8430 282.8430 100
29 -400.0000 0.0000 100
30 -282.8430 -282.8430 100
31 0.0000 -400.0000 100
32 282.8430 -282.8430 100
33 500.0000 0.0000 100
34 353.5530 353.5530 100
35 0.0000 500.0000 100
36 -353.5530 353.5530 100
37 -500.0000 0.0000 100
38 -353.5530 -353.5530 100
Continued on next page
572
Table C.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
39 0.0000 -500.0000 100
40 353.5530 -353.5530 100
41 600.0000 0.0000 100
42 424.2640 424.2640 100
43 0.0000 600.0000 100
44 -424.2640 424.2640 100
45 -600.0000 0.0000 100
46 -424.2640 -424.2640 100
47 0.0000 -600.0000 100
48 424.2640 -424.2640 100
49 700.0000 0.0000 100
50 494.9750 494.9750 100
51 0.0000 700.0000 100
52 -494.9750 494.9750 100
53 -700.0000 0.0000 100
54 -494.9750 -494.9750 100
55 0.0000 -700.0000 100
56 494.9750 -494.9750 100
57 800.0000 0.0000 100
58 565.6850 565.6850 100
59 0.0000 800.0000 100
60 -565.6850 565.6850 100
61 -800.0000 0.0000 100
62 -565.6850 -565.6850 100
63 0.0000 -800.0000 100
64 565.6850 -565.6850 100
65 900.0000 0.0000 100
66 636.3960 636.3960 100
67 0.0000 900.0000 100
68 -636.3960 636.3960 100
69 -900.0000 0.0000 100
70 -636.3960 -636.3960 100
71 0.0000 -900.0000 100
72 636.3960 -636.3960 100
73 1000.0000 0.0000 100
74 707.1070 707.1070 100
75 0.0000 1000.0000 100
76 -707.1070 707.1070 100
77 -1000.0000 0.0000 100
78 -707.1070 -707.1070 100
79 0.0000 -1000.0000 100
Continued on next page
573
Table C.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
80 707.1070 -707.1070 100
81 1100.0000 0.0000 100
82 777.8170 777.8170 100
83 0.0000 1100.0000 100
84 -777.8170 777.8170 100
85 -1100.0000 0.0000 100
86 -777.8170 -777.8170 100
87 0.0000 -1100.0000 100
88 777.8170 -777.8170 100
89 1200.0000 0.0000 100
90 848.5280 848.5280 100
91 0.0000 1200.0000 100
92 -848.5280 848.5280 100
93 -1200.0000 0.0000 100
94 -848.5280 -848.5280 100
95 0.0000 -1200.0000 100
96 848.5280 -848.5280 100
97 1300.0000 0.0000 100
98 919.2390 919.2390 100
99 0.0000 1300.0000 100
100 -919.2390 919.2390 100
101 -1300.0000 0.0000 100
102 -919.2390 -919.2390 100
103 0.0000 -1300.0000 100
104 919.2390 -919.2390 100
105 1400.0000 0.0000 100
106 989.9490 989.9490 100
107 0.0000 1400.0000 100
108 -989.9490 989.9490 100
109 -1400.0000 0.0000 100
110 -989.9490 -989.9490 100
111 0.0000 -1400.0000 100
112 989.9490 -989.9490 100
113 1500.0000 0.0000 100
114 1060.6600 1060.6600 100
115 0.0000 1500.0000 100
116 -1060.6600 1060.6600 100
117 -1500.0000 0.0000 100
118 -1060.6600 -1060.6600 100
119 0.0000 -1500.0000 100
120 1060.6600 -1060.6600 100
Continued on next page
574
Table C.18 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
121 1600.0000 0.0000 100
122 1131.3700 1131.3700 100
123 0.0000 1600.0000 100
124 -1131.3700 1131.3700 100
125 -1600.0000 0.0000 100
126 -1131.3700 -1131.3700 100
127 0.0000 -1600.0000 100
128 1131.3700 -1131.3700 100
129 1700.0000 0.0000 100
130 1202.0800 1202.0800 100
131 0.0000 1700.0000 100
132 -1202.0800 1202.0800 100
133 -1700.0000 0.0000 100
134 -1202.0800 -1202.0800 100
135 0.0000 -1700.0000 100
136 1202.0800 -1202.0800 100
137 1800.0000 0.0000 100
138 1272.7900 1272.7900 100
139 0.0000 1800.0000 100
140 -1272.7900 1272.7900 100
141 -1800.0000 0.0000 100
142 -1272.7900 -1272.7900 100
143 0.0000 -1800.0000 100
144 1272.7900 -1272.7900 100
145 1900.0000 0.0000 100
146 1343.5000 1343.5000 100
147 0.0000 1900.0000 100
148 -1343.5000 1343.5000 100
149 -1900.0000 0.0000 100
150 -1343.5000 -1343.5000 100
151 0.0000 -1900.0000 100
152 1343.5000 -1343.5000 100
153 2000.0000 0.0000 100
154 1414.2100 1414.2100 100
155 0.0000 2000.0000 100
156 -1414.2100 1414.2100 100
157 -2000.0000 0.0000 100
158 -1414.2100 -1414.2100 100
159 0.0000 -2000.0000 100
160 1414.2100 -1414.2100 100
Depot 0 0 N.A.
575
Table C.19: Min-Max Single-Depot Split-Delivery VRP
instance SD18
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 92.3880 38.2683 100
3 70.7107 70.7107 100
4 38.2683 92.3880 100
5 0.0000 100.0000 100
6 -38.2683 92.3880 100
7 -70.7107 70.7107 100
8 -92.3880 38.2683 100
9 -100.0000 0.0000 100
10 -92.3880 -38.2683 100
11 -70.7107 -70.7107 100
12 -38.2683 -92.3880 100
13 0.0000 -100.0000 100
14 38.2683 -92.3880 100
15 70.7107 -70.7107 100
16 92.3880 -38.2683 100
17 200.0000 0.0000 100
18 184.7760 76.5367 100
19 141.4210 141.4210 100
20 76.5367 184.7760 100
21 0.0000 200.0000 100
22 -76.5367 184.7760 100
23 -141.4210 141.4210 100
24 -184.7760 76.5367 100
25 -200.0000 0.0000 100
26 -184.7760 -76.5367 100
27 -141.4210 -141.4210 100
28 -76.5367 -184.7760 100
29 0.0000 -200.0000 100
30 76.5367 -184.7760 100
31 141.4210 -141.4210 100
32 184.7760 -76.5367 100
33 300.0000 0.0000 100
34 277.1640 114.8050 100
35 212.1320 212.1320 100
36 114.8050 277.1640 100
37 0.0000 300.0000 100
38 -114.8050 277.1640 100
Continued on next page
576
Table C.19 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
39 -212.1320 212.1320 100
40 -277.1640 114.8050 100
41 -300.0000 0.0000 100
42 -277.1640 -114.8050 100
43 -212.1320 -212.1320 100
44 -114.8050 -277.1640 100
45 0.0000 -300.0000 100
46 114.8050 -277.1640 100
47 212.1320 -212.1320 100
48 277.1640 -114.8050 100
49 400.0000 0.0000 100
50 369.5520 153.0730 100
51 282.8430 282.8430 100
52 153.0730 369.5520 100
53 0.0000 400.0000 100
54 -153.0730 369.5520 100
55 -282.8430 282.8430 100
56 -369.5520 153.0730 100
57 -400.0000 0.0000 100
58 -369.5520 -153.0730 100
59 -282.8430 -282.8430 100
60 -153.0730 -369.5520 100
61 0.0000 -400.0000 100
62 153.0730 -369.5520 100
63 282.8430 -282.8430 100
64 369.5520 -153.0730 100
65 500.0000 0.0000 100
66 461.9400 191.3420 100
67 353.5530 353.5530 100
68 191.3420 461.9400 100
69 0.0000 500.0000 100
70 -191.3420 461.9400 100
71 -353.5530 353.5530 100
72 -461.9400 191.3420 100
73 -500.0000 0.0000 100
74 -461.9400 -191.3420 100
75 -353.5530 -353.5530 100
76 -191.3420 -461.9400 100
77 0.0000 -500.0000 100
78 191.3420 -461.9400 100
79 353.5530 -353.5530 100
Continued on next page
577
Table C.19 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
80 461.9400 -191.3420 100
81 600.0000 0.0000 100
82 554.3280 229.6100 100
83 424.2640 424.2640 100
84 229.6100 554.3280 100
85 0.0000 600.0000 100
86 -229.6100 554.3280 100
87 -424.2640 424.2640 100
88 -554.3280 229.6100 100
89 -600.0000 0.0000 100
90 -554.3280 -229.6100 100
91 -424.2640 -424.2640 100
92 -229.6100 -554.3280 100
93 0.0000 -600.0000 100
94 229.6100 -554.3280 100
95 424.2640 -424.2640 100
96 554.3280 -229.6100 100
97 700.0000 0.0000 100
98 646.7160 267.8780 100
99 494.9750 494.9750 100
100 267.8780 646.7160 100
101 0.0000 700.0000 100
102 -267.8780 646.7160 100
103 -494.9750 494.9750 100
104 -646.7160 267.8780 100
105 -700.0000 0.0000 100
106 -646.7160 -267.8780 100
107 -494.9750 -494.9750 100
108 -267.8780 -646.7160 100
109 0.0000 -700.0000 100
110 267.8780 -646.7160 100
111 494.9750 -494.9750 100
112 646.7160 -267.8780 100
113 800.0000 0.0000 100
114 739.1040 306.1470 100
115 565.6850 565.6850 100
116 306.1470 739.1040 100
117 0.0000 800.0000 100
118 -306.1470 739.1040 100
119 -565.6850 565.6850 100
120 -739.1040 306.1470 100
Continued on next page
578
Table C.19 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
121 -800.0000 0.0000 100
122 -739.1040 -306.1470 100
123 -565.6850 -565.6850 100
124 -306.1470 -739.1040 100
125 0.0000 -800.0000 100
126 306.1470 -739.1040 100
127 565.6850 -565.6850 100
128 739.1040 -306.1470 100
129 900.0000 0.0000 100
130 831.4920 344.4150 100
131 636.3960 636.3960 100
132 344.4150 831.4920 100
133 0.0000 900.0000 100
134 -344.4150 831.4920 100
135 -636.3960 636.3960 100
136 -831.4920 344.4150 100
137 -900.0000 0.0000 100
138 -831.4920 -344.4150 100
139 -636.3960 -636.3960 100
140 -344.4150 -831.4920 100
141 0.0000 -900.0000 100
142 344.4150 -831.4920 100
143 636.3960 -636.3960 100
144 831.4920 -344.4150 100
145 1000.0000 0.0000 100
146 923.8800 382.6830 100
147 707.1070 707.1070 100
148 382.6830 923.8800 100
149 0.0000 1000.0000 100
150 -382.6830 923.8800 100
151 -707.1070 707.1070 100
152 -923.8800 382.6830 100
153 -1000.0000 0.0000 100
154 -923.8800 -382.6830 100
155 -707.1070 -707.1070 100
156 -382.6830 -923.8800 100
157 0.0000 -1000.0000 100
158 382.6830 -923.8800 100
159 707.1070 -707.1070 100
160 923.8800 -382.6830 100
Depot 0 0 N.A.
579
Table C.20: Min-Max Single-Depot Split-Delivery VRP
instance SD19
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 92.3880 38.2683 100
3 70.7107 70.7107 100
4 38.2683 92.3880 100
5 0.0000 100.0000 100
6 -38.2683 92.3880 100
7 -70.7107 70.7107 100
8 -92.3880 38.2683 100
9 -100.0000 0.0000 100
10 -92.3880 -38.2683 100
11 -70.7107 -70.7107 100
12 -38.2683 -92.3880 100
13 0.0000 -100.0000 100
14 38.2683 -92.3880 100
15 70.7107 -70.7107 100
16 92.3880 -38.2683 100
17 200.0000 0.0000 100
18 184.7760 76.5367 100
19 141.4210 141.4210 100
20 76.5367 184.7760 100
21 0.0000 200.0000 100
22 -76.5367 184.7760 100
23 -141.4210 141.4210 100
24 -184.7760 76.5367 100
25 -200.0000 0.0000 100
26 -184.7760 -76.5367 100
27 -141.4210 -141.4210 100
28 -76.5367 -184.7760 100
29 0.0000 -200.0000 100
30 76.5367 -184.7760 100
31 141.4210 -141.4210 100
32 184.7760 -76.5367 100
33 300.0000 0.0000 100
34 277.1640 114.8050 100
35 212.1320 212.1320 100
36 114.8050 277.1640 100
37 0.0000 300.0000 100
38 -114.8050 277.1640 100
Continued on next page
580
Table C.20 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
39 -212.1320 212.1320 100
40 -277.1640 114.8050 100
41 -300.0000 0.0000 100
42 -277.1640 -114.8050 100
43 -212.1320 -212.1320 100
44 -114.8050 -277.1640 100
45 0.0000 -300.0000 100
46 114.8050 -277.1640 100
47 212.1320 -212.1320 100
48 277.1640 -114.8050 100
49 400.0000 0.0000 100
50 369.5520 153.0730 100
51 282.8430 282.8430 100
52 153.0730 369.5520 100
53 0.0000 400.0000 100
54 -153.0730 369.5520 100
55 -282.8430 282.8430 100
56 -369.5520 153.0730 100
57 -400.0000 0.0000 100
58 -369.5520 -153.0730 100
59 -282.8430 -282.8430 100
60 -153.0730 -369.5520 100
61 0.0000 -400.0000 100
62 153.0730 -369.5520 100
63 282.8430 -282.8430 100
64 369.5520 -153.0730 100
65 500.0000 0.0000 100
66 461.9400 191.3420 100
67 353.5530 353.5530 100
68 191.3420 461.9400 100
69 0.0000 500.0000 100
70 -191.3420 461.9400 100
71 -353.5530 353.5530 100
72 -461.9400 191.3420 100
73 -500.0000 0.0000 100
74 -461.9400 -191.3420 100
75 -353.5530 -353.5530 100
76 -191.3420 -461.9400 100
77 0.0000 -500.0000 100
78 191.3420 -461.9400 100
79 353.5530 -353.5530 100
Continued on next page
581
Table C.20 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
80 461.9400 -191.3420 100
81 600.0000 0.0000 100
82 554.3280 229.6100 100
83 424.2640 424.2640 100
84 229.6100 554.3280 100
85 0.0000 600.0000 100
86 -229.6100 554.3280 100
87 -424.2640 424.2640 100
88 -554.3280 229.6100 100
89 -600.0000 0.0000 100
90 -554.3280 -229.6100 100
91 -424.2640 -424.2640 100
92 -229.6100 -554.3280 100
93 0.0000 -600.0000 100
94 229.6100 -554.3280 100
95 424.2640 -424.2640 100
96 554.3280 -229.6100 100
97 700.0000 0.0000 100
98 646.7160 267.8780 100
99 494.9750 494.9750 100
100 267.8780 646.7160 100
101 0.0000 700.0000 100
102 -267.8780 646.7160 100
103 -494.9750 494.9750 100
104 -646.7160 267.8780 100
105 -700.0000 0.0000 100
106 -646.7160 -267.8780 100
107 -494.9750 -494.9750 100
108 -267.8780 -646.7160 100
109 0.0000 -700.0000 100
110 267.8780 -646.7160 100
111 494.9750 -494.9750 100
112 646.7160 -267.8780 100
113 800.0000 0.0000 100
114 739.1040 306.1470 100
115 565.6850 565.6850 100
116 306.1470 739.1040 100
117 0.0000 800.0000 100
118 -306.1470 739.1040 100
119 -565.6850 565.6850 100
120 -739.1040 306.1470 100
Continued on next page
582
Table C.20 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
121 -800.0000 0.0000 100
122 -739.1040 -306.1470 100
123 -565.6850 -565.6850 100
124 -306.1470 -739.1040 100
125 0.0000 -800.0000 100
126 306.1470 -739.1040 100
127 565.6850 -565.6850 100
128 739.1040 -306.1470 100
129 900.0000 0.0000 100
130 831.4920 344.4150 100
131 636.3960 636.3960 100
132 344.4150 831.4920 100
133 0.0000 900.0000 100
134 -344.4150 831.4920 100
135 -636.3960 636.3960 100
136 -831.4920 344.4150 100
137 -900.0000 0.0000 100
138 -831.4920 -344.4150 100
139 -636.3960 -636.3960 100
140 -344.4150 -831.4920 100
141 0.0000 -900.0000 100
142 344.4150 -831.4920 100
143 636.3960 -636.3960 100
144 831.4920 -344.4150 100
145 1000.0000 0.0000 100
146 923.8800 382.6830 100
147 707.1070 707.1070 100
148 382.6830 923.8800 100
149 0.0000 1000.0000 100
150 -382.6830 923.8800 100
151 -707.1070 707.1070 100
152 -923.8800 382.6830 100
153 -1000.0000 0.0000 100
154 -923.8800 -382.6830 100
155 -707.1070 -707.1070 100
156 -382.6830 -923.8800 100
157 0.0000 -1000.0000 100
158 382.6830 -923.8800 100
159 707.1070 -707.1070 100
160 923.8800 -382.6830 100
161 1100.0000 0.0000 100
Continued on next page
583
Table C.20 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
162 1016.2700 420.9520 100
163 777.8170 777.8170 100
164 420.9520 1016.2700 100
165 0.0000 1100.0000 100
166 -420.9520 1016.2700 100
167 -777.8170 777.8170 100
168 -1016.2700 420.9520 100
169 -1100.0000 0.0000 100
170 -1016.2700 -420.9520 100
171 -777.8170 -777.8170 100
172 -420.9520 -1016.2700 100
173 0.0000 -1100.0000 100
174 420.9520 -1016.2700 100
175 777.8170 -777.8170 100
176 1016.2700 -420.9520 100
177 1200.0000 0.0000 100
178 1108.6600 459.2200 100
179 848.5280 848.5280 100
180 459.2200 1108.6600 100
181 0.0000 1200.0000 100
182 -459.2200 1108.6600 100
183 -848.5280 848.5280 100
184 -1108.6600 459.2200 100
185 -1200.0000 0.0000 100
186 -1108.6600 -459.2200 100
187 -848.5280 -848.5280 100
188 -459.2200 -1108.6600 100
189 0.0000 -1200.0000 100
190 459.2200 -1108.6600 100
191 848.5280 -848.5280 100
192 1108.6600 -459.2200 100
Depot 0 0 N.A.
Table C.21: Min-Max Single-Depot Split-Delivery VRP
instance SD20
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
Continued on next page
584
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
2 86.6025 50.0000 100
3 50.0000 86.6025 100
4 0.0000 100.0000 100
5 -50.0000 86.6025 100
6 -86.6025 50.0000 100
7 -100.0000 0.0000 100
8 -86.6025 -50.0000 100
9 -50.0000 -86.6025 100
10 0.0000 -100.0000 100
11 50.0000 -86.6025 100
12 86.6025 -50.0000 100
13 200.0000 0.0000 100
14 173.2050 100.0000 100
15 100.0000 173.2050 100
16 0.0000 200.0000 100
17 -100.0000 173.2050 100
18 -173.2050 100.0000 100
19 -200.0000 0.0000 100
20 -173.2050 -100.0000 100
21 -100.0000 -173.2050 100
22 0.0000 -200.0000 100
23 100.0000 -173.2050 100
24 173.2050 -100.0000 100
25 300.0000 0.0000 100
26 259.8080 150.0000 100
27 150.0000 259.8080 100
28 0.0000 300.0000 100
29 -150.0000 259.8080 100
30 -259.8080 150.0000 100
31 -300.0000 0.0000 100
32 -259.8080 -150.0000 100
33 -150.0000 -259.8080 100
34 0.0000 -300.0000 100
35 150.0000 -259.8080 100
36 259.8080 -150.0000 100
37 400.0000 0.0000 100
38 346.4100 200.0000 100
39 200.0000 346.4100 100
40 0.0000 400.0000 100
41 -200.0000 346.4100 100
42 -346.4100 200.0000 100
Continued on next page
585
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
43 -400.0000 0.0000 100
44 -346.4100 -200.0000 100
45 -200.0000 -346.4100 100
46 0.0000 -400.0000 100
47 200.0000 -346.4100 100
48 346.4100 -200.0000 100
49 500.0000 0.0000 100
50 433.0130 250.0000 100
51 250.0000 433.0130 100
52 0.0000 500.0000 100
53 -250.0000 433.0130 100
54 -433.0130 250.0000 100
55 -500.0000 0.0000 100
56 -433.0130 -250.0000 100
57 -250.0000 -433.0130 100
58 0.0000 -500.0000 100
59 250.0000 -433.0130 100
60 433.0130 -250.0000 100
61 600.0000 0.0000 100
62 519.6150 300.0000 100
63 300.0000 519.6150 100
64 0.0000 600.0000 100
65 -300.0000 519.6150 100
66 -519.6150 300.0000 100
67 -600.0000 0.0000 100
68 -519.6150 -300.0000 100
69 -300.0000 -519.6150 100
70 0.0000 -600.0000 100
71 300.0000 -519.6150 100
72 519.6150 -300.0000 100
73 700.0000 0.0000 100
74 606.2180 350.0000 100
75 350.0000 606.2180 100
76 0.0000 700.0000 100
77 -350.0000 606.2180 100
78 -606.2180 350.0000 100
79 -700.0000 0.0000 100
80 -606.2180 -350.0000 100
81 -350.0000 -606.2180 100
82 0.0000 -700.0000 100
83 350.0000 -606.2180 100
Continued on next page
586
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
84 606.2180 -350.0000 100
85 800.0000 0.0000 100
86 692.8200 400.0000 100
87 400.0000 692.8200 100
88 0.0000 800.0000 100
89 -400.0000 692.8200 100
90 -692.8200 400.0000 100
91 -800.0000 0.0000 100
92 -692.8200 -400.0000 100
93 -400.0000 -692.8200 100
94 0.0000 -800.0000 100
95 400.0000 -692.8200 100
96 692.8200 -400.0000 100
97 900.0000 0.0000 100
98 779.4230 450.0000 100
99 450.0000 779.4230 100
100 0.0000 900.0000 100
101 -450.0000 779.4230 100
102 -779.4230 450.0000 100
103 -900.0000 0.0000 100
104 -779.4230 -450.0000 100
105 -450.0000 -779.4230 100
106 0.0000 -900.0000 100
107 450.0000 -779.4230 100
108 779.4230 -450.0000 100
109 1000.0000 0.0000 100
110 866.0250 500.0000 100
111 500.0000 866.0250 100
112 0.0000 1000.0000 100
113 -500.0000 866.0250 100
114 -866.0250 500.0000 100
115 -1000.0000 0.0000 100
116 -866.0250 -500.0000 100
117 -500.0000 -866.0250 100
118 0.0000 -1000.0000 100
119 500.0000 -866.0250 100
120 866.0250 -500.0000 100
121 1100.0000 0.0000 100
122 952.6280 550.0000 100
123 550.0000 952.6280 100
124 0.0000 1100.0000 100
Continued on next page
587
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
125 -550.0000 952.6280 100
126 -952.6280 550.0000 100
127 -1100.0000 0.0000 100
128 -952.6280 -550.0000 100
129 -550.0000 -952.6280 100
130 0.0000 -1100.0000 100
131 550.0000 -952.6280 100
132 952.6280 -550.0000 100
133 1200.0000 0.0000 100
134 1039.2300 600.0000 100
135 600.0000 1039.2300 100
136 0.0000 1200.0000 100
137 -600.0000 1039.2300 100
138 -1039.2300 600.0000 100
139 -1200.0000 0.0000 100
140 -1039.2300 -600.0000 100
141 -600.0000 -1039.2300 100
142 0.0000 -1200.0000 100
143 600.0000 -1039.2300 100
144 1039.2300 -600.0000 100
145 1300.0000 0.0000 100
146 1125.8300 650.0000 100
147 650.0000 1125.8300 100
148 0.0000 1300.0000 100
149 -650.0000 1125.8300 100
150 -1125.8300 650.0000 100
151 -1300.0000 0.0000 100
152 -1125.8300 -650.0000 100
153 -650.0000 -1125.8300 100
154 0.0000 -1300.0000 100
155 650.0000 -1125.8300 100
156 1125.8300 -650.0000 100
157 1400.0000 0.0000 100
158 1212.4400 700.0000 100
159 700.0000 1212.4400 100
160 0.0000 1400.0000 100
161 -700.0000 1212.4400 100
162 -1212.4400 700.0000 100
163 -1400.0000 0.0000 100
164 -1212.4400 -700.0000 100
165 -700.0000 -1212.4400 100
Continued on next page
588
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
166 0.0000 -1400.0000 100
167 700.0000 -1212.4400 100
168 1212.4400 -700.0000 100
169 1500.0000 0.0000 100
170 1299.0400 750.0000 100
171 750.0000 1299.0400 100
172 0.0000 1500.0000 100
173 -750.0000 1299.0400 100
174 -1299.0400 750.0000 100
175 -1500.0000 0.0000 100
176 -1299.0400 -750.0000 100
177 -750.0000 -1299.0400 100
178 0.0000 -1500.0000 100
179 750.0000 -1299.0400 100
180 1299.0400 -750.0000 100
181 1600.0000 0.0000 100
182 1385.6400 800.0000 100
183 800.0000 1385.6400 100
184 0.0000 1600.0000 100
185 -800.0000 1385.6400 100
186 -1385.6400 800.0000 100
187 -1600.0000 0.0000 100
188 -1385.6400 -800.0000 100
189 -800.0000 -1385.6400 100
190 0.0000 -1600.0000 100
191 800.0000 -1385.6400 100
192 1385.6400 -800.0000 100
193 1700.0000 0.0000 100
194 1472.2400 850.0000 100
195 850.0000 1472.2400 100
196 0.0000 1700.0000 100
197 -850.0000 1472.2400 100
198 -1472.2400 850.0000 100
199 -1700.0000 0.0000 100
200 -1472.2400 -850.0000 100
201 -850.0000 -1472.2400 100
202 0.0000 -1700.0000 100
203 850.0000 -1472.2400 100
204 1472.2400 -850.0000 100
205 1800.0000 0.0000 100
206 1558.8500 900.0000 100
Continued on next page
589
Table C.21 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
207 900.0000 1558.8500 100
208 0.0000 1800.0000 100
209 -900.0000 1558.8500 100
210 -1558.8500 900.0000 100
211 -1800.0000 0.0000 100
212 -1558.8500 -900.0000 100
213 -900.0000 -1558.8500 100
214 0.0000 -1800.0000 100
215 900.0000 -1558.8500 100
216 1558.8500 -900.0000 100
217 1900.0000 0.0000 100
218 1645.4500 950.0000 100
219 950.0000 1645.4500 100
220 0.0000 1900.0000 100
221 -950.0000 1645.4500 100
222 -1645.4500 950.0000 100
223 -1900.0000 0.0000 100
224 -1645.4500 -950.0000 100
225 -950.0000 -1645.4500 100
226 0.0000 -1900.0000 100
227 950.0000 -1645.4500 100
228 1645.4500 -950.0000 100
229 2000.0000 0.0000 100
230 1732.0500 1000.0000 100
231 1000.0000 1732.0500 100
232 0.0000 2000.0000 100
233 -1000.0000 1732.0500 100
234 -1732.0500 1000.0000 100
235 -2000.0000 0.0000 100
236 -1732.0500 -1000.0000 100
237 -1000.0000 -1732.0500 100
238 0.0000 -2000.0000 100
239 1000.0000 -1732.0500 100
240 1732.0500 -1000.0000 100
Depot 0 0 N.A.
590
Table C.22: Min-Max Single-Depot Split-Delivery VRP
instance SD21
Customer index x-coordinate y-coordinate Service time
1 100.0000 0.0000 100
2 99.6195 8.7156 100
3 98.4808 17.3648 100
4 96.5926 25.8819 100
5 93.9693 34.2020 100
6 90.6308 42.2618 100
7 86.6025 50.0000 100
8 81.9152 57.3576 100
9 76.6044 64.2788 100
10 70.7107 70.7107 100
11 64.2788 76.6044 100
12 57.3576 81.9152 100
13 50.0000 86.6025 100
14 42.2618 90.6308 100
15 34.2020 93.9693 100
16 25.8819 96.5926 100
17 17.3648 98.4808 100
18 8.7156 99.6195 100
19 0.0000 100.0000 100
20 -8.7156 99.6195 100
21 -17.3648 98.4808 100
22 -25.8819 96.5926 100
23 -34.2020 93.9693 100
24 -42.2618 90.6308 100
25 -50.0000 86.6025 100
26 -57.3576 81.9152 100
27 -64.2788 76.6044 100
28 -70.7107 70.7107 100
29 -76.6044 64.2788 100
30 -81.9152 57.3576 100
31 -86.6025 50.0000 100
32 -90.6308 42.2618 100
33 -93.9693 34.2020 100
34 -96.5926 25.8819 100
35 -98.4808 17.3648 100
36 -99.6195 8.7156 100
37 -100.0000 0.0000 100
38 -99.6195 -8.7156 100
39 -98.4808 -17.3648 100
40 -96.5926 -25.8819 100
Continued on next page
591
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
41 -93.9693 -34.2020 100
42 -90.6308 -42.2618 100
43 -86.6025 -50.0000 100
44 -81.9152 -57.3576 100
45 -76.6044 -64.2788 100
46 -70.7107 -70.7107 100
47 -64.2788 -76.6044 100
48 -57.3576 -81.9152 100
49 -50.0000 -86.6025 100
50 -42.2618 -90.6308 100
51 -34.2020 -93.9693 100
52 -25.8819 -96.5926 100
53 -17.3648 -98.4808 100
54 -8.7156 -99.6195 100
55 0.0000 -100.0000 100
56 8.7156 -99.6195 100
57 17.3648 -98.4808 100
58 25.8819 -96.5926 100
59 34.2020 -93.9693 100
60 42.2618 -90.6308 100
61 50.0000 -86.6025 100
62 57.3576 -81.9152 100
63 64.2788 -76.6044 100
64 70.7107 -70.7107 100
65 76.6044 -64.2788 100
66 81.9152 -57.3576 100
67 86.6025 -50.0000 100
68 90.6308 -42.2618 100
69 93.9693 -34.2020 100
70 96.5926 -25.8819 100
71 98.4808 -17.3648 100
72 99.6195 -8.7156 100
73 200.0000 0.0000 100
74 199.2390 17.4311 100
75 196.9620 34.7296 100
76 193.1850 51.7638 100
77 187.9390 68.4040 100
78 181.2620 84.5237 100
79 173.2050 100.0000 100
80 163.8300 114.7150 100
81 153.2090 128.5580 100
Continued on next page
592
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
82 141.4210 141.4210 100
83 128.5580 153.2090 100
84 114.7150 163.8300 100
85 100.0000 173.2050 100
86 84.5237 181.2620 100
87 68.4040 187.9390 100
88 51.7638 193.1850 100
89 34.7296 196.9620 100
90 17.4311 199.2390 100
91 0.0000 200.0000 100
92 -17.4311 199.2390 100
93 -34.7296 196.9620 100
94 -51.7638 193.1850 100
95 -68.4040 187.9390 100
96 -84.5237 181.2620 100
97 -100.0000 173.2050 100
98 -114.7150 163.8300 100
99 -128.5580 153.2090 100
100 -141.4210 141.4210 100
101 -153.2090 128.5580 100
102 -163.8300 114.7150 100
103 -173.2050 100.0000 100
104 -181.2620 84.5237 100
105 -187.9390 68.4040 100
106 -193.1850 51.7638 100
107 -196.9620 34.7296 100
108 -199.2390 17.4311 100
109 -200.0000 0.0000 100
110 -199.2390 -17.4311 100
111 -196.9620 -34.7296 100
112 -193.1850 -51.7638 100
113 -187.9390 -68.4040 100
114 -181.2620 -84.5237 100
115 -173.2050 -100.0000 100
116 -163.8300 -114.7150 100
117 -153.2090 -128.5580 100
118 -141.4210 -141.4210 100
119 -128.5580 -153.2090 100
120 -114.7150 -163.8300 100
121 -100.0000 -173.2050 100
122 -84.5237 -181.2620 100
Continued on next page
593
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
123 -68.4040 -187.9390 100
124 -51.7638 -193.1850 100
125 -34.7296 -196.9620 100
126 -17.4311 -199.2390 100
127 0.0000 -200.0000 100
128 17.4311 -199.2390 100
129 34.7296 -196.9620 100
130 51.7638 -193.1850 100
131 68.4040 -187.9390 100
132 84.5237 -181.2620 100
133 100.0000 -173.2050 100
134 114.7150 -163.8300 100
135 128.5580 -153.2090 100
136 141.4210 -141.4210 100
137 153.2090 -128.5580 100
138 163.8300 -114.7150 100
139 173.2050 -100.0000 100
140 181.2620 -84.5237 100
141 187.9390 -68.4040 100
142 193.1850 -51.7638 100
143 196.9620 -34.7296 100
144 199.2390 -17.4311 100
145 300.0000 0.0000 100
146 298.8580 26.1467 100
147 295.4420 52.0945 100
148 289.7780 77.6457 100
149 281.9080 102.6060 100
150 271.8920 126.7850 100
151 259.8080 150.0000 100
152 245.7460 172.0730 100
153 229.8130 192.8360 100
154 212.1320 212.1320 100
155 192.8360 229.8130 100
156 172.0730 245.7460 100
157 150.0000 259.8080 100
158 126.7850 271.8920 100
159 102.6060 281.9080 100
160 77.6457 289.7780 100
161 52.0945 295.4420 100
162 26.1467 298.8580 100
163 0.0000 300.0000 100
Continued on next page
594
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
164 -26.1467 298.8580 100
165 -52.0945 295.4420 100
166 -77.6457 289.7780 100
167 -102.6060 281.9080 100
168 -126.7850 271.8920 100
169 -150.0000 259.8080 100
170 -172.0730 245.7460 100
171 -192.8360 229.8130 100
172 -212.1320 212.1320 100
173 -229.8130 192.8360 100
174 -245.7460 172.0730 100
175 -259.8080 150.0000 100
176 -271.8920 126.7850 100
177 -281.9080 102.6060 100
178 -289.7780 77.6457 100
179 -295.4420 52.0945 100
180 -298.8580 26.1467 100
181 -300.0000 0.0000 100
182 -298.8580 -26.1467 100
183 -295.4420 -52.0945 100
184 -289.7780 -77.6457 100
185 -281.9080 -102.6060 100
186 -271.8920 -126.7850 100
187 -259.8080 -150.0000 100
188 -245.7460 -172.0730 100
189 -229.8130 -192.8360 100
190 -212.1320 -212.1320 100
191 -192.8360 -229.8130 100
192 -172.0730 -245.7460 100
193 -150.0000 -259.8080 100
194 -126.7850 -271.8920 100
195 -102.6060 -281.9080 100
196 -77.6457 -289.7780 100
197 -52.0945 -295.4420 100
198 -26.1467 -298.8580 100
199 0.0000 -300.0000 100
200 26.1467 -298.8580 100
201 52.0945 -295.4420 100
202 77.6457 -289.7780 100
203 102.6060 -281.9080 100
204 126.7850 -271.8920 100
Continued on next page
595
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
205 150.0000 -259.8080 100
206 172.0730 -245.7460 100
207 192.8360 -229.8130 100
208 212.1320 -212.1320 100
209 229.8130 -192.8360 100
210 245.7460 -172.0730 100
211 259.8080 -150.0000 100
212 271.8920 -126.7850 100
213 281.9080 -102.6060 100
214 289.7780 -77.6457 100
215 295.4420 -52.0945 100
216 298.8580 -26.1467 100
217 400.0000 0.0000 100
218 398.4780 34.8623 100
219 393.9230 69.4593 100
220 386.3700 103.5280 100
221 375.8770 136.8080 100
222 362.5230 169.0470 100
223 346.4100 200.0000 100
224 327.6610 229.4310 100
225 306.4180 257.1150 100
226 282.8430 282.8430 100
227 257.1150 306.4180 100
228 229.4310 327.6610 100
229 200.0000 346.4100 100
230 169.0470 362.5230 100
231 136.8080 375.8770 100
232 103.5280 386.3700 100
233 69.4593 393.9230 100
234 34.8623 398.4780 100
235 0.0000 400.0000 100
236 -34.8623 398.4780 100
237 -69.4593 393.9230 100
238 -103.5280 386.3700 100
239 -136.8080 375.8770 100
240 -169.0470 362.5230 100
241 -200.0000 346.4100 100
242 -229.4310 327.6610 100
243 -257.1150 306.4180 100
244 -282.8430 282.8430 100
245 -306.4180 257.1150 100
Continued on next page
596
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
246 -327.6610 229.4310 100
247 -346.4100 200.0000 100
248 -362.5230 169.0470 100
249 -375.8770 136.8080 100
250 -386.3700 103.5280 100
251 -393.9230 69.4593 100
252 -398.4780 34.8623 100
253 -400.0000 0.0000 100
254 -398.4780 -34.8623 100
255 -393.9230 -69.4593 100
256 -386.3700 -103.5280 100
257 -375.8770 -136.8080 100
258 -362.5230 -169.0470 100
259 -346.4100 -200.0000 100
260 -327.6610 -229.4310 100
261 -306.4180 -257.1150 100
262 -282.8430 -282.8430 100
263 -257.1150 -306.4180 100
264 -229.4310 -327.6610 100
265 -200.0000 -346.4100 100
266 -169.0470 -362.5230 100
267 -136.8080 -375.8770 100
268 -103.5280 -386.3700 100
269 -69.4593 -393.9230 100
270 -34.8623 -398.4780 100
271 0.0000 -400.0000 100
272 34.8623 -398.4780 100
273 69.4593 -393.9230 100
274 103.5280 -386.3700 100
275 136.8080 -375.8770 100
276 169.0470 -362.5230 100
277 200.0000 -346.4100 100
278 229.4310 -327.6610 100
279 257.1150 -306.4180 100
280 282.8430 -282.8430 100
281 306.4180 -257.1150 100
282 327.6610 -229.4310 100
283 346.4100 -200.0000 100
284 362.5230 -169.0470 100
285 375.8770 -136.8080 100
286 386.3700 -103.5280 100
Continued on next page
597
Table C.22 –Continued from previous page
Customer index x-coordinate y-coordinate Service time
287 393.9230 -69.4593 100
288 398.4780 -34.8623 100
Depot 0 0 N.A.
598
Appendix D: Close-Enough Traveling Salesman Problem test instances
In this appendix, we present the test instances for the Close-Enough Travel-
ing Salesman Problem in Chapter 6. (The min-max Close-Enough Vehicle Routing
Problem has exactly the same customer locations.) There are 14 instances. Each
instance is presented in one table. For example, instance kroD100rdmRad is pre-
sented in Table D.1. The first column gives the customer index. The second and
third columns give the x and y coordinates of the location. The fourth column gives
the customer’s service range. The last row of each table gives the location of the
depot.
We also present the solutions produced by MMSZ in Figures D.1 to D.14. The
depot is represented by a red ’*’. The customers are drawn using blue circles to
show both their locations and service ranges. The route is shown by a thick black
line.
599
Table D.1: CETSP instance kroD100rdmRad
Customer index x-coordinate y-coordinate Service range
1 29.9500 2.6400 1.4400
2 2.0200 2.3300 1.4400
3 9.8100 8.4800 1.4400
4 13.4600 4.0800 1.4400
5 7.8100 6.7000 1.4400
6 10.0900 10.0100 1.4400
7 29.2700 17.7700 1.4400
8 29.8200 9.4900 1.4400
9 5.5500 11.2100 1.4400
10 4.6400 13.0200 1.4400
11 34.5200 6.3700 1.4400
12 5.7100 19.8200 1.4400
13 26.5600 1.2800 1.4400
14 16.2300 17.2300 1.4400
15 20.6700 6.9400 1.4400
16 17.2500 9.2700 1.4400
17 36.0000 4.5900 1.4400
18 11.0900 11.9600 1.4400
19 3.6600 3.3900 1.4400
20 7.7800 12.8200 1.4400
21 3.8600 16.1600 1.4400
22 39.1800 12.1700 1.4400
23 33.3200 10.4900 1.4400
24 25.9700 3.4900 1.4400
25 8.1100 12.9500 1.4400
26 2.4100 10.6900 1.4400
27 26.5800 3.6000 1.4400
28 3.9400 19.4400 1.4400
29 37.8600 18.6200 1.4400
30 2.6400 0.3600 1.4400
31 20.5000 18.3300 1.4400
32 35.3800 1.2500 1.4400
33 16.4600 18.1700 1.4400
34 29.9300 6.2400 1.4400
35 5.4700 0.2500 1.4400
36 33.7300 19.0200 1.4400
37 4.6000 2.6700 1.4400
38 30.6000 7.8100 1.4400
39 18.2800 4.5600 1.4400
40 10.2100 9.6200 1.4400
41 23.4700 3.8800 1.4400
Continued on next page
600
Table D.1 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 35.3500 11.1200 1.4400
43 15.2900 5.8100 1.4400
44 12.0300 3.8500 1.4400
45 17.8700 19.0200 1.4400
46 27.4000 11.0100 1.4400
47 5.5500 17.5300 1.4400
48 0.4700 3.6300 1.4400
49 39.3500 5.4000 1.4400
50 30.6200 3.2900 1.4400
51 3.8700 1.9900 1.4400
52 29.0100 9.2000 1.4400
53 9.3100 5.1200 1.4400
54 17.6600 6.9200 1.4400
55 4.0100 9.8000 1.4400
56 1.4900 16.2900 1.4400
57 22.1400 19.7700 1.4400
58 38.0500 16.1900 1.4400
59 11.7900 9.6900 1.4400
60 10.1700 3.3300 1.4400
61 28.3400 15.1200 1.4400
62 6.3400 2.9400 1.4400
63 18.1900 8.1400 1.4400
64 13.9300 8.5900 1.4400
65 17.6800 15.7800 1.4400
66 30.2300 8.7100 1.4400
67 32.4800 19.0600 1.4400
68 16.3200 17.4200 1.4400
69 22.2300 9.9000 1.4400
70 38.6800 6.9700 1.4400
71 15.4100 3.5400 1.4400
72 23.7400 19.4400 1.4400
73 19.6200 3.8900 1.4400
74 30.0700 15.2400 1.4400
75 32.2000 19.4500 1.4400
76 23.5600 15.6800 1.4400
77 16.0400 7.0600 1.4400
78 20.2800 17.3600 1.4400
79 25.8100 1.2100 1.4400
80 22.2100 15.7800 1.4400
81 29.4400 6.3200 1.4400
82 10.8200 15.6100 1.4400
Continued on next page
601
Table D.1 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 9.9700 9.4200 1.4400
84 23.3400 5.2300 1.4400
85 12.6400 10.9000 1.4400
86 16.9900 12.9400 1.4400
87 2.3500 10.5900 1.4400
88 25.9200 2.4800 1.4400
89 36.4200 6.9900 1.4400
90 35.9900 5.1400 1.4400
91 17.6600 6.7800 1.4400
92 2.4000 6.1900 1.4400
93 12.7200 2.4600 1.4400
94 35.0300 3.0100 1.4400
95 0.8000 15.3300 1.4400
96 16.7700 12.3800 1.4400
97 37.6600 1.5400 1.4400
98 39.4600 4.5900 1.4400
99 19.9400 18.5200 1.4400
Depot 2.7800 1.6500 N.A.
602
Table D.2: CETSP instance rat195rdmRad
Customer index x-coordinate y-coordinate Service range
1 0.3000 1.2000 18.1000
2 1.7000 1.2000 18.1000
3 2.3000 0.9000 18.1000
4 3.4000 1.1000 18.1000
5 4.7000 1.1000 18.1000
6 5.4000 1.2000 18.1000
7 6.6000 1.6000 18.1000
8 7.5000 0.7000 18.1000
9 8.6000 0.6000 18.1000
10 9.4000 0.8000 18.1000
11 10.7000 0.9000 18.1000
12 11.5000 1.4000 18.1000
13 12.3000 1.5000 18.1000
14 0.3000 3.2000 18.1000
15 1.5000 3.2000 18.1000
16 2.6000 3.4000 18.1000
17 3.3000 3.4000 18.1000
18 4.2000 3.4000 18.1000
19 5.3000 2.5000 18.1000
20 6.4000 3.2000 18.1000
21 7.4000 3.2000 18.1000
22 8.5000 3.4000 18.1000
23 9.5000 2.8000 18.1000
24 10.4000 2.5000 18.1000
25 11.3000 3.1000 18.1000
26 12.5000 3.4000 18.1000
27 0.3000 4.8000 18.1000
28 1.5000 4.6000 18.1000
29 2.6000 5.0000 18.1000
30 3.6000 5.4000 18.1000
31 4.8000 5.0000 18.1000
32 5.4000 4.6000 18.1000
33 6.4000 5.4000 18.1000
34 7.5000 4.4000 18.1000
35 8.8000 4.9000 18.1000
36 9.8000 5.0000 18.1000
37 10.3000 5.4000 18.1000
38 11.5000 4.7000 18.1000
39 12.7000 4.9000 18.1000
40 0.6000 7.5000 18.1000
41 1.5000 7.5000 18.1000
Continued on next page
603
Table D.2 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 2.7000 7.3000 18.1000
43 3.6000 7.3000 18.1000
44 4.7000 6.8000 18.1000
45 5.4000 7.2000 18.1000
46 6.6000 6.8000 18.1000
47 7.4000 6.7000 18.1000
48 8.5000 6.5000 18.1000
49 9.4000 7.4000 18.1000
50 10.7000 6.5000 18.1000
51 11.7000 6.5000 18.1000
52 12.5000 6.8000 18.1000
53 0.6000 8.4000 18.1000
54 1.3000 9.5000 18.1000
55 2.5000 9.4000 18.1000
56 3.7000 8.4000 18.1000
57 4.7000 8.7000 18.1000
58 5.3000 9.5000 18.1000
59 6.3000 8.6000 18.1000
60 7.7000 9.3000 18.1000
61 8.3000 8.9000 18.1000
62 9.4000 9.5000 18.1000
63 10.3000 9.2000 18.1000
64 11.5000 9.5000 18.1000
65 12.3000 9.3000 18.1000
66 0.7000 11.4000 18.1000
67 1.5000 11.1000 18.1000
68 2.4000 11.2000 18.1000
69 3.6000 10.8000 18.1000
70 4.3000 11.2000 18.1000
71 5.6000 10.5000 18.1000
72 6.4000 11.2000 18.1000
73 7.3000 11.2000 18.1000
74 8.6000 10.7000 18.1000
75 9.8000 10.8000 18.1000
76 10.4000 11.3000 18.1000
77 11.7000 11.5000 18.1000
78 12.6000 10.9000 18.1000
79 0.6000 12.7000 18.1000
80 1.7000 12.5000 18.1000
81 2.7000 13.4000 18.1000
82 3.5000 12.6000 18.1000
Continued on next page
604
Table D.2 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 4.4000 13.1000 18.1000
84 5.4000 13.2000 18.1000
85 6.3000 12.4000 18.1000
86 7.7000 12.7000 18.1000
87 8.2000 13.4000 18.1000
88 9.6000 12.8000 18.1000
89 10.3000 12.6000 18.1000
90 11.6000 13.0000 18.1000
91 12.6000 13.4000 18.1000
92 0.7000 15.2000 18.1000
93 1.6000 14.7000 18.1000
94 2.4000 15.3000 18.1000
95 3.5000 15.1000 18.1000
96 4.5000 15.4000 18.1000
97 5.5000 14.6000 18.1000
98 6.3000 15.5000 18.1000
99 7.5000 15.1000 18.1000
100 8.7000 15.4000 18.1000
101 9.3000 15.6000 18.1000
102 10.4000 15.1000 18.1000
103 11.7000 15.3000 18.1000
104 12.7000 14.8000 18.1000
105 0.3000 16.4000 18.1000
106 1.6000 17.2000 18.1000
107 2.5000 16.5000 18.1000
108 3.5000 17.5000 18.1000
109 4.4000 16.9000 18.1000
110 5.3000 17.4000 18.1000
111 6.4000 16.8000 18.1000
112 7.6000 17.1000 18.1000
113 8.7000 17.3000 18.1000
114 9.5000 17.4000 18.1000
115 10.6000 16.8000 18.1000
116 11.4000 16.9000 18.1000
117 12.5000 16.9000 18.1000
118 0.3000 19.0000 18.1000
119 1.6000 18.8000 18.1000
120 2.5000 19.5000 18.1000
121 3.7000 18.6000 18.1000
122 4.4000 18.9000 18.1000
123 5.4000 19.4000 18.1000
Continued on next page
605
Table D.2 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 6.6000 19.2000 18.1000
125 7.7000 19.2000 18.1000
126 8.5000 18.8000 18.1000
127 9.3000 18.5000 18.1000
128 10.6000 19.2000 18.1000
129 11.3000 19.3000 18.1000
130 12.5000 19.5000 18.1000
131 0.5000 20.7000 18.1000
132 1.5000 21.3000 18.1000
133 2.4000 20.9000 18.1000
134 3.3000 21.4000 18.1000
135 4.3000 20.6000 18.1000
136 5.3000 21.1000 18.1000
137 6.4000 21.3000 18.1000
138 7.4000 21.2000 18.1000
139 8.4000 21.2000 18.1000
140 9.4000 20.9000 18.1000
141 10.4000 21.5000 18.1000
142 11.5000 20.6000 18.1000
143 12.7000 20.9000 18.1000
144 0.6000 22.9000 18.1000
145 1.3000 22.7000 18.1000
146 2.6000 23.5000 18.1000
147 3.4000 22.5000 18.1000
148 4.3000 22.7000 18.1000
149 5.5000 22.5000 18.1000
150 6.7000 22.9000 18.1000
151 7.5000 23.4000 18.1000
152 8.7000 23.0000 18.1000
153 9.5000 23.5000 18.1000
154 10.5000 22.8000 18.1000
155 11.7000 22.5000 18.1000
156 12.7000 23.0000 18.1000
157 0.6000 24.9000 18.1000
158 1.5000 24.6000 18.1000
159 2.6000 25.5000 18.1000
160 3.3000 24.6000 18.1000
161 4.7000 24.8000 18.1000
162 5.8000 25.2000 18.1000
163 6.5000 24.8000 18.1000
164 7.3000 24.7000 18.1000
Continued on next page
606
Table D.2 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 8.7000 24.9000 18.1000
166 9.4000 24.5000 18.1000
167 10.4000 25.6000 18.1000
168 11.3000 24.6000 18.1000
169 12.5000 25.3000 18.1000
170 0.5000 26.6000 18.1000
171 1.6000 27.4000 18.1000
172 2.4000 26.7000 18.1000
173 3.7000 26.6000 18.1000
174 4.5000 26.7000 18.1000
175 5.4000 26.6000 18.1000
176 6.7000 26.7000 18.1000
177 7.4000 26.5000 18.1000
178 8.7000 26.4000 18.1000
179 9.5000 27.1000 18.1000
180 10.6000 26.4000 18.1000
181 11.6000 27.1000 18.1000
182 12.7000 27.3000 18.1000
183 0.7000 28.7000 18.1000
184 1.7000 29.4000 18.1000
185 2.3000 28.7000 18.1000
186 3.3000 28.4000 18.1000
187 4.3000 28.8000 18.1000
188 5.3000 29.5000 18.1000
189 6.7000 28.8000 18.1000
190 7.3000 28.6000 18.1000
191 8.7000 29.3000 18.1000
192 9.4000 28.4000 18.1000
193 10.4000 29.1000 18.1000
194 11.4000 29.4000 18.1000
Depot 12.7000 29.0000 N.A.
607
Table D.3: CETSP instance lin318rdmRad
Customer index x-coordinate y-coordinate Service range
1 6.3000 7.1000 39.2000
2 9.4000 7.1000 39.2000
3 14.2000 37.0000 39.2000
4 17.3000 127.6000 39.2000
5 20.5000 121.3000 39.2000
6 21.3000 6.9000 39.2000
7 24.4000 6.9000 39.2000
8 27.6000 63.0000 39.2000
9 28.3000 73.2000 39.2000
10 36.2000 6.9000 39.2000
11 39.4000 6.9000 39.2000
12 44.9000 37.0000 39.2000
13 48.0000 127.6000 39.2000
14 51.2000 121.3000 39.2000
15 52.8000 15.7000 39.2000
16 58.3000 63.0000 39.2000
17 59.1000 73.2000 39.2000
18 63.8000 65.4000 39.2000
19 63.8000 49.6000 39.2000
20 63.8000 31.4000 39.2000
21 63.8000 14.2000 39.2000
22 66.9000 14.2000 39.2000
23 67.7000 31.5000 39.2000
24 67.7000 49.6000 39.2000
25 67.7000 65.4000 39.2000
26 70.9000 65.4000 39.2000
27 70.9000 49.6000 39.2000
28 70.9000 31.5000 39.2000
29 70.1000 14.2000 39.2000
30 76.4000 22.0000 39.2000
31 81.1000 18.9000 39.2000
32 84.3000 17.3000 39.2000
33 85.8000 37.0000 39.2000
34 89.0000 127.6000 39.2000
35 92.1000 121.3000 39.2000
36 99.2000 63.0000 39.2000
37 100.0000 73.2000 39.2000
38 119.7000 127.6000 39.2000
39 122.8000 121.3000 39.2000
40 127.6000 20.5000 39.2000
41 129.9000 63.0000 39.2000
Continued on next page
608
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 130.7000 73.2000 39.2000
43 136.2000 65.4000 39.2000
44 136.2000 49.6000 39.2000
45 136.2000 29.1000 39.2000
46 142.5000 65.4000 39.2000
47 142.5000 49.6000 39.2000
48 142.5000 29.1000 39.2000
49 141.7000 17.3000 39.2000
50 148.8000 29.1000 39.2000
51 148.8000 49.6000 39.2000
52 148.8000 65.4000 39.2000
53 155.1000 65.4000 39.2000
54 155.1000 49.6000 39.2000
55 155.1000 29.1000 39.2000
56 161.4000 29.1000 39.2000
57 161.4000 49.6000 39.2000
58 161.4000 65.4000 39.2000
59 173.2000 18.9000 39.2000
60 181.1000 127.6000 39.2000
61 184.3000 121.3000 39.2000
62 191.3000 63.0000 39.2000
63 192.1000 73.2000 39.2000
64 208.7000 37.0000 39.2000
65 211.8000 127.6000 39.2000
66 215.0000 121.3000 39.2000
67 218.9000 20.5000 39.2000
68 222.0000 18.9000 39.2000
69 222.0000 63.0000 39.2000
70 222.8000 73.2000 39.2000
71 224.4000 14.2000 39.2000
72 227.6000 31.5000 39.2000
73 227.6000 49.6000 39.2000
74 227.6000 65.4000 39.2000
75 231.5000 65.4000 39.2000
76 231.5000 49.6000 39.2000
77 231.5000 31.5000 39.2000
78 233.1000 14.2000 39.2000
79 234.6000 31.5000 39.2000
80 234.6000 49.6000 39.2000
81 234.6000 65.4000 39.2000
82 236.2000 14.2000 39.2000
Continued on next page
609
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 240.2000 15.7000 39.2000
84 240.2000 22.0000 39.2000
85 248.0000 14.2000 39.2000
86 249.6000 37.0000 39.2000
87 252.8000 127.6000 39.2000
88 255.9000 121.3000 39.2000
89 263.0000 63.0000 39.2000
90 263.8000 73.2000 39.2000
91 275.6000 6.9000 39.2000
92 278.7000 6.9000 39.2000
93 280.3000 37.0000 39.2000
94 283.5000 127.6000 39.2000
95 286.6000 121.3000 39.2000
96 290.6000 6.9000 39.2000
97 293.7000 6.9000 39.2000
98 293.7000 63.0000 39.2000
99 294.5000 73.2000 39.2000
100 301.6000 127.6000 39.2000
101 305.5000 6.9000 39.2000
102 308.7000 6.9000 39.2000
103 60.6000 22.0000 39.2000
104 116.5000 37.0000 39.2000
105 178.0000 37.0000 39.2000
106 6.3000 140.2000 39.2000
107 9.4000 140.2000 39.2000
108 14.2000 170.1000 39.2000
109 17.3000 260.7000 39.2000
110 20.5000 254.4000 39.2000
111 21.3000 140.0000 39.2000
112 24.4000 140.0000 39.2000
113 27.6000 196.1000 39.2000
114 28.3000 206.3000 39.2000
115 36.2000 140.0000 39.2000
116 39.4000 140.0000 39.2000
117 44.9000 170.1000 39.2000
118 48.0000 260.7000 39.2000
119 51.2000 254.4000 39.2000
120 52.8000 148.8000 39.2000
121 58.3000 196.1000 39.2000
122 59.1000 206.3000 39.2000
123 63.8000 198.5000 39.2000
Continued on next page
610
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 63.8000 182.7000 39.2000
125 63.8000 164.5000 39.2000
126 63.8000 147.3000 39.2000
127 66.9000 147.3000 39.2000
128 67.7000 164.6000 39.2000
129 67.7000 182.7000 39.2000
130 67.7000 198.5000 39.2000
131 70.9000 198.5000 39.2000
132 70.9000 182.7000 39.2000
133 70.9000 164.6000 39.2000
134 70.1000 147.3000 39.2000
135 76.4000 155.1000 39.2000
136 81.1000 152.0000 39.2000
137 84.3000 150.4000 39.2000
138 85.8000 170.1000 39.2000
139 89.0000 260.7000 39.2000
140 92.1000 254.4000 39.2000
141 99.2000 196.1000 39.2000
142 100.0000 206.3000 39.2000
143 119.7000 260.7000 39.2000
144 122.8000 254.4000 39.2000
145 127.6000 153.6000 39.2000
146 129.9000 196.1000 39.2000
147 130.7000 206.3000 39.2000
148 136.2000 198.5000 39.2000
149 136.2000 182.7000 39.2000
150 136.2000 162.2000 39.2000
151 142.5000 198.5000 39.2000
152 142.5000 182.7000 39.2000
153 142.5000 162.2000 39.2000
154 141.7000 150.4000 39.2000
155 148.8000 162.2000 39.2000
156 148.8000 182.7000 39.2000
157 148.8000 198.5000 39.2000
158 155.1000 198.5000 39.2000
159 155.1000 182.7000 39.2000
160 155.1000 162.2000 39.2000
161 161.4000 162.2000 39.2000
162 161.4000 182.7000 39.2000
163 161.4000 198.5000 39.2000
164 173.2000 152.0000 39.2000
Continued on next page
611
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 181.1000 260.7000 39.2000
166 184.3000 254.4000 39.2000
167 191.3000 196.1000 39.2000
168 192.1000 206.3000 39.2000
169 208.7000 170.1000 39.2000
170 211.8000 260.7000 39.2000
171 215.0000 254.4000 39.2000
172 218.9000 153.6000 39.2000
173 222.0000 152.0000 39.2000
174 222.0000 196.1000 39.2000
175 222.8000 206.3000 39.2000
176 224.4000 147.3000 39.2000
177 227.6000 164.6000 39.2000
178 227.6000 182.7000 39.2000
179 227.6000 198.5000 39.2000
180 231.5000 198.5000 39.2000
181 231.5000 182.7000 39.2000
182 231.5000 164.6000 39.2000
183 233.1000 147.3000 39.2000
184 234.6000 164.6000 39.2000
185 234.6000 182.7000 39.2000
186 234.6000 198.5000 39.2000
187 236.2000 147.3000 39.2000
188 240.2000 148.8000 39.2000
189 240.2000 155.1000 39.2000
190 248.0000 147.3000 39.2000
191 249.6000 170.1000 39.2000
192 252.8000 260.7000 39.2000
193 255.9000 254.4000 39.2000
194 263.0000 196.1000 39.2000
195 263.8000 206.3000 39.2000
196 275.6000 140.0000 39.2000
197 278.7000 140.0000 39.2000
198 280.3000 170.1000 39.2000
199 283.5000 260.7000 39.2000
200 286.6000 254.4000 39.2000
201 290.6000 140.0000 39.2000
202 293.7000 140.0000 39.2000
203 293.7000 196.1000 39.2000
204 294.5000 206.3000 39.2000
205 301.6000 260.7000 39.2000
Continued on next page
612
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 305.5000 140.0000 39.2000
207 308.7000 140.0000 39.2000
208 60.6000 155.1000 39.2000
209 116.5000 170.1000 39.2000
210 178.0000 170.1000 39.2000
211 6.3000 273.3000 39.2000
212 9.4000 273.3000 39.2000
213 14.2000 303.2000 39.2000
214 17.3000 393.8000 39.2000
215 20.5000 387.5000 39.2000
216 21.3000 273.1000 39.2000
217 24.4000 273.1000 39.2000
218 27.6000 329.2000 39.2000
219 28.3000 339.4000 39.2000
220 36.2000 273.1000 39.2000
221 39.4000 273.1000 39.2000
222 44.9000 303.2000 39.2000
223 48.0000 393.8000 39.2000
224 51.2000 387.5000 39.2000
225 52.8000 281.9000 39.2000
226 58.3000 329.2000 39.2000
227 59.1000 339.4000 39.2000
228 63.8000 331.6000 39.2000
229 63.8000 315.8000 39.2000
230 63.8000 297.6000 39.2000
231 63.8000 280.4000 39.2000
232 66.9000 280.4000 39.2000
233 67.7000 297.7000 39.2000
234 67.7000 315.8000 39.2000
235 67.7000 331.6000 39.2000
236 70.9000 331.6000 39.2000
237 70.9000 315.8000 39.2000
238 70.9000 297.7000 39.2000
239 70.1000 280.4000 39.2000
240 76.4000 288.2000 39.2000
241 81.1000 285.1000 39.2000
242 84.3000 283.5000 39.2000
243 85.8000 303.2000 39.2000
244 89.0000 393.8000 39.2000
245 92.1000 387.5000 39.2000
246 99.2000 329.2000 39.2000
Continued on next page
613
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 100.0000 339.4000 39.2000
248 119.7000 393.8000 39.2000
249 122.8000 387.5000 39.2000
250 127.6000 286.7000 39.2000
251 129.9000 329.2000 39.2000
252 130.7000 339.4000 39.2000
253 136.2000 331.6000 39.2000
254 136.2000 315.8000 39.2000
255 136.2000 295.3000 39.2000
256 142.5000 331.6000 39.2000
257 142.5000 315.8000 39.2000
258 142.5000 295.3000 39.2000
259 141.7000 283.5000 39.2000
260 148.8000 295.3000 39.2000
261 148.8000 315.8000 39.2000
262 148.8000 331.6000 39.2000
263 155.1000 331.6000 39.2000
264 155.1000 315.8000 39.2000
265 155.1000 295.3000 39.2000
266 161.4000 295.3000 39.2000
267 161.4000 315.8000 39.2000
268 161.4000 331.6000 39.2000
269 173.2000 285.1000 39.2000
270 181.1000 393.8000 39.2000
271 184.3000 387.5000 39.2000
272 191.3000 329.2000 39.2000
273 192.1000 339.4000 39.2000
274 208.7000 303.2000 39.2000
275 211.8000 393.8000 39.2000
276 215.0000 387.5000 39.2000
277 218.9000 286.7000 39.2000
278 222.0000 285.1000 39.2000
279 222.0000 329.2000 39.2000
280 222.8000 339.4000 39.2000
281 224.4000 280.4000 39.2000
282 227.6000 297.7000 39.2000
283 227.6000 315.8000 39.2000
284 227.6000 331.6000 39.2000
285 231.5000 331.6000 39.2000
286 231.5000 315.8000 39.2000
287 231.5000 297.7000 39.2000
Continued on next page
614
Table D.3 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 233.1000 280.4000 39.2000
289 234.6000 297.7000 39.2000
290 234.6000 315.8000 39.2000
291 234.6000 331.6000 39.2000
292 236.2000 280.4000 39.2000
293 240.2000 281.9000 39.2000
294 240.2000 288.2000 39.2000
295 248.0000 280.4000 39.2000
296 249.6000 303.2000 39.2000
297 252.8000 393.8000 39.2000
298 255.9000 387.5000 39.2000
299 263.0000 329.2000 39.2000
300 263.8000 339.4000 39.2000
301 275.6000 273.1000 39.2000
302 278.7000 273.1000 39.2000
303 280.3000 303.2000 39.2000
304 283.5000 393.8000 39.2000
305 286.6000 387.5000 39.2000
306 290.6000 273.1000 39.2000
307 293.7000 273.1000 39.2000
308 293.7000 329.2000 39.2000
309 294.5000 339.4000 39.2000
310 301.6000 393.8000 39.2000
311 305.5000 273.1000 39.2000
312 308.7000 273.1000 39.2000
313 60.6000 288.2000 39.2000
314 116.5000 303.2000 39.2000
315 178.0000 303.2000 39.2000
316 141.7000 -7.9000 39.2000
317 149.6000 -7.9000 39.2000
Depot 169.3000 405.5000 N.A.
615
Table D.4: CETSP instance rd400rdmRad
Customer index x-coordinate y-coordinate Service range
1 43.5841 58.7522 0.0954
2 60.2539 80.1704 0.0954
3 86.1563 95.4019 0.0954
4 44.4217 55.3301 0.0954
5 79.6042 79.6519 0.0954
6 8.8906 83.8954 0.0954
7 23.3569 85.0798 0.0954
8 47.6864 20.3976 0.0954
9 40.6271 60.1839 0.0954
10 95.4573 78.5053 0.0954
11 59.3326 96.8644 0.0954
12 94.6100 43.2995 0.0954
13 8.3074 60.1487 0.0954
14 86.1254 75.4120 0.0954
15 24.7619 69.8637 0.0954
16 96.3227 96.5824 0.0954
17 12.5872 53.6987 0.0954
18 56.3237 2.0737 0.0954
19 5.5259 61.9092 0.0954
20 69.1414 57.6653 0.0954
21 23.7167 70.7298 0.0954
22 58.3448 60.9201 0.0954
23 40.4171 94.2218 0.0954
24 1.5771 61.4642 0.0954
25 2.0081 6.2897 0.0954
26 19.6656 61.3862 0.0954
27 91.3249 42.8902 0.0954
28 82.8340 58.4111 0.0954
29 4.9605 4.0606 0.0954
30 27.1361 73.6904 0.0954
31 97.9153 71.6970 0.0954
32 48.9418 95.7946 0.0954
33 81.7106 28.1120 0.0954
34 33.2771 46.6520 0.0954
35 27.8353 94.5623 0.0954
36 16.8540 97.4806 0.0954
37 80.6139 53.7748 0.0954
38 44.5404 30.6860 0.0954
39 30.6696 55.2626 0.0954
40 55.5492 35.9315 0.0954
41 15.6444 17.8995 0.0954
Continued on next page
616
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 14.0141 70.4084 0.0954
43 96.3235 44.2629 0.0954
44 46.0829 25.5503 0.0954
45 38.5534 48.7846 0.0954
46 93.1464 19.8146 0.0954
47 27.9893 89.6021 0.0954
48 33.1283 92.3481 0.0954
49 3.3536 88.9860 0.0954
50 51.1528 6.0410 0.0954
51 23.2874 32.7742 0.0954
52 87.0562 74.7862 0.0954
53 12.6307 2.7083 0.0954
54 2.5716 38.4711 0.0954
55 55.0990 31.7710 0.0954
56 42.1545 66.9856 0.0954
57 69.9395 64.1832 0.0954
58 3.0606 88.1315 0.0954
59 48.6626 98.7924 0.0954
60 54.7886 87.0165 0.0954
61 76.4190 22.7841 0.0954
62 48.9340 88.5471 0.0954
63 90.8764 48.3318 0.0954
64 19.5225 82.1483 0.0954
65 17.1854 11.1942 0.0954
66 59.9164 58.7500 0.0954
67 13.2524 50.7626 0.0954
68 32.7208 86.8800 0.0954
69 26.7929 78.8352 0.0954
70 79.2919 13.6517 0.0954
71 15.6993 18.7479 0.0954
72 18.6101 90.3489 0.0954
73 74.5996 81.8744 0.0954
74 67.2670 14.1516 0.0954
75 79.5061 49.6701 0.0954
76 29.8827 79.6840 0.0954
77 9.1600 37.8018 0.0954
78 91.7898 10.5225 0.0954
79 37.0272 27.4581 0.0954
80 78.9206 73.8168 0.0954
81 80.0350 15.8589 0.0954
82 74.8357 53.7031 0.0954
Continued on next page
617
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 48.6979 8.8591 0.0954
84 14.8737 9.5107 0.0954
85 23.1984 1.0131 0.0954
86 97.2905 22.0419 0.0954
87 4.0560 25.9589 0.0954
88 19.2470 29.2712 0.0954
89 2.4039 50.9808 0.0954
90 31.6686 31.1822 0.0954
91 49.4944 16.3270 0.0954
92 52.5118 68.1256 0.0954
93 83.5669 88.2708 0.0954
94 77.5205 18.1054 0.0954
95 10.9477 2.7353 0.0954
96 65.3011 67.1869 0.0954
97 62.8285 19.7058 0.0954
98 0.1949 71.2335 0.0954
99 73.0640 44.6995 0.0954
100 58.0371 93.3465 0.0954
101 37.7453 86.3505 0.0954
102 25.8125 25.1372 0.0954
103 65.9297 69.3415 0.0954
104 70.0979 43.9308 0.0954
105 80.1207 32.7664 0.0954
106 75.5117 58.1702 0.0954
107 16.8354 77.4785 0.0954
108 60.7710 67.3196 0.0954
109 56.9788 35.9946 0.0954
110 50.5772 79.5094 0.0954
111 69.2786 47.5055 0.0954
112 61.5258 41.6034 0.0954
113 43.3068 85.4106 0.0954
114 22.6997 14.9199 0.0954
115 32.6410 61.5676 0.0954
116 75.6359 99.7073 0.0954
117 17.5187 55.1629 0.0954
118 20.7262 75.3080 0.0954
119 12.7313 98.6134 0.0954
120 24.5176 59.5849 0.0954
121 36.8488 32.2474 0.0954
122 61.8453 80.8454 0.0954
123 28.4623 90.5817 0.0954
Continued on next page
618
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 34.7487 93.2543 0.0954
125 94.2046 73.3577 0.0954
126 92.3029 41.0170 0.0954
127 15.3759 23.0999 0.0954
128 47.6331 25.3181 0.0954
129 23.2085 58.8069 0.0954
130 43.9629 81.9344 0.0954
131 95.9404 38.2332 0.0954
132 65.9332 98.9174 0.0954
133 47.5220 42.2920 0.0954
134 73.4709 7.6166 0.0954
135 84.4594 85.6238 0.0954
136 1.0251 82.9527 0.0954
137 35.9094 68.8825 0.0954
138 90.1100 20.7153 0.0954
139 60.7208 77.8844 0.0954
140 68.2389 8.4710 0.0954
141 84.0931 75.7357 0.0954
142 44.9959 88.3516 0.0954
143 72.5650 40.2263 0.0954
144 88.2698 14.9994 0.0954
145 42.9870 22.9253 0.0954
146 98.0879 82.1977 0.0954
147 57.8122 54.5104 0.0954
148 54.1690 81.8375 0.0954
149 50.9211 16.4053 0.0954
150 87.5589 25.1226 0.0954
151 10.1219 82.0450 0.0954
152 48.5894 0.5480 0.0954
153 13.4000 22.8874 0.0954
154 16.7243 94.3593 0.0954
155 15.6372 44.5891 0.0954
156 26.7979 6.9020 0.0954
157 47.6475 71.1843 0.0954
158 45.6946 80.9262 0.0954
159 21.7245 2.0113 0.0954
160 16.5471 81.1813 0.0954
161 38.1612 45.7549 0.0954
162 31.0765 22.0815 0.0954
163 0.2198 2.5849 0.0954
164 13.5318 57.9262 0.0954
Continued on next page
619
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 25.7714 33.2927 0.0954
166 67.8108 54.6502 0.0954
167 17.6011 61.1721 0.0954
168 56.0389 33.1015 0.0954
169 41.6783 52.1535 0.0954
170 85.2354 42.0312 0.0954
171 85.0689 32.1301 0.0954
172 74.5771 5.7082 0.0954
173 10.4725 58.8780 0.0954
174 6.4345 8.7023 0.0954
175 41.7205 19.4188 0.0954
176 88.4474 55.9131 0.0954
177 86.8707 18.0065 0.0954
178 26.2003 42.5604 0.0954
179 66.9764 66.2314 0.0954
180 42.0178 3.4429 0.0954
181 42.4972 23.9973 0.0954
182 61.5069 0.4821 0.0954
183 96.7473 23.5618 0.0954
184 18.0640 96.3276 0.0954
185 15.3897 25.3897 0.0954
186 13.8308 54.4775 0.0954
187 2.3883 24.0295 0.0954
188 70.1018 4.3454 0.0954
189 95.1537 79.2325 0.0954
190 19.0116 0.9770 0.0954
191 34.7579 99.7518 0.0954
192 33.1085 0.8828 0.0954
193 54.7387 20.4852 0.0954
194 77.6794 29.1288 0.0954
195 75.6586 91.7899 0.0954
196 17.2306 77.2747 0.0954
197 8.5705 3.3673 0.0954
198 90.4883 12.6216 0.0954
199 8.7542 38.9280 0.0954
200 2.1973 10.2510 0.0954
201 41.7302 58.1199 0.0954
202 20.5641 47.7219 0.0954
203 48.6743 62.5481 0.0954
204 37.2177 7.7925 0.0954
205 11.7937 48.0467 0.0954
Continued on next page
620
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 29.5533 92.3189 0.0954
207 87.9339 96.7331 0.0954
208 88.9914 10.7701 0.0954
209 63.6977 85.2552 0.0954
210 38.2491 9.6174 0.0954
211 13.4598 41.6191 0.0954
212 75.9957 81.4020 0.0954
213 4.4507 94.0863 0.0954
214 24.4594 47.3987 0.0954
215 64.2573 58.9530 0.0954
216 22.8193 53.7552 0.0954
217 64.5769 3.6618 0.0954
218 88.1955 43.6361 0.0954
219 68.0574 15.6194 0.0954
220 81.1997 46.6210 0.0954
221 96.3481 58.4969 0.0954
222 31.2678 61.1344 0.0954
223 85.3959 62.1638 0.0954
224 51.8363 98.9629 0.0954
225 27.2482 20.2425 0.0954
226 76.2214 75.1456 0.0954
227 64.8783 60.3790 0.0954
228 78.3667 74.2083 0.0954
229 39.9475 19.2268 0.0954
230 3.2499 93.8751 0.0954
231 81.4209 43.6493 0.0954
232 29.1053 29.2049 0.0954
233 60.7013 1.3612 0.0954
234 9.2745 43.3967 0.0954
235 76.9072 18.2917 0.0954
236 17.5856 40.8861 0.0954
237 34.4656 38.8185 0.0954
238 22.7183 34.3604 0.0954
239 49.1148 32.8614 0.0954
240 2.5522 66.9796 0.0954
241 78.9060 18.0381 0.0954
242 98.0725 73.5090 0.0954
243 5.8182 20.7452 0.0954
244 19.5262 30.4483 0.0954
245 54.3707 99.6057 0.0954
246 55.7170 37.8511 0.0954
Continued on next page
621
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 25.6513 60.6643 0.0954
248 80.5435 37.2793 0.0954
249 46.2037 41.7062 0.0954
250 81.8209 62.9891 0.0954
251 41.5460 82.3742 0.0954
252 20.3288 28.0220 0.0954
253 32.5896 90.7590 0.0954
254 51.2472 90.6526 0.0954
255 82.6909 80.2719 0.0954
256 37.4105 49.4356 0.0954
257 59.9164 61.9972 0.0954
258 32.7353 38.4372 0.0954
259 36.0033 17.5038 0.0954
260 80.9911 75.8316 0.0954
261 26.0672 21.3383 0.0954
262 93.4248 68.5015 0.0954
263 17.6023 36.5196 0.0954
264 60.6972 35.5066 0.0954
265 66.7645 81.0279 0.0954
266 85.2864 82.4650 0.0954
267 74.6320 5.6044 0.0954
268 9.3555 53.1101 0.0954
269 81.8774 60.6902 0.0954
270 74.6616 49.1772 0.0954
271 23.1083 96.0553 0.0954
272 68.3546 93.0491 0.0954
273 43.1006 68.5786 0.0954
274 70.9830 56.1077 0.0954
275 45.2184 66.3382 0.0954
276 38.4806 81.2568 0.0954
277 88.6343 0.4944 0.0954
278 5.2584 27.1001 0.0954
279 15.2733 95.1553 0.0954
280 80.8889 76.3527 0.0954
281 77.5352 78.0347 0.0954
282 17.8085 51.9553 0.0954
283 98.8743 25.6460 0.0954
284 11.4258 37.7412 0.0954
285 23.6126 49.4214 0.0954
286 31.4339 43.8079 0.0954
287 27.3595 17.3028 0.0954
Continued on next page
622
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 4.9997 74.2733 0.0954
289 0.6429 35.3950 0.0954
290 54.0007 52.8659 0.0954
291 78.6058 43.2582 0.0954
292 99.5164 7.7748 0.0954
293 50.9984 83.4341 0.0954
294 89.0360 30.7257 0.0954
295 30.4468 53.5688 0.0954
296 47.3917 2.2305 0.0954
297 86.8559 48.4797 0.0954
298 9.1727 66.1356 0.0954
299 61.6789 74.8507 0.0954
300 41.4131 74.8199 0.0954
301 23.6206 68.3440 0.0954
302 97.4766 17.1802 0.0954
303 73.2088 32.0501 0.0954
304 33.4192 59.4830 0.0954
305 56.1254 1.4053 0.0954
306 3.3012 54.5758 0.0954
307 45.1636 79.7971 0.0954
308 19.7287 0.1987 0.0954
309 23.6339 40.0124 0.0954
310 74.7866 36.0265 0.0954
311 43.0779 81.6476 0.0954
312 2.1823 25.6845 0.0954
313 34.4638 23.0393 0.0954
314 75.4786 92.9344 0.0954
315 25.7178 17.8950 0.0954
316 23.3293 78.9181 0.0954
317 10.9638 55.5178 0.0954
318 81.8496 38.8539 0.0954
319 43.8962 13.6901 0.0954
320 34.4937 83.7515 0.0954
321 92.0634 46.0336 0.0954
322 95.0473 3.3982 0.0954
323 12.3803 91.1149 0.0954
324 82.6839 23.4883 0.0954
325 96.7716 16.6523 0.0954
326 76.3859 55.8636 0.0954
327 47.7087 83.4773 0.0954
328 18.9042 62.1271 0.0954
Continued on next page
623
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 50.0418 88.5256 0.0954
330 80.7777 87.9354 0.0954
331 0.6136 12.2624 0.0954
332 68.0526 97.9535 0.0954
333 75.2455 17.3084 0.0954
334 74.0572 35.9870 0.0954
335 49.4045 19.9610 0.0954
336 22.5447 55.6169 0.0954
337 78.2186 68.7569 0.0954
338 55.9929 17.1432 0.0954
339 46.3399 71.1700 0.0954
340 9.9608 19.2347 0.0954
341 25.7615 81.4539 0.0954
342 4.2889 92.6489 0.0954
343 17.2907 17.3232 0.0954
344 48.3206 81.4332 0.0954
345 53.7144 89.3849 0.0954
346 0.2990 97.3272 0.0954
347 28.6889 43.6077 0.0954
348 3.4457 28.2052 0.0954
349 38.2173 22.8740 0.0954
350 40.7053 85.7824 0.0954
351 95.7659 2.5535 0.0954
352 53.4254 44.9898 0.0954
353 89.1084 77.1611 0.0954
354 60.9907 71.4945 0.0954
355 80.0506 36.8529 0.0954
356 0.6594 19.6999 0.0954
357 12.2621 43.6923 0.0954
358 51.7930 64.9464 0.0954
359 23.5387 4.1313 0.0954
360 60.3560 72.3736 0.0954
361 91.0373 94.8618 0.0954
362 49.8328 92.6571 0.0954
363 54.8665 95.2849 0.0954
364 77.9110 9.9019 0.0954
365 58.2097 7.5607 0.0954
366 21.4744 8.2189 0.0954
367 56.0439 62.2937 0.0954
368 69.3672 55.5594 0.0954
369 9.0496 1.6796 0.0954
Continued on next page
624
Table D.4 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 76.0500 41.1841 0.0954
371 62.6521 52.6724 0.0954
372 99.5853 23.4577 0.0954
373 91.8947 87.6684 0.0954
374 98.9579 4.7321 0.0954
375 37.7688 31.4408 0.0954
376 96.1419 41.3034 0.0954
377 82.5413 70.9361 0.0954
378 82.7455 58.0479 0.0954
379 3.5780 99.0366 0.0954
380 62.0154 28.1819 0.0954
381 10.9524 12.0779 0.0954
382 73.8931 82.0767 0.0954
383 27.4222 25.8428 0.0954
384 8.2541 64.3565 0.0954
385 59.2712 76.4167 0.0954
386 72.4782 47.1166 0.0954
387 77.8131 90.2453 0.0954
388 88.5712 66.6382 0.0954
389 2.6887 16.3883 0.0954
390 74.1314 97.2935 0.0954
391 16.5760 71.2313 0.0954
392 25.6231 12.6549 0.0954
393 92.7385 89.9534 0.0954
394 52.4925 5.3725 0.0954
395 7.2192 42.3799 0.0954
396 36.7230 86.3354 0.0954
397 34.9224 79.9328 0.0954
398 12.7116 4.2915 0.0954
399 58.7637 13.9566 0.0954
Depot 2.2832 35.5085 N.A.
625
Table D.5: CETSP instance pcb442rdmRad
Customer index x-coordinate y-coordinate Service range
1 2.0000 4.0000 6.0000
2 2.0000 5.0000 6.0000
3 2.0000 6.0000 6.0000
4 2.0000 7.0000 6.0000
5 2.0000 8.0000 6.0000
6 2.0000 9.0000 6.0000
7 2.0000 10.0000 6.0000
8 2.0000 11.0000 6.0000
9 2.0000 12.0000 6.0000
10 2.0000 13.0000 6.0000
11 2.0000 14.0000 6.0000
12 2.0000 15.0000 6.0000
13 2.0000 16.0000 6.0000
14 2.0000 17.0000 6.0000
15 2.0000 18.0000 6.0000
16 2.0000 19.0000 6.0000
17 2.0000 20.0000 6.0000
18 2.0000 21.0000 6.0000
19 2.0000 22.0000 6.0000
20 2.0000 23.0000 6.0000
21 2.0000 24.0000 6.0000
22 2.0000 25.0000 6.0000
23 2.0000 26.0000 6.0000
24 2.0000 27.0000 6.0000
25 2.0000 28.0000 6.0000
26 2.0000 29.0000 6.0000
27 2.0000 30.0000 6.0000
28 2.0000 31.0000 6.0000
29 2.0000 32.0000 6.0000
30 2.0000 33.0000 6.0000
31 2.0000 34.0000 6.0000
32 2.0000 35.0000 6.0000
33 2.0000 36.0000 6.0000
34 3.0000 4.0000 6.0000
35 3.0000 5.0000 6.0000
36 3.0000 6.0000 6.0000
37 3.0000 7.0000 6.0000
38 3.0000 8.0000 6.0000
39 3.0000 9.0000 6.0000
40 3.0000 10.0000 6.0000
Continued on next page
626
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
41 3.0000 11.0000 6.0000
42 3.0000 12.0000 6.0000
43 3.0000 13.0000 6.0000
44 3.0000 14.0000 6.0000
45 3.0000 15.0000 6.0000
46 3.0000 16.0000 6.0000
47 3.0000 17.0000 6.0000
48 3.0000 18.0000 6.0000
49 3.0000 19.0000 6.0000
50 3.0000 20.0000 6.0000
51 3.0000 21.0000 6.0000
52 3.0000 22.0000 6.0000
53 3.0000 23.0000 6.0000
54 3.0000 24.0000 6.0000
55 3.0000 25.0000 6.0000
56 3.0000 26.0000 6.0000
57 3.0000 27.0000 6.0000
58 3.0000 28.0000 6.0000
59 3.0000 29.0000 6.0000
60 3.0000 30.0000 6.0000
61 3.0000 31.0000 6.0000
62 3.0000 32.0000 6.0000
63 3.0000 33.0000 6.0000
64 3.0000 34.0000 6.0000
65 3.0000 35.0000 6.0000
66 4.0000 4.0000 6.0000
67 4.0000 5.0000 6.0000
68 4.0000 6.0000 6.0000
69 4.0000 7.0000 6.0000
70 4.0000 8.0000 6.0000
71 4.0000 9.0000 6.0000
72 4.0000 10.0000 6.0000
73 4.0000 11.0000 6.0000
74 4.0000 12.0000 6.0000
75 4.0000 13.0000 6.0000
76 4.0000 14.0000 6.0000
77 4.0000 15.0000 6.0000
78 4.0000 16.0000 6.0000
79 4.0000 17.0000 6.0000
80 4.0000 18.0000 6.0000
81 4.0000 19.0000 6.0000
Continued on next page
627
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
82 4.0000 20.0000 6.0000
83 4.0000 21.0000 6.0000
84 4.0000 22.0000 6.0000
85 4.0000 23.0000 6.0000
86 4.0000 24.0000 6.0000
87 4.0000 25.0000 6.0000
88 4.0000 26.0000 6.0000
89 4.0000 27.0000 6.0000
90 4.0000 28.0000 6.0000
91 4.0000 29.0000 6.0000
92 4.0000 30.0000 6.0000
93 4.0000 31.0000 6.0000
94 4.0000 32.0000 6.0000
95 4.0000 33.0000 6.0000
96 4.0000 34.0000 6.0000
97 4.0000 35.0000 6.0000
98 4.0000 36.0000 6.0000
99 5.0000 15.0000 6.0000
100 5.0000 18.3000 6.0000
101 5.0000 31.0000 6.0000
102 6.0000 4.0000 6.0000
103 7.0000 3.0000 6.0000
104 7.0000 6.0000 6.0000
105 7.0000 15.0000 6.0000
106 7.0000 16.0000 6.0000
107 7.0000 18.0000 6.0000
108 7.0000 21.0000 6.0000
109 7.0000 24.0000 6.0000
110 7.0000 27.0000 6.0000
111 7.0000 30.0000 6.0000
112 7.0000 33.0000 6.0000
113 7.0000 36.0000 6.0000
114 8.0000 3.0000 6.0000
115 8.0000 6.0000 6.0000
116 8.0000 10.3000 6.0000
117 8.0000 15.0000 6.0000
118 8.0000 18.0000 6.0000
119 8.0000 21.0000 6.0000
120 8.0000 24.0000 6.0000
121 8.0000 26.0000 6.0000
122 8.0000 27.0000 6.0000
Continued on next page
628
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
123 8.0000 30.0000 6.0000
124 8.0000 33.0000 6.0000
125 8.0000 36.0000 6.0000
126 9.0000 3.0000 6.0000
127 9.0000 6.0000 6.0000
128 9.0000 15.0000 6.0000
129 9.0000 18.0000 6.0000
130 9.0000 21.0000 6.0000
131 9.0000 24.0000 6.0000
132 9.0000 27.0000 6.0000
133 9.0000 30.0000 6.0000
134 9.0000 33.0000 6.0000
135 9.0000 36.0000 6.0000
136 10.0000 3.0000 6.0000
137 10.0000 6.0000 6.0000
138 10.0000 11.0000 6.0000
139 10.0000 15.0000 6.0000
140 10.0000 16.3000 6.0000
141 10.0000 18.0000 6.0000
142 10.0000 21.0000 6.0000
143 10.0000 24.0000 6.0000
144 10.0000 26.0000 6.0000
145 10.0000 27.0000 6.0000
146 10.0000 30.0000 6.0000
147 10.0000 33.0000 6.0000
148 10.0000 36.0000 6.0000
149 11.0000 3.0000 6.0000
150 11.0000 6.0000 6.0000
151 11.0000 7.0000 6.0000
152 11.0000 9.0000 6.0000
153 11.0000 15.0000 6.0000
154 11.0000 18.0000 6.0000
155 11.0000 21.0000 6.0000
156 11.0000 24.0000 6.0000
157 11.0000 27.0000 6.0000
158 11.0000 30.0000 6.0000
159 11.0000 33.0000 6.0000
160 11.0000 36.0000 6.0000
161 12.0000 3.0000 6.0000
162 12.0000 6.0000 6.0000
163 12.0000 15.0000 6.0000
Continued on next page
629
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
164 12.0000 17.0000 6.0000
165 12.0000 18.0000 6.0000
166 12.0000 21.0000 6.0000
167 12.0000 24.0000 6.0000
168 12.0000 27.0000 6.0000
169 12.0000 30.0000 6.0000
170 12.0000 33.0000 6.0000
171 12.0000 36.0000 6.0000
172 13.0000 3.0000 6.0000
173 13.0000 6.0000 6.0000
174 13.0000 7.0000 6.0000
175 13.0000 11.3000 6.0000
176 13.0000 15.0000 6.0000
177 13.0000 18.0000 6.0000
178 13.0000 21.0000 6.0000
179 13.0000 22.0000 6.0000
180 13.0000 24.0000 6.0000
181 13.0000 27.0000 6.0000
182 13.0000 30.0000 6.0000
183 13.0000 33.0000 6.0000
184 13.0000 36.0000 6.0000
185 14.0000 3.0000 6.0000
186 14.0000 6.0000 6.0000
187 14.0000 9.3000 6.0000
188 14.0000 15.0000 6.0000
189 14.0000 18.0000 6.0000
190 14.0000 20.0000 6.0000
191 14.0000 21.0000 6.0000
192 14.0000 24.0000 6.0000
193 14.0000 25.0000 6.0000
194 14.0000 27.0000 6.0000
195 14.0000 28.2000 6.0000
196 14.0000 29.0000 6.0000
197 14.0000 30.0000 6.0000
198 14.0000 33.0000 6.0000
199 14.0000 36.0000 6.0000
200 15.0000 15.0000 6.0000
201 15.0000 18.0000 6.0000
202 15.0000 19.0000 6.0000
203 15.0000 21.0000 6.0000
204 15.0000 24.0000 6.0000
Continued on next page
630
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
205 15.0000 27.0000 6.0000
206 15.0000 28.0000 6.0000
207 15.0000 28.6000 6.0000
208 15.0000 30.0000 6.0000
209 15.0000 33.0000 6.0000
210 15.0000 36.0000 6.0000
211 16.0000 11.0000 6.0000
212 16.0000 13.0000 6.0000
213 16.0000 15.0000 6.0000
214 16.0000 18.0000 6.0000
215 16.0000 21.0000 6.0000
216 16.0000 24.0000 6.0000
217 16.0000 27.0000 6.0000
218 16.0000 30.0000 6.0000
219 16.0000 33.0000 6.0000
220 16.0000 36.0000 6.0000
221 17.0000 12.0000 6.0000
222 17.0000 15.0000 6.0000
223 17.0000 18.0000 6.0000
224 17.0000 21.0000 6.0000
225 17.0000 24.0000 6.0000
226 17.0000 36.0000 6.0000
227 18.0000 3.0000 6.0000
228 18.0000 6.0000 6.0000
229 18.0000 12.3000 6.0000
230 18.0000 15.0000 6.0000
231 18.0000 18.0000 6.0000
232 18.0000 21.0000 6.0000
233 18.0000 24.0000 6.0000
234 19.0000 3.0000 6.0000
235 19.0000 6.0000 6.0000
236 19.0000 30.0000 6.0000
237 19.0000 35.2000 6.0000
238 20.0000 3.0000 6.0000
239 20.0000 3.7000 6.0000
240 20.0000 6.0000 6.0000
241 20.0000 8.0000 6.0000
242 20.0000 9.0000 6.0000
243 20.0000 10.0000 6.0000
244 20.0000 11.0000 6.0000
245 20.0000 12.0000 6.0000
Continued on next page
631
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
246 20.0000 13.0000 6.0000
247 20.0000 14.0000 6.0000
248 20.0000 15.0000 6.0000
249 20.0000 16.0000 6.0000
250 20.0000 17.0000 6.0000
251 20.0000 18.0000 6.0000
252 20.0000 19.0000 6.0000
253 20.0000 20.0000 6.0000
254 20.0000 21.0000 6.0000
255 20.0000 22.0000 6.0000
256 20.0000 23.0000 6.0000
257 20.0000 24.0000 6.0000
258 20.0000 25.0000 6.0000
259 20.0000 26.0000 6.0000
260 20.0000 27.0000 6.0000
261 20.0000 28.0000 6.0000
262 20.0000 29.0000 6.0000
263 20.0000 30.0000 6.0000
264 20.0000 31.0000 6.0000
265 20.0000 35.0000 6.0000
266 21.0000 3.0000 6.0000
267 21.0000 6.0000 6.0000
268 21.0000 32.0000 6.0000
269 22.0000 3.0000 6.0000
270 22.0000 4.7000 6.0000
271 22.0000 6.0000 6.0000
272 22.0000 32.0000 6.0000
273 23.0000 3.0000 6.0000
274 23.0000 6.0000 6.0000
275 23.0000 34.0000 6.0000
276 24.0000 3.0000 6.0000
277 24.0000 6.0000 6.0000
278 24.0000 21.0000 6.0000
279 25.0000 3.0000 6.0000
280 25.0000 8.0000 6.0000
281 26.0000 4.0000 6.0000
282 26.0000 5.0000 6.0000
283 26.0000 8.0000 6.0000
284 26.0000 9.0000 6.0000
285 26.0000 10.0000 6.0000
286 26.0000 11.0000 6.0000
Continued on next page
632
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
287 26.0000 12.0000 6.0000
288 26.0000 13.0000 6.0000
289 26.0000 14.0000 6.0000
290 26.0000 15.0000 6.0000
291 26.0000 16.0000 6.0000
292 26.0000 17.0000 6.0000
293 26.0000 18.0000 6.0000
294 26.0000 19.0000 6.0000
295 26.0000 20.0000 6.0000
296 26.0000 21.0000 6.0000
297 26.0000 22.0000 6.0000
298 26.0000 23.0000 6.0000
299 26.0000 24.0000 6.0000
300 26.0000 25.0000 6.0000
301 26.0000 26.0000 6.0000
302 26.0000 27.0000 6.0000
303 26.0000 28.0000 6.0000
304 26.0000 29.0000 6.0000
305 26.0000 30.0000 6.0000
306 26.0000 31.0000 6.0000
307 26.0000 34.0000 6.0000
308 27.0000 7.0000 6.0000
309 27.0000 8.0000 6.0000
310 27.0000 9.0000 6.0000
311 27.0000 10.0000 6.0000
312 27.0000 11.0000 6.0000
313 27.0000 12.0000 6.0000
314 27.0000 13.0000 6.0000
315 27.0000 14.0000 6.0000
316 27.0000 15.0000 6.0000
317 27.0000 16.0000 6.0000
318 27.0000 17.0000 6.0000
319 27.0000 18.0000 6.0000
320 27.0000 19.0000 6.0000
321 27.0000 20.0000 6.0000
322 27.0000 21.0000 6.0000
323 27.0000 22.0000 6.0000
324 27.0000 23.0000 6.0000
325 27.0000 25.0000 6.0000
326 27.0000 26.0000 6.0000
327 27.0000 27.0000 6.0000
Continued on next page
633
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
328 27.0000 28.0000 6.0000
329 27.0000 29.0000 6.0000
330 27.0000 30.0000 6.0000
331 27.0000 31.0000 6.0000
332 27.0000 32.0000 6.0000
333 27.0000 33.0000 6.0000
334 27.0000 34.0000 6.0000
335 27.0000 35.0000 6.0000
336 27.0000 36.0000 6.0000
337 27.0000 37.0000 6.0000
338 27.0000 38.0000 6.0000
339 28.0000 9.0000 6.0000
340 28.0000 11.3000 6.0000
341 29.0000 4.0000 6.0000
342 29.0000 5.0000 6.0000
343 29.0000 14.0000 6.0000
344 29.0000 24.0000 6.0000
345 29.0000 30.0000 6.0000
346 30.0000 7.0000 6.0000
347 30.0000 8.0000 6.0000
348 30.0000 9.0000 6.0000
349 30.0000 10.0000 6.0000
350 30.0000 11.0000 6.0000
351 30.0000 12.0000 6.0000
352 30.0000 13.0000 6.0000
353 30.0000 15.0000 6.0000
354 30.0000 16.0000 6.0000
355 30.0000 17.0000 6.0000
356 30.0000 18.0000 6.0000
357 30.0000 19.0000 6.0000
358 30.0000 20.0000 6.0000
359 30.0000 21.0000 6.0000
360 30.0000 22.0000 6.0000
361 30.0000 23.0000 6.0000
362 30.0000 25.0000 6.0000
363 30.0000 26.0000 6.0000
364 30.0000 27.0000 6.0000
365 30.0000 28.0000 6.0000
366 30.0000 29.0000 6.0000
367 30.0000 30.0000 6.0000
368 30.0000 31.0000 6.0000
Continued on next page
634
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
369 30.0000 32.0000 6.0000
370 30.0000 33.0000 6.0000
371 30.0000 34.0000 6.0000
372 30.0000 35.0000 6.0000
373 30.0000 36.0000 6.0000
374 30.0000 37.0000 6.0000
375 30.0000 38.0000 6.0000
376 1.5000 35.0000 6.0000
377 1.5000 35.5000 6.0000
378 4.7000 25.5000 6.0000
379 4.7000 33.5000 6.0000
380 4.7000 34.5000 6.0000
381 5.4000 23.3000 6.0000
382 5.4000 24.3000 6.0000
383 6.2000 36.5000 6.0000
384 6.2000 37.1000 6.0000
385 7.5000 25.5000 6.0000
386 8.5000 5.2000 6.0000
387 8.5000 7.0000 6.0000
388 8.5000 22.8000 6.0000
389 9.4000 7.4000 6.0000
390 9.5000 22.2000 6.0000
391 9.1000 26.0000 6.0000
392 10.5000 10.5000 6.0000
393 11.5000 13.5000 6.0000
394 11.7000 22.8000 6.0000
395 12.2000 22.1000 6.0000
396 13.5000 7.5000 6.0000
397 13.5000 17.0000 6.0000
398 13.5000 21.4000 6.0000
399 14.5000 7.7000 6.0000
400 15.5000 3.0000 6.0000
401 15.5000 5.0000 6.0000
402 15.5000 18.5000 6.0000
403 16.5000 10.5000 6.0000
404 16.9000 26.8000 6.0000
405 17.1000 3.1000 6.0000
406 17.1000 5.1000 6.0000
407 17.5000 7.5000 6.0000
408 17.9000 25.8000 6.0000
409 17.2000 26.1000 6.0000
Continued on next page
635
Table D.5 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
410 17.9000 33.3000 6.0000
411 17.2000 34.1000 6.0000
412 18.3000 27.0000 6.0000
413 18.3000 28.0000 6.0000
414 18.3000 34.5000 6.0000
415 20.6000 16.5000 6.0000
416 20.5000 31.5000 6.0000
417 21.7000 19.0000 6.0000
418 21.1000 20.0000 6.0000
419 21.2000 27.5000 6.0000
420 21.5000 32.5000 6.0000
421 22.9000 14.0000 6.0000
422 22.2000 28.2000 6.0000
423 22.8000 32.5000 6.0000
424 23.9000 13.0000 6.0000
425 23.2000 15.0000 6.0000
426 24.5000 7.1000 6.0000
427 26.2000 36.5000 6.0000
428 27.5000 5.2000 6.0000
429 27.6000 23.6000 6.0000
430 28.5000 22.0000 6.0000
431 28.5000 27.0000 6.0000
432 28.5000 33.5000 6.0000
433 29.3000 9.5000 6.0000
434 29.5000 17.5000 6.0000
435 29.5000 20.5000 6.0000
436 5.2000 32.0000 6.0000
437 23.0000 35.0000 6.0000
438 23.2000 31.5000 6.0000
439 5.3000 21.0000 6.0000
440 25.5000 7.1000 6.0000
441 7.5000 4.9000 6.0000
Depot 0.0000 0.0000 N.A.
636
Table D.6: CETSP instance d493rdmRad
Customer index x-coordinate y-coordinate Service range
1 11.1630 15.5520 0.6510
2 13.5760 14.7900 0.6510
3 11.4810 17.7110 0.6510
4 11.8620 17.9650 0.6510
5 12.0520 18.8540 0.6510
6 12.3700 19.9340 0.6510
7 13.0050 20.0610 0.6510
8 11.6080 20.2510 0.6510
9 11.7350 20.3780 0.6510
10 12.2430 20.5050 0.6510
11 13.5130 22.4100 0.6510
12 17.3230 21.3310 0.6510
13 17.4500 21.9020 0.6510
14 17.6400 22.9180 0.6510
15 17.6400 23.4260 0.6510
16 17.3230 23.9340 0.6510
17 17.4500 24.1880 0.6510
18 16.4970 24.3150 0.6510
19 17.5770 25.2040 0.6510
20 22.9740 17.7110 0.6510
21 22.1490 14.2820 0.6510
22 22.2760 13.3930 0.6510
23 21.8310 13.2030 0.6510
24 26.1490 11.1070 0.6510
25 25.0700 11.6150 0.6510
26 23.4820 9.5200 0.6510
27 22.2120 10.0910 0.6510
28 22.0850 10.8530 0.6510
29 22.0220 11.3610 0.6510
30 22.1490 11.7420 0.6510
31 20.2440 11.2340 0.6510
32 20.4340 13.0120 0.6510
33 19.4820 13.0760 0.6510
34 19.4180 13.9010 0.6510
35 18.4660 14.1550 0.6510
36 17.5770 13.6470 0.6510
37 18.0210 13.5200 0.6510
38 18.3390 12.6310 0.6510
39 17.3230 12.5040 0.6510
40 20.4340 15.8060 0.6510
41 20.4980 17.4570 0.6510
Continued on next page
637
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 19.9900 18.0290 0.6510
43 19.6090 18.1560 0.6510
44 20.5610 18.2190 0.6510
45 20.1170 18.2830 0.6510
46 20.4340 18.5370 0.6510
47 18.4660 17.8380 0.6510
48 18.2120 18.2830 0.6510
49 18.4660 18.6640 0.6510
50 18.1480 16.5050 0.6510
51 16.6880 18.0920 0.6510
52 18.5930 21.6480 0.6510
53 19.8630 21.3310 0.6510
54 20.1170 21.7750 0.6510
55 19.4820 21.9660 0.6510
56 18.9100 22.4740 0.6510
57 20.1170 22.7280 0.6510
58 20.3710 23.0450 0.6510
59 20.5610 23.5530 0.6510
60 18.9740 24.1250 0.6510
61 18.9740 24.5690 0.6510
62 19.1640 24.6960 0.6510
63 20.5610 24.6960 0.6510
64 21.5770 21.3940 0.6510
65 16.3700 26.9820 0.6510
66 17.0690 27.0460 0.6510
67 17.6400 27.4900 0.6510
68 17.0690 27.7440 0.6510
69 17.6400 27.9980 0.6510
70 18.7200 30.6650 0.6510
71 18.5290 30.0300 0.6510
72 18.7200 29.9670 0.6510
73 18.9740 29.9670 0.6510
74 22.1490 29.7130 0.6510
75 21.9580 29.3950 0.6510
76 22.4660 28.8870 0.6510
77 18.9100 28.6970 0.6510
78 22.0220 28.4430 0.6510
79 19.0370 28.1890 0.6510
80 18.7200 28.1890 0.6510
81 20.1170 27.6170 0.6510
82 19.0370 26.9820 0.6510
Continued on next page
638
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 19.5450 25.8390 0.6510
84 20.5610 25.7760 0.6510
85 20.9420 25.6490 0.6510
86 21.9580 24.7600 0.6510
87 25.8950 29.9030 0.6510
88 26.0860 29.9030 0.6510
89 25.0700 30.0300 0.6510
90 28.9430 30.4750 0.6510
91 28.9430 30.0300 0.6510
92 29.0700 29.7130 0.6510
93 30.2770 30.4750 0.6510
94 27.9270 28.1250 0.6510
95 22.2760 28.1250 0.6510
96 25.8320 27.9980 0.6510
97 25.9590 27.7440 0.6510
98 25.0700 27.7440 0.6510
99 27.2290 27.5540 0.6510
100 26.1490 27.4900 0.6510
101 28.8800 27.3000 0.6510
102 32.1180 27.3000 0.6510
103 31.4200 27.1730 0.6510
104 27.5460 26.9820 0.6510
105 24.5620 26.9820 0.6510
106 25.7050 26.2200 0.6510
107 27.2290 26.2200 0.6510
108 33.6420 26.2200 0.6510
109 29.0070 26.1570 0.6510
110 31.3560 26.0300 0.6510
111 27.1020 25.9660 0.6510
112 27.1650 25.4580 0.6510
113 28.8800 25.3310 0.6510
114 28.4990 25.1410 0.6510
115 22.9740 25.1410 0.6510
116 26.0860 24.9500 0.6510
117 32.2450 24.8870 0.6510
118 26.9110 24.7600 0.6510
119 28.7530 24.3790 0.6510
120 25.0060 24.1880 0.6510
121 24.3080 23.9980 0.6510
122 28.7530 23.9980 0.6510
123 31.2930 23.6800 0.6510
Continued on next page
639
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 25.8320 23.6800 0.6510
125 24.9430 23.6800 0.6510
126 27.8000 23.6170 0.6510
127 23.3550 23.5530 0.6510
128 26.1490 23.1720 0.6510
129 29.2610 23.0450 0.6510
130 28.0540 22.9180 0.6510
131 25.8320 22.9180 0.6510
132 28.2450 22.8550 0.6510
133 28.6260 22.7910 0.6510
134 27.9910 22.6010 0.6510
135 26.9110 22.6010 0.6510
136 27.5460 22.5370 0.6510
137 29.1340 22.5370 0.6510
138 23.4820 22.4100 0.6510
139 29.0700 22.3470 0.6510
140 31.3560 22.3470 0.6510
141 29.2610 22.2830 0.6510
142 34.3410 22.0290 0.6510
143 28.8160 21.9020 0.6510
144 26.0220 21.9020 0.6510
145 27.1020 21.6480 0.6510
146 27.9270 21.4580 0.6510
147 28.2450 21.3310 0.6510
148 24.2440 21.0770 0.6510
149 28.6890 21.0130 0.6510
150 34.3410 21.0130 0.6510
151 26.1490 20.8860 0.6510
152 30.7850 20.8230 0.6510
153 25.8950 20.7590 0.6510
154 24.8790 20.6320 0.6510
155 27.3560 20.6320 0.6510
156 34.4680 20.4420 0.6510
157 33.5150 20.3150 0.6510
158 26.2760 20.1880 0.6510
159 26.9750 20.0610 0.6510
160 24.8790 19.9340 0.6510
161 26.8480 19.7430 0.6510
162 24.6250 19.6800 0.6510
163 31.3560 19.6800 0.6510
164 33.9600 19.6800 0.6510
Continued on next page
640
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 27.4830 19.6160 0.6510
166 27.2290 19.6160 0.6510
167 32.3090 19.5530 0.6510
168 29.7050 19.4260 0.6510
169 24.7520 19.3620 0.6510
170 25.1330 19.2350 0.6510
171 29.2610 19.1720 0.6510
172 24.9430 19.1080 0.6510
173 26.1490 19.0450 0.6510
174 25.1970 18.9180 0.6510
175 25.8950 18.9180 0.6510
176 34.0870 18.9180 0.6510
177 36.4360 18.9180 0.6510
178 27.8640 18.8540 0.6510
179 26.5940 18.8540 0.6510
180 24.9430 18.7910 0.6510
181 29.5780 18.7910 0.6510
182 34.5950 18.7910 0.6510
183 30.5310 18.6640 0.6510
184 27.7370 18.6640 0.6510
185 27.1020 18.6640 0.6510
186 32.3720 18.5370 0.6510
187 33.2610 18.5370 0.6510
188 27.3560 18.4730 0.6510
189 24.9430 18.3460 0.6510
190 32.6900 18.3460 0.6510
191 33.0710 18.3460 0.6510
192 33.6420 18.3460 0.6510
193 26.7210 18.2830 0.6510
194 33.5150 18.2190 0.6510
195 34.7220 18.2190 0.6510
196 28.6890 18.1560 0.6510
197 28.1180 18.0920 0.6510
198 33.5150 18.0290 0.6510
199 32.9440 17.9650 0.6510
200 25.4510 17.9650 0.6510
201 31.1020 17.7750 0.6510
202 31.6100 17.7750 0.6510
203 32.8170 17.7750 0.6510
204 33.3880 17.5840 0.6510
205 29.9590 17.5840 0.6510
Continued on next page
641
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 31.9910 17.2030 0.6510
207 30.0230 17.2030 0.6510
208 26.3400 17.2030 0.6510
209 25.0700 17.0760 0.6510
210 29.6420 17.0760 0.6510
211 30.5940 17.0760 0.6510
212 30.9750 17.0760 0.6510
213 36.4360 17.0760 0.6510
214 28.0540 17.0130 0.6510
215 25.8320 16.9490 0.6510
216 30.7850 16.9490 0.6510
217 28.9430 16.8860 0.6510
218 31.4830 16.8220 0.6510
219 32.1820 16.6320 0.6510
220 31.9910 16.6320 0.6510
221 27.2920 16.6320 0.6510
222 29.5150 16.5050 0.6510
223 24.3080 16.4410 0.6510
224 25.0700 16.3140 0.6510
225 35.9920 16.3140 0.6510
226 31.3560 16.2510 0.6510
227 30.7850 16.2510 0.6510
228 30.5940 16.2510 0.6510
229 27.7370 16.2510 0.6510
230 29.1340 16.1870 0.6510
231 33.0710 16.1870 0.6510
232 31.3560 16.0600 0.6510
233 30.1500 16.0600 0.6510
234 24.2440 15.9970 0.6510
235 28.3080 15.9330 0.6510
236 32.9440 15.9330 0.6510
237 31.2930 15.8060 0.6510
238 33.7690 15.6790 0.6510
239 26.1490 15.6790 0.6510
240 29.3240 15.4890 0.6510
241 30.4620 15.4730 0.6510
242 30.7220 15.4730 0.6510
243 30.9820 15.4730 0.6510
244 31.2420 15.4730 0.6510
245 31.5020 15.4730 0.6510
246 31.7620 15.4730 0.6510
Continued on next page
642
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 32.0220 15.4730 0.6510
248 32.2820 15.4730 0.6510
249 32.5420 15.4730 0.6510
250 32.8020 15.4730 0.6510
251 33.0620 15.4730 0.6510
252 33.3220 15.4730 0.6510
253 33.5820 15.4730 0.6510
254 27.2290 15.3620 0.6510
255 30.6570 15.2460 0.6510
256 31.1120 15.2460 0.6510
257 31.3720 15.2460 0.6510
258 31.6320 15.2460 0.6510
259 31.8920 15.2460 0.6510
260 32.1520 15.2460 0.6510
261 32.4120 15.2460 0.6510
262 32.6720 15.2460 0.6510
263 32.9320 15.2460 0.6510
264 33.4520 15.2460 0.6510
265 24.3710 15.2350 0.6510
266 29.6420 15.1080 0.6510
267 27.4190 15.0440 0.6510
268 24.3080 15.0440 0.6510
269 34.1350 14.9860 0.6510
270 29.9750 14.9210 0.6510
271 28.2450 14.8540 0.6510
272 30.2020 14.7910 0.6510
273 33.9070 14.7910 0.6510
274 34.1350 14.7260 0.6510
275 28.3720 14.6630 0.6510
276 26.0860 14.6630 0.6510
277 29.9750 14.6610 0.6510
278 31.0470 14.6610 0.6510
279 31.3070 14.6610 0.6510
280 31.5670 14.6610 0.6510
281 31.8270 14.6610 0.6510
282 32.0870 14.6610 0.6510
283 32.3470 14.6610 0.6510
284 32.6070 14.6610 0.6510
285 32.8670 14.6610 0.6510
286 33.1270 14.6610 0.6510
287 34.1350 14.4660 0.6510
Continued on next page
643
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 30.7870 14.4660 0.6510
289 31.1770 14.4330 0.6510
290 31.4370 14.4330 0.6510
291 31.6970 14.4330 0.6510
292 31.9570 14.4330 0.6510
293 32.2170 14.4330 0.6510
294 32.4770 14.4330 0.6510
295 32.7370 14.4330 0.6510
296 29.0070 14.4090 0.6510
297 26.9110 14.4090 0.6510
298 29.9750 14.4010 0.6510
299 33.3220 14.4010 0.6510
300 24.3710 14.3460 0.6510
301 33.9070 14.3360 0.6510
302 33.0950 14.2710 0.6510
303 30.2020 14.2710 0.6510
304 25.8320 14.2190 0.6510
305 30.7870 14.2060 0.6510
306 34.1350 14.2060 0.6510
307 32.8350 14.1730 0.6510
308 31.2750 14.1730 0.6510
309 29.9750 14.1410 0.6510
310 33.3220 14.1410 0.6510
311 32.3720 14.0920 0.6510
312 31.9910 14.0920 0.6510
313 31.0150 14.0760 0.6510
314 33.9070 14.0760 0.6510
315 34.4040 14.0280 0.6510
316 29.5150 14.0280 0.6510
317 30.2020 14.0110 0.6510
318 33.0950 14.0110 0.6510
319 34.1350 13.9460 0.6510
320 30.7870 13.9460 0.6510
321 31.6100 13.9010 0.6510
322 29.9750 13.8810 0.6510
323 33.3220 13.8810 0.6510
324 29.3880 13.8380 0.6510
325 28.7530 13.8380 0.6510
326 31.0150 13.8160 0.6510
327 33.9070 13.8160 0.6510
328 31.3990 13.7540 0.6510
Continued on next page
644
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 30.2020 13.7510 0.6510
330 33.0950 13.7510 0.6510
331 34.1350 13.6860 0.6510
332 30.7870 13.6860 0.6510
333 27.9910 13.6470 0.6510
334 35.9920 13.6470 0.6510
335 33.3220 13.6210 0.6510
336 29.9750 13.6210 0.6510
337 31.0150 13.5560 0.6510
338 33.9070 13.5560 0.6510
339 32.6900 13.5200 0.6510
340 29.1970 13.5200 0.6510
341 28.3720 13.5200 0.6510
342 30.2020 13.4910 0.6510
343 33.0950 13.4910 0.6510
344 28.7530 13.4570 0.6510
345 30.7870 13.4260 0.6510
346 34.1350 13.4260 0.6510
347 34.8490 13.3930 0.6510
348 29.7050 13.3930 0.6510
349 29.9750 13.3610 0.6510
350 33.3220 13.3610 0.6510
351 29.1340 13.3300 0.6510
352 31.0150 13.2960 0.6510
353 33.9070 13.2960 0.6510
354 33.0950 13.2310 0.6510
355 32.4360 13.2310 0.6510
356 30.2020 13.2310 0.6510
357 29.5780 13.2030 0.6510
358 31.5470 13.2030 0.6510
359 30.7870 13.1660 0.6510
360 34.1350 13.1660 0.6510
361 36.1190 13.1390 0.6510
362 33.3220 13.1010 0.6510
363 29.9750 13.1010 0.6510
364 31.0150 13.0360 0.6510
365 33.9070 13.0360 0.6510
366 33.0950 12.9710 0.6510
367 30.2020 12.9710 0.6510
368 28.4990 12.9490 0.6510
369 28.7530 12.9490 0.6510
Continued on next page
645
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 29.0070 12.9490 0.6510
371 35.4200 12.9490 0.6510
372 34.1350 12.9060 0.6510
373 30.7870 12.9060 0.6510
374 31.7370 12.8850 0.6510
375 33.3220 12.8410 0.6510
376 29.9750 12.8410 0.6510
377 31.0150 12.7760 0.6510
378 33.9070 12.7760 0.6510
379 33.0950 12.7110 0.6510
380 30.2020 12.7110 0.6510
381 27.6730 12.6950 0.6510
382 30.7870 12.6460 0.6510
383 34.1350 12.6460 0.6510
384 26.0220 12.6310 0.6510
385 31.2750 12.6130 0.6510
386 32.8350 12.6130 0.6510
387 33.3220 12.5810 0.6510
388 29.9750 12.5810 0.6510
389 28.8160 12.5680 0.6510
390 27.9270 12.5680 0.6510
391 25.5780 12.5680 0.6510
392 31.0150 12.5160 0.6510
393 33.9070 12.5160 0.6510
394 34.7850 12.5040 0.6510
395 30.2020 12.4510 0.6510
396 29.1970 12.4410 0.6510
397 28.1810 12.4410 0.6510
398 25.1970 12.4410 0.6510
399 30.7870 12.3860 0.6510
400 34.1350 12.3860 0.6510
401 32.9320 12.3530 0.6510
402 32.6720 12.3530 0.6510
403 32.4120 12.3530 0.6510
404 32.1520 12.3530 0.6510
405 31.8920 12.3530 0.6510
406 31.6320 12.3530 0.6510
407 31.3720 12.3530 0.6510
408 29.9750 12.3210 0.6510
409 33.3220 12.3210 0.6510
410 28.8160 12.2500 0.6510
Continued on next page
646
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
411 30.9820 12.1260 0.6510
412 31.2420 12.1260 0.6510
413 31.5020 12.1260 0.6510
414 31.7620 12.1260 0.6510
415 32.0220 12.1260 0.6510
416 32.2820 12.1260 0.6510
417 32.5420 12.1260 0.6510
418 32.8020 12.1260 0.6510
419 33.0620 12.1260 0.6510
420 34.1350 12.1260 0.6510
421 25.8950 12.1230 0.6510
422 25.7050 12.1230 0.6510
423 29.9750 12.0610 0.6510
424 30.2020 11.9960 0.6510
425 33.9070 11.9960 0.6510
426 34.5950 11.9960 0.6510
427 34.8490 11.9960 0.6510
428 26.5940 11.9330 0.6510
429 34.1350 11.8660 0.6510
430 29.3880 11.8040 0.6510
431 29.9750 11.8010 0.6510
432 30.6570 11.5410 0.6510
433 31.1770 11.5410 0.6510
434 31.4370 11.5410 0.6510
435 31.6970 11.5410 0.6510
436 31.9570 11.5410 0.6510
437 32.2170 11.5410 0.6510
438 32.4770 11.5410 0.6510
439 32.7370 11.5410 0.6510
440 32.9970 11.5410 0.6510
441 33.4520 11.5410 0.6510
442 29.2610 11.4250 0.6510
443 30.5270 11.3130 0.6510
444 30.7870 11.3130 0.6510
445 31.0470 11.3130 0.6510
446 31.3070 11.3130 0.6510
447 31.5670 11.3130 0.6510
448 31.8270 11.3130 0.6510
449 32.0870 11.3130 0.6510
450 32.3470 11.3130 0.6510
451 32.6070 11.3130 0.6510
Continued on next page
647
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
452 32.8670 11.3130 0.6510
453 33.1270 11.3130 0.6510
454 33.3870 11.3130 0.6510
455 33.6470 11.3130 0.6510
456 27.4190 11.2980 0.6510
457 28.6260 11.2340 0.6510
458 30.6580 10.9800 0.6510
459 30.3400 10.9170 0.6510
460 28.7530 10.7900 0.6510
461 27.9270 10.4090 0.6510
462 29.0070 10.2820 0.6510
463 28.3720 10.2180 0.6510
464 29.4510 10.1550 0.6510
465 28.6260 10.0910 0.6510
466 29.3880 8.3130 0.6510
467 30.7210 9.3290 0.6510
468 30.5940 9.5200 0.6510
469 30.3400 9.6470 0.6510
470 30.6580 9.7100 0.6510
471 30.9120 9.9010 0.6510
472 32.0550 9.8370 0.6510
473 34.0870 8.7580 0.6510
474 34.5950 9.2020 0.6510
475 35.1030 10.1550 0.6510
476 33.6420 10.1550 0.6510
477 33.8330 10.2820 0.6510
478 34.9760 10.2820 0.6510
479 33.9600 10.5360 0.6510
480 32.9440 10.5360 0.6510
481 35.1660 10.7260 0.6510
482 32.1820 10.9800 0.6510
483 35.6740 11.0440 0.6510
484 35.5470 11.2340 0.6510
485 33.9600 11.2340 0.6510
486 35.4840 11.4250 0.6510
487 35.2930 11.5520 0.6510
488 34.0870 11.6150 0.6510
489 34.7220 11.7420 0.6510
490 36.9440 13.0120 0.6510
491 37.4520 12.7580 0.6510
492 37.4520 10.2180 0.6510
Continued on next page
648
Table D.6 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
Depot 0.0000 0.0000 N.A.
649
Table D.7: CETSP instance dsj1000rdmRad
Customer index x-coordinate y-coordinate Service range
1 98.1036 50.8139 1.1045
2 53.4120 -4.2453 1.1045
3 57.7878 -4.3732 1.1045
4 53.2890 -9.6645 1.1045
5 20.5322 21.5891 1.1045
6 22.5923 19.7950 1.1045
7 6.9842 66.7632 1.1045
8 39.1965 105.4524 1.1045
9 31.0065 -1.0714 1.1045
10 24.7401 75.4523 1.1045
11 21.7951 21.8350 1.1045
12 44.3097 5.4051 1.1045
13 4.7342 63.0935 1.1045
14 31.7515 71.3679 1.1045
15 30.1816 102.1772 1.1045
16 95.0864 33.2234 1.1045
17 27.6433 72.5657 1.1045
18 92.1801 41.0349 1.1045
19 55.5508 6.7090 1.1045
20 40.9959 37.9409 1.1045
21 96.8097 54.0588 1.1045
22 4.0089 72.1860 1.1045
23 70.2011 52.7050 1.1045
24 72.6191 32.6684 1.1045
25 99.0428 19.6959 1.1045
26 38.1890 100.3805 1.1045
27 40.9527 105.6227 1.1045
28 67.5609 49.6310 1.1045
29 97.1071 18.8552 1.1045
30 93.2494 81.8793 1.1045
31 93.6083 38.4774 1.1045
32 83.5076 51.7826 1.1045
33 12.0444 66.3239 1.1045
34 64.8516 39.5774 1.1045
35 40.2323 12.6508 1.1045
36 30.7839 5.7178 1.1045
37 39.7333 98.7582 1.1045
38 31.4281 94.9219 1.1045
39 10.5042 66.7806 1.1045
40 100.6036 46.8020 1.1045
Continued on next page
650
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
41 47.3356 31.1656 1.1045
42 97.0499 25.7334 1.1045
43 91.9732 45.8332 1.1045
44 103.3956 43.6231 1.1045
45 93.4265 31.4744 1.1045
46 23.9142 5.5856 1.1045
47 72.0304 52.5053 1.1045
48 48.0764 105.8084 1.1045
49 97.0063 39.6578 1.1045
50 54.3132 33.4794 1.1045
51 75.5587 49.1352 1.1045
52 97.5653 74.5618 1.1045
53 27.2842 5.8331 1.1045
54 53.7123 16.5900 1.1045
55 51.9742 12.9315 1.1045
56 3.5924 94.7451 1.1045
57 106.4442 49.0895 1.1045
58 48.9393 11.7496 1.1045
59 63.1320 27.7543 1.1045
60 26.1674 96.1159 1.1045
61 53.4617 5.8056 1.1045
62 69.1689 51.2673 1.1045
63 18.2654 71.5277 1.1045
64 94.5838 45.9916 1.1045
65 62.7821 -0.0838 1.1045
66 102.2110 28.3893 1.1045
67 45.8725 14.3747 1.1045
68 27.3755 -1.0984 1.1045
69 29.3760 80.5861 1.1045
70 46.6598 16.0110 1.1045
71 90.6179 26.4649 1.1045
72 71.2619 53.5794 1.1045
73 24.0847 21.2619 1.1045
74 99.3782 93.0601 1.1045
75 32.2034 92.5655 1.1045
76 95.4600 44.3790 1.1045
77 99.5817 52.1789 1.1045
78 26.7943 -2.6353 1.1045
79 67.4673 33.2544 1.1045
80 97.8160 74.8015 1.1045
81 35.3466 107.7036 1.1045
Continued on next page
651
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
82 37.1788 95.0118 1.1045
83 77.9223 44.6051 1.1045
84 52.5136 31.1620 1.1045
85 102.6402 60.9181 1.1045
86 61.9524 -0.3330 1.1045
87 64.4232 44.0581 1.1045
88 19.8821 27.2321 1.1045
89 28.0990 29.8348 1.1045
90 47.5893 27.8934 1.1045
91 29.1897 96.4145 1.1045
92 47.6091 10.2274 1.1045
93 3.4538 93.5151 1.1045
94 98.5493 33.1624 1.1045
95 2.5533 99.1767 1.1045
96 102.9016 24.8202 1.1045
97 104.1034 98.3317 1.1045
98 92.2880 83.6157 1.1045
99 75.4748 37.8532 1.1045
100 19.3676 20.9011 1.1045
101 26.9511 99.1097 1.1045
102 60.8351 33.4935 1.1045
103 22.1344 71.2137 1.1045
104 94.0795 80.8773 1.1045
105 3.5503 90.3653 1.1045
106 19.4163 -0.8394 1.1045
107 45.9581 33.5048 1.1045
108 33.1638 109.6815 1.1045
109 53.8796 31.7093 1.1045
110 50.5069 12.3029 1.1045
111 70.6191 48.1820 1.1045
112 97.4314 81.9460 1.1045
113 33.5170 80.8699 1.1045
114 77.4079 49.1470 1.1045
115 72.7757 56.7077 1.1045
116 46.9054 30.8841 1.1045
117 98.2345 80.8600 1.1045
118 63.5739 32.9982 1.1045
119 55.9782 19.9329 1.1045
120 86.5983 36.2039 1.1045
121 56.6229 3.2945 1.1045
122 94.5355 44.3621 1.1045
Continued on next page
652
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
123 34.3074 104.3145 1.1045
124 45.6407 35.6580 1.1045
125 93.0994 86.3608 1.1045
126 46.5030 16.5426 1.1045
127 58.5931 27.1316 1.1045
128 7.8142 89.6258 1.1045
129 22.8762 75.7017 1.1045
130 64.1748 30.2745 1.1045
131 26.5500 96.7350 1.1045
132 -1.8619 98.5581 1.1045
133 43.7681 7.8375 1.1045
134 65.7303 47.3671 1.1045
135 20.7311 19.0512 1.1045
136 103.9916 60.6173 1.1045
137 50.1654 34.2980 1.1045
138 80.8872 43.1227 1.1045
139 97.9141 29.0493 1.1045
140 96.2582 32.5713 1.1045
141 85.8477 60.7859 1.1045
142 68.2062 28.5319 1.1045
143 101.8123 94.8910 1.1045
144 55.5686 2.3786 1.1045
145 89.5287 45.4109 1.1045
146 37.3296 94.7968 1.1045
147 -0.3116 97.6012 1.1045
148 61.7542 11.5270 1.1045
149 73.5268 49.2611 1.1045
150 95.4724 61.7777 1.1045
151 56.5140 2.6652 1.1045
152 89.2688 56.3248 1.1045
153 91.1677 84.1211 1.1045
154 107.9810 80.0957 1.1045
155 77.8264 55.5164 1.1045
156 41.9974 13.5778 1.1045
157 51.1106 98.2963 1.1045
158 68.2826 55.0673 1.1045
159 53.4554 15.0784 1.1045
160 25.4767 75.4810 1.1045
161 34.0163 93.2553 1.1045
162 50.8592 31.2824 1.1045
163 57.9508 29.6187 1.1045
Continued on next page
653
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
164 96.1560 30.1327 1.1045
165 49.3862 17.5735 1.1045
166 50.1386 26.6573 1.1045
167 46.3909 8.8190 1.1045
168 33.8390 67.1668 1.1045
169 96.5235 92.1962 1.1045
170 71.0505 50.7680 1.1045
171 36.7928 9.6586 1.1045
172 106.1692 29.0085 1.1045
173 57.7618 2.6586 1.1045
174 56.8778 27.6180 1.1045
175 12.0097 66.7734 1.1045
176 43.9840 9.2005 1.1045
177 40.0650 98.6098 1.1045
178 94.4072 76.9857 1.1045
179 60.4630 30.4795 1.1045
180 93.3823 48.5086 1.1045
181 33.6792 4.7017 1.1045
182 98.4258 65.8894 1.1045
183 66.5887 34.1226 1.1045
184 68.3701 31.3080 1.1045
185 28.6989 1.5656 1.1045
186 72.7013 43.6681 1.1045
187 19.6457 23.2311 1.1045
188 48.9533 90.4759 1.1045
189 0.4838 63.8626 1.1045
190 96.4356 62.0951 1.1045
191 1.4019 97.5847 1.1045
192 101.1610 45.7653 1.1045
193 108.6560 34.8419 1.1045
194 33.1881 90.5996 1.1045
195 44.6028 29.9319 1.1045
196 98.9521 56.5952 1.1045
197 63.8645 34.3723 1.1045
198 8.0472 76.1743 1.1045
199 91.8795 37.1845 1.1045
200 96.2133 40.5576 1.1045
201 9.0002 73.0359 1.1045
202 106.6231 51.9460 1.1045
203 31.4455 71.7336 1.1045
204 69.8977 54.8286 1.1045
Continued on next page
654
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
205 99.0152 86.1550 1.1045
206 42.0156 103.5929 1.1045
207 98.9198 48.0008 1.1045
208 102.4997 24.4075 1.1045
209 67.5765 27.7962 1.1045
210 101.7295 28.4449 1.1045
211 27.9452 7.0873 1.1045
212 6.6701 63.5082 1.1045
213 79.9479 46.2913 1.1045
214 35.9551 95.9225 1.1045
215 -2.1508 94.1499 1.1045
216 17.9606 81.6588 1.1045
217 68.0220 53.7678 1.1045
218 10.9416 69.7746 1.1045
219 102.0461 86.7072 1.1045
220 26.4488 5.1021 1.1045
221 51.3200 11.9016 1.1045
222 32.4952 97.9758 1.1045
223 -2.3037 90.7079 1.1045
224 42.5793 100.4271 1.1045
225 24.5076 73.1150 1.1045
226 73.2401 49.0047 1.1045
227 49.5432 29.0024 1.1045
228 86.3374 85.7586 1.1045
229 100.0845 45.3198 1.1045
230 0.5802 93.7511 1.1045
231 32.2488 71.8762 1.1045
232 29.7064 94.0211 1.1045
233 7.8039 17.6061 1.1045
234 31.0707 1.7474 1.1045
235 43.1057 91.7939 1.1045
236 101.2985 78.2917 1.1045
237 91.0332 34.8187 1.1045
238 103.6911 80.6200 1.1045
239 60.4167 1.4088 1.1045
240 103.4615 37.3033 1.1045
241 59.5552 26.5288 1.1045
242 48.0446 14.6778 1.1045
243 96.8706 83.0827 1.1045
244 52.0827 15.9727 1.1045
245 92.7178 89.1801 1.1045
Continued on next page
655
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
246 5.8502 91.8647 1.1045
247 67.8857 28.9512 1.1045
248 92.1982 53.9806 1.1045
249 106.6895 31.0233 1.1045
250 98.2152 53.7701 1.1045
251 55.3647 9.0137 1.1045
252 54.6523 25.2022 1.1045
253 97.0347 92.0258 1.1045
254 54.2786 24.4277 1.1045
255 103.8062 50.1176 1.1045
256 93.9444 64.9000 1.1045
257 75.5201 48.6107 1.1045
258 24.5208 1.7631 1.1045
259 85.9154 51.5363 1.1045
260 92.8209 56.9207 1.1045
261 22.8581 29.0039 1.1045
262 89.8350 77.7460 1.1045
263 48.6326 32.1618 1.1045
264 35.4152 92.5489 1.1045
265 30.7482 95.8761 1.1045
266 92.0851 66.8651 1.1045
267 9.6606 65.5604 1.1045
268 92.6699 80.6400 1.1045
269 74.8417 48.5823 1.1045
270 63.3607 23.5913 1.1045
271 52.0306 12.0787 1.1045
272 25.9081 14.4892 1.1045
273 45.9850 27.4123 1.1045
274 14.5018 68.1646 1.1045
275 95.9481 74.2510 1.1045
276 -3.1358 95.2162 1.1045
277 33.1686 108.6172 1.1045
278 10.7344 66.9849 1.1045
279 103.8959 45.4099 1.1045
280 88.0225 60.7529 1.1045
281 66.9490 50.6855 1.1045
282 54.8257 29.6059 1.1045
283 32.6970 74.6737 1.1045
284 42.9285 106.2179 1.1045
285 97.5519 44.8528 1.1045
286 61.1622 34.1592 1.1045
Continued on next page
656
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
287 98.9119 80.0767 1.1045
288 55.8132 15.4408 1.1045
289 56.0470 -0.6998 1.1045
290 93.4941 85.8189 1.1045
291 85.0650 35.2948 1.1045
292 95.4289 57.3916 1.1045
293 47.4903 33.2139 1.1045
294 47.2412 18.0641 1.1045
295 27.1736 83.2653 1.1045
296 91.8600 79.7087 1.1045
297 54.5895 27.7676 1.1045
298 6.0914 73.9114 1.1045
299 91.1842 48.1207 1.1045
300 99.5987 51.3246 1.1045
301 33.6244 92.4492 1.1045
302 66.9624 36.7077 1.1045
303 21.3113 31.7798 1.1045
304 38.2186 96.6747 1.1045
305 85.1876 33.1130 1.1045
306 37.9917 90.5379 1.1045
307 47.9603 31.0225 1.1045
308 26.4587 69.6793 1.1045
309 50.5738 30.8854 1.1045
310 100.5275 34.9543 1.1045
311 1.1743 92.9818 1.1045
312 96.6284 43.2460 1.1045
313 6.6564 74.2265 1.1045
314 98.5933 78.8152 1.1045
315 17.7323 26.9057 1.1045
316 58.2741 0.1622 1.1045
317 104.1728 96.9352 1.1045
318 44.7075 13.3055 1.1045
319 35.7224 107.3600 1.1045
320 93.9524 73.1450 1.1045
321 98.0763 43.3554 1.1045
322 46.6840 28.1154 1.1045
323 20.8129 26.0745 1.1045
324 99.0651 51.1078 1.1045
325 87.5583 39.2312 1.1045
326 56.6752 3.9284 1.1045
327 64.9829 35.6055 1.1045
Continued on next page
657
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
328 58.3955 -2.2935 1.1045
329 105.5782 30.6326 1.1045
330 22.0744 6.6433 1.1045
331 106.8535 30.7643 1.1045
332 95.7576 96.9635 1.1045
333 42.4155 0.0668 1.1045
334 58.2864 0.0731 1.1045
335 45.0704 101.2748 1.1045
336 73.6428 45.1426 1.1045
337 70.0624 50.1219 1.1045
338 59.4358 8.0877 1.1045
339 103.8313 82.5056 1.1045
340 103.0838 43.6629 1.1045
341 46.2130 15.3079 1.1045
342 41.5990 92.4813 1.1045
343 23.1689 25.5900 1.1045
344 36.4279 -4.3699 1.1045
345 98.9301 33.2654 1.1045
346 42.0978 97.5030 1.1045
347 22.4229 -2.1641 1.1045
348 99.9754 58.6633 1.1045
349 66.2863 51.2705 1.1045
350 80.8076 41.6004 1.1045
351 49.1677 19.2175 1.1045
352 0.6138 95.4238 1.1045
353 1.6453 95.7178 1.1045
354 24.4797 75.3540 1.1045
355 101.5830 94.8217 1.1045
356 95.8908 32.6754 1.1045
357 58.0726 3.0503 1.1045
358 29.9497 8.0977 1.1045
359 12.0877 66.3858 1.1045
360 102.0152 42.2262 1.1045
361 9.4578 72.6847 1.1045
362 61.1452 36.2851 1.1045
363 9.1700 97.1621 1.1045
364 92.2396 41.0703 1.1045
365 40.7150 18.8306 1.1045
366 98.8373 99.4165 1.1045
367 25.2224 21.1268 1.1045
368 102.9211 31.8790 1.1045
Continued on next page
658
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
369 22.8228 67.5784 1.1045
370 18.1963 16.0602 1.1045
371 19.4151 20.4264 1.1045
372 99.0429 61.6589 1.1045
373 96.2485 47.1277 1.1045
374 48.7027 4.8736 1.1045
375 42.8212 36.4305 1.1045
376 73.6395 46.5004 1.1045
377 43.7231 10.6871 1.1045
378 95.9325 86.7596 1.1045
379 62.9268 27.0211 1.1045
380 47.0712 4.3382 1.1045
381 40.2693 101.3043 1.1045
382 40.5226 102.8002 1.1045
383 19.4476 21.0876 1.1045
384 100.7126 88.5952 1.1045
385 100.6388 53.8259 1.1045
386 90.2672 64.2791 1.1045
387 99.4285 63.8276 1.1045
388 52.1655 19.1446 1.1045
389 71.5231 31.8286 1.1045
390 72.9198 44.5581 1.1045
391 73.9110 51.0144 1.1045
392 104.3693 90.8389 1.1045
393 44.0393 95.7757 1.1045
394 64.6914 7.7788 1.1045
395 70.1037 27.3839 1.1045
396 97.8831 81.9659 1.1045
397 85.9182 41.8430 1.1045
398 97.1852 78.7831 1.1045
399 26.9783 71.0141 1.1045
400 73.7963 57.8273 1.1045
401 48.4930 25.1860 1.1045
402 50.0191 -2.6033 1.1045
403 36.2059 6.8965 1.1045
404 61.2083 54.3519 1.1045
405 55.4854 26.8201 1.1045
406 87.8413 47.1867 1.1045
407 53.9006 102.5381 1.1045
408 24.5354 72.6275 1.1045
409 94.5490 73.3405 1.1045
Continued on next page
659
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
410 15.1112 64.3610 1.1045
411 81.9079 40.1742 1.1045
412 23.9369 61.5866 1.1045
413 9.3844 71.5303 1.1045
414 65.4552 32.6167 1.1045
415 55.9275 34.3566 1.1045
416 100.6204 94.7646 1.1045
417 98.8530 91.6792 1.1045
418 46.4115 30.3033 1.1045
419 52.3173 10.0275 1.1045
420 92.1151 81.2598 1.1045
421 67.6588 29.7348 1.1045
422 93.3932 53.1876 1.1045
423 40.8939 84.3555 1.1045
424 42.9721 90.3177 1.1045
425 46.8369 6.4403 1.1045
426 29.8552 101.3038 1.1045
427 70.6940 53.8562 1.1045
428 78.0993 54.3894 1.1045
429 21.1184 76.9048 1.1045
430 -1.9602 93.9224 1.1045
431 101.1976 33.4905 1.1045
432 -2.5612 92.1356 1.1045
433 92.4623 94.7340 1.1045
434 67.2420 26.9141 1.1045
435 102.4507 89.6037 1.1045
436 26.6904 96.1713 1.1045
437 13.2613 67.7948 1.1045
438 87.5129 47.9594 1.1045
439 104.9423 23.5210 1.1045
440 58.8992 5.3006 1.1045
441 107.8221 37.3636 1.1045
442 55.0890 27.0379 1.1045
443 95.6122 103.8055 1.1045
444 23.1228 16.7524 1.1045
445 46.7163 23.0055 1.1045
446 45.4650 105.2608 1.1045
447 99.6903 41.4772 1.1045
448 94.0924 96.5838 1.1045
449 105.6149 29.5786 1.1045
450 -3.2639 94.8889 1.1045
Continued on next page
660
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
451 31.1050 77.2121 1.1045
452 96.5473 37.5774 1.1045
453 58.2987 1.8222 1.1045
454 29.7849 97.5299 1.1045
455 88.6062 92.2681 1.1045
456 12.5389 66.9051 1.1045
457 13.7649 76.0563 1.1045
458 49.9475 19.2284 1.1045
459 103.2876 94.1817 1.1045
460 28.0443 7.2557 1.1045
461 46.7677 27.4481 1.1045
462 58.4334 33.3219 1.1045
463 21.6596 11.2130 1.1045
464 35.5392 31.6783 1.1045
465 4.7737 93.7785 1.1045
466 96.8865 41.9997 1.1045
467 96.8345 90.0197 1.1045
468 33.7832 8.5886 1.1045
469 48.3020 2.6164 1.1045
470 63.0749 1.8033 1.1045
471 50.8742 24.2729 1.1045
472 73.8072 55.2741 1.1045
473 -4.2807 74.2616 1.1045
474 21.4132 25.3225 1.1045
475 42.7704 10.2739 1.1045
476 19.6468 14.5775 1.1045
477 32.8593 93.0881 1.1045
478 67.6648 48.1141 1.1045
479 98.5859 34.5756 1.1045
480 58.6228 31.6703 1.1045
481 24.1578 73.3792 1.1045
482 14.2239 63.9607 1.1045
483 26.2460 7.8923 1.1045
484 104.5599 87.8351 1.1045
485 31.4906 71.3219 1.1045
486 70.5527 57.3223 1.1045
487 57.3839 0.9502 1.1045
488 102.0076 93.0750 1.1045
489 40.2335 17.1357 1.1045
490 23.4089 84.0628 1.1045
491 60.4719 1.0667 1.1045
Continued on next page
661
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
492 47.1260 99.3914 1.1045
493 69.9782 57.1009 1.1045
494 80.3964 49.7264 1.1045
495 98.1138 89.5940 1.1045
496 26.4833 65.6457 1.1045
497 20.5046 21.2685 1.1045
498 54.7376 29.7596 1.1045
499 93.9129 43.6355 1.1045
500 27.6562 5.4902 1.1045
501 42.4716 105.6496 1.1045
502 37.4272 33.8061 1.1045
503 60.9493 37.7343 1.1045
504 45.4903 38.3462 1.1045
505 98.0879 44.5657 1.1045
506 58.6741 1.1796 1.1045
507 -6.6860 94.6391 1.1045
508 22.6294 -1.9579 1.1045
509 63.3795 20.1125 1.1045
510 96.2085 41.8253 1.1045
511 93.6941 39.0671 1.1045
512 95.1558 61.2395 1.1045
513 73.7989 28.6287 1.1045
514 93.5538 62.1822 1.1045
515 42.9226 100.4615 1.1045
516 19.0397 19.3917 1.1045
517 52.7074 28.2489 1.1045
518 39.6285 91.4521 1.1045
519 55.1607 27.7715 1.1045
520 35.4006 103.6799 1.1045
521 98.8606 57.9963 1.1045
522 29.2451 9.0499 1.1045
523 29.3468 93.7461 1.1045
524 102.1595 55.9791 1.1045
525 14.0233 68.3418 1.1045
526 47.5448 13.9665 1.1045
527 70.4096 46.4113 1.1045
528 93.9312 28.9768 1.1045
529 56.2795 36.0371 1.1045
530 26.4747 67.9787 1.1045
531 73.2283 44.0709 1.1045
532 90.4865 46.0315 1.1045
Continued on next page
662
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
533 88.0687 81.4777 1.1045
534 102.8738 56.4102 1.1045
535 70.1344 58.5671 1.1045
536 46.0729 100.6780 1.1045
537 1.7661 66.5446 1.1045
538 92.4120 50.9961 1.1045
539 89.3668 41.3430 1.1045
540 72.4429 44.8985 1.1045
541 101.1477 85.2681 1.1045
542 94.4828 106.1237 1.1045
543 28.1717 107.4546 1.1045
544 94.5987 62.0376 1.1045
545 21.1889 21.2670 1.1045
546 33.8351 99.3235 1.1045
547 96.9541 82.6989 1.1045
548 39.1960 99.7694 1.1045
549 62.0243 36.1020 1.1045
550 98.9319 91.3958 1.1045
551 98.3241 22.4412 1.1045
552 3.1448 100.7200 1.1045
553 47.2642 16.1804 1.1045
554 0.3096 68.1954 1.1045
555 84.6532 51.7406 1.1045
556 72.0385 47.6030 1.1045
557 90.1236 40.7240 1.1045
558 23.1615 20.5337 1.1045
559 32.3564 -1.4633 1.1045
560 100.6297 27.3107 1.1045
561 95.9041 59.3009 1.1045
562 92.7490 64.7326 1.1045
563 66.7168 38.6980 1.1045
564 6.3198 96.0864 1.1045
565 44.7902 101.1589 1.1045
566 70.6462 49.6735 1.1045
567 98.4033 39.6451 1.1045
568 53.5890 37.6567 1.1045
569 53.8048 -5.0553 1.1045
570 72.4926 42.7909 1.1045
571 101.6020 92.3175 1.1045
572 24.8641 0.1355 1.1045
573 15.3124 65.2050 1.1045
Continued on next page
663
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
574 16.9397 16.1570 1.1045
575 94.1971 38.0204 1.1045
576 98.5670 80.2017 1.1045
577 67.7055 32.9993 1.1045
578 28.2891 98.2700 1.1045
579 73.2561 47.9132 1.1045
580 1.2023 90.7259 1.1045
581 61.5106 34.0654 1.1045
582 70.5497 45.0925 1.1045
583 29.5221 90.7635 1.1045
584 43.7884 36.8808 1.1045
585 88.6759 82.3658 1.1045
586 -0.1009 90.0487 1.1045
587 67.4955 46.0347 1.1045
588 63.4530 34.6286 1.1045
589 14.2076 63.0144 1.1045
590 12.7300 75.2001 1.1045
591 96.1169 76.0362 1.1045
592 73.3859 52.8201 1.1045
593 68.5789 56.8701 1.1045
594 91.1655 36.0648 1.1045
595 66.0257 55.1875 1.1045
596 -0.0468 93.7668 1.1045
597 37.0706 93.0168 1.1045
598 43.0828 99.6317 1.1045
599 46.5714 10.1740 1.1045
600 94.3087 39.6383 1.1045
601 92.9131 56.6287 1.1045
602 62.5649 23.4331 1.1045
603 92.5654 91.5305 1.1045
604 99.1261 78.6323 1.1045
605 68.7356 47.8890 1.1045
606 25.8989 0.7413 1.1045
607 21.5395 100.4343 1.1045
608 98.7715 55.3698 1.1045
609 28.1449 5.3771 1.1045
610 94.6583 60.3511 1.1045
611 31.0449 71.9995 1.1045
612 77.9078 47.2474 1.1045
613 47.7278 5.7114 1.1045
614 105.6501 47.8555 1.1045
Continued on next page
664
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
615 100.6854 61.8170 1.1045
616 11.6475 70.8021 1.1045
617 53.9650 12.2967 1.1045
618 54.7597 1.1902 1.1045
619 71.8327 48.0379 1.1045
620 94.6877 57.1733 1.1045
621 92.4351 33.0022 1.1045
622 18.9682 67.0820 1.1045
623 96.9343 84.9430 1.1045
624 97.9579 54.2407 1.1045
625 103.5291 67.9060 1.1045
626 49.0558 10.2790 1.1045
627 32.8361 107.2479 1.1045
628 49.5265 1.5006 1.1045
629 97.7943 87.7833 1.1045
630 7.0214 70.8048 1.1045
631 53.5826 -3.7128 1.1045
632 99.7789 45.6905 1.1045
633 99.7259 57.0659 1.1045
634 101.7941 49.0832 1.1045
635 98.3613 42.0392 1.1045
636 92.6340 40.1716 1.1045
637 54.6465 1.3270 1.1045
638 30.8807 93.5109 1.1045
639 27.2709 73.9256 1.1045
640 101.7780 67.1686 1.1045
641 77.9705 58.8491 1.1045
642 93.2846 41.9379 1.1045
643 41.1669 5.3004 1.1045
644 107.2392 85.9448 1.1045
645 42.2565 98.7398 1.1045
646 70.1179 52.2878 1.1045
647 2.5704 90.3092 1.1045
648 101.0606 82.9382 1.1045
649 102.2936 85.0217 1.1045
650 87.5726 32.8781 1.1045
651 87.1149 58.1702 1.1045
652 90.6435 28.0536 1.1045
653 31.7997 5.4917 1.1045
654 44.2621 15.3855 1.1045
655 94.6788 63.8911 1.1045
Continued on next page
665
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
656 79.5330 47.2684 1.1045
657 98.2007 80.5294 1.1045
658 99.2720 31.5703 1.1045
659 95.0304 53.2116 1.1045
660 50.3723 32.2399 1.1045
661 66.7818 30.0369 1.1045
662 94.5726 47.3613 1.1045
663 31.4187 76.5703 1.1045
664 97.4429 30.1528 1.1045
665 47.4524 12.1509 1.1045
666 95.7654 46.8722 1.1045
667 34.0458 95.0903 1.1045
668 2.7376 84.0979 1.1045
669 48.4975 2.4432 1.1045
670 10.0835 69.7230 1.1045
671 104.0844 32.9988 1.1045
672 93.6487 25.1273 1.1045
673 35.0473 98.5367 1.1045
674 44.7872 36.1398 1.1045
675 3.5998 89.8159 1.1045
676 43.0131 -4.6452 1.1045
677 75.9022 40.5634 1.1045
678 69.1853 30.9522 1.1045
679 94.6798 69.1984 1.1045
680 71.8965 50.0142 1.1045
681 81.1686 57.7423 1.1045
682 96.3928 32.1668 1.1045
683 39.9467 -2.3317 1.1045
684 60.1370 35.2014 1.1045
685 32.1756 91.0244 1.1045
686 96.6051 36.0943 1.1045
687 80.0004 48.0282 1.1045
688 86.2321 62.7290 1.1045
689 45.9074 18.6439 1.1045
690 94.4684 44.7163 1.1045
691 51.5450 -0.7619 1.1045
692 49.9971 19.9155 1.1045
693 48.2378 10.8880 1.1045
694 101.5683 27.6266 1.1045
695 77.6289 48.4559 1.1045
696 64.2784 38.8059 1.1045
Continued on next page
666
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
697 35.7306 102.2767 1.1045
698 35.5571 102.2950 1.1045
699 70.5469 25.0661 1.1045
700 9.9143 75.8382 1.1045
701 53.9046 16.3668 1.1045
702 91.0116 75.8870 1.1045
703 97.0865 83.6094 1.1045
704 98.7317 39.6579 1.1045
705 18.7531 32.5360 1.1045
706 -5.5457 98.4014 1.1045
707 34.0464 97.1856 1.1045
708 105.6506 92.4297 1.1045
709 49.2438 -0.5725 1.1045
710 49.3090 3.6922 1.1045
711 76.5498 52.2180 1.1045
712 33.2241 90.2072 1.1045
713 40.9431 96.0349 1.1045
714 97.3283 27.0933 1.1045
715 31.1128 -2.8096 1.1045
716 36.4235 4.5159 1.1045
717 58.5415 3.6684 1.1045
718 102.9023 68.4164 1.1045
719 23.5270 73.6169 1.1045
720 70.8564 51.5507 1.1045
721 8.8648 72.0358 1.1045
722 39.7266 17.3977 1.1045
723 61.5650 4.5717 1.1045
724 31.1391 0.2266 1.1045
725 58.8785 37.4935 1.1045
726 48.3250 36.1010 1.1045
727 95.4790 61.1306 1.1045
728 97.7133 51.9341 1.1045
729 104.3617 84.8664 1.1045
730 46.0937 -5.8176 1.1045
731 62.5325 1.7660 1.1045
732 44.1303 30.8739 1.1045
733 25.7737 68.9159 1.1045
734 99.0228 31.9463 1.1045
735 18.4916 22.0310 1.1045
736 52.4859 17.4578 1.1045
737 24.3218 77.9732 1.1045
Continued on next page
667
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
738 94.9909 83.4209 1.1045
739 -0.3390 97.1979 1.1045
740 74.5598 39.2546 1.1045
741 88.7937 67.4470 1.1045
742 3.8110 100.5395 1.1045
743 77.8794 45.0468 1.1045
744 87.2346 40.5435 1.1045
745 103.8628 98.4843 1.1045
746 58.6318 9.4344 1.1045
747 89.3464 46.1786 1.1045
748 91.9372 36.8319 1.1045
749 100.8882 91.1406 1.1045
750 92.5592 25.4331 1.1045
751 51.2901 7.6487 1.1045
752 14.7433 68.1941 1.1045
753 15.4332 72.9689 1.1045
754 19.5225 24.6717 1.1045
755 93.1133 78.1389 1.1045
756 72.1444 51.2772 1.1045
757 100.5945 52.9653 1.1045
758 57.2331 12.7874 1.1045
759 98.2349 98.4363 1.1045
760 88.2545 36.0660 1.1045
761 5.2812 65.5492 1.1045
762 65.2110 38.9167 1.1045
763 90.0140 39.9150 1.1045
764 41.6896 94.8028 1.1045
765 3.0162 107.1796 1.1045
766 42.6808 88.2098 1.1045
767 108.1531 76.0691 1.1045
768 34.7819 91.1147 1.1045
769 100.8862 48.4618 1.1045
770 68.3676 27.3310 1.1045
771 42.8352 101.6931 1.1045
772 22.0389 18.6688 1.1045
773 95.0373 98.5247 1.1045
774 98.6560 92.6213 1.1045
775 47.4152 28.2569 1.1045
776 89.9500 80.2132 1.1045
777 90.4784 41.2284 1.1045
778 28.2410 67.9653 1.1045
Continued on next page
668
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
779 36.1694 94.3523 1.1045
780 100.5649 91.4192 1.1045
781 93.1284 88.6615 1.1045
782 18.7218 26.0511 1.1045
783 35.2297 94.8683 1.1045
784 36.8108 99.4487 1.1045
785 7.5677 74.3816 1.1045
786 100.3840 25.6874 1.1045
787 96.2545 87.1498 1.1045
788 74.3979 53.0985 1.1045
789 68.0366 38.8903 1.1045
790 8.4928 63.9998 1.1045
791 44.5228 11.8645 1.1045
792 35.4073 87.2216 1.1045
793 53.2794 21.4994 1.1045
794 33.9629 96.8355 1.1045
795 -0.7351 89.6931 1.1045
796 76.2244 51.9684 1.1045
797 94.4551 58.0456 1.1045
798 82.0477 53.0979 1.1045
799 46.0043 6.8606 1.1045
800 90.0385 42.8005 1.1045
801 8.3117 72.2049 1.1045
802 34.9317 80.2335 1.1045
803 44.2937 4.7268 1.1045
804 17.2669 18.1061 1.1045
805 16.9754 26.2994 1.1045
806 92.8093 39.7693 1.1045
807 31.6341 101.1443 1.1045
808 15.0509 21.8739 1.1045
809 33.4349 0.0139 1.1045
810 35.2228 101.4244 1.1045
811 88.4465 41.4478 1.1045
812 -0.1710 97.1566 1.1045
813 44.0031 6.0986 1.1045
814 58.0725 5.2013 1.1045
815 45.5397 7.2979 1.1045
816 29.4417 11.4808 1.1045
817 97.7455 51.8526 1.1045
818 59.6709 -1.5476 1.1045
819 76.0043 50.5809 1.1045
Continued on next page
669
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
820 -1.2335 86.0108 1.1045
821 74.4488 50.3129 1.1045
822 94.6945 78.5720 1.1045
823 60.5785 6.8128 1.1045
824 91.1400 83.5499 1.1045
825 89.6611 52.1615 1.1045
826 97.7624 79.6432 1.1045
827 29.6205 6.6839 1.1045
828 69.5886 28.6002 1.1045
829 94.3452 48.7818 1.1045
830 93.0102 50.1223 1.1045
831 45.9242 19.9000 1.1045
832 95.1298 37.6897 1.1045
833 26.6151 77.1467 1.1045
834 37.1983 106.3470 1.1045
835 98.3827 22.3334 1.1045
836 92.9420 26.4511 1.1045
837 12.0587 67.8257 1.1045
838 54.0368 23.8586 1.1045
839 47.9812 30.2306 1.1045
840 70.7664 48.6137 1.1045
841 62.6603 37.1290 1.1045
842 97.9014 66.9835 1.1045
843 -4.1255 85.5960 1.1045
844 67.4683 58.2291 1.1045
845 31.9656 14.6164 1.1045
846 38.0686 7.3443 1.1045
847 61.6430 23.6955 1.1045
848 22.0857 71.4539 1.1045
849 26.2205 72.9044 1.1045
850 51.6732 17.1776 1.1045
851 21.2889 20.2133 1.1045
852 95.2026 90.5293 1.1045
853 35.7481 97.1257 1.1045
854 97.0806 39.3994 1.1045
855 73.6611 50.4924 1.1045
856 35.1535 70.6086 1.1045
857 80.7698 50.7290 1.1045
858 97.3108 57.8200 1.1045
859 63.8119 26.0212 1.1045
860 51.6292 37.4529 1.1045
Continued on next page
670
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
861 2.1469 96.6722 1.1045
862 103.1106 83.2736 1.1045
863 49.1449 22.3659 1.1045
864 102.9297 48.0592 1.1045
865 92.7124 33.4453 1.1045
866 0.6193 91.0377 1.1045
867 16.7224 69.1113 1.1045
868 78.2967 50.1808 1.1045
869 15.0856 70.6386 1.1045
870 22.9431 70.0987 1.1045
871 96.0562 52.3857 1.1045
872 18.7356 77.2891 1.1045
873 4.4426 63.6871 1.1045
874 88.3633 87.3681 1.1045
875 29.2732 5.6917 1.1045
876 104.1102 44.8822 1.1045
877 63.4243 4.3429 1.1045
878 97.3132 81.5365 1.1045
879 58.9981 26.6128 1.1045
880 51.5390 18.7116 1.1045
881 10.4334 62.8220 1.1045
882 93.0933 68.7697 1.1045
883 45.0418 3.8658 1.1045
884 93.2379 56.4517 1.1045
885 72.0955 52.6394 1.1045
886 100.0565 80.1054 1.1045
887 43.4311 0.4843 1.1045
888 52.2056 3.4977 1.1045
889 44.8479 -0.9391 1.1045
890 62.4332 -0.6840 1.1045
891 3.1184 98.9240 1.1045
892 90.3356 51.1932 1.1045
893 101.3770 48.1816 1.1045
894 64.2717 31.7627 1.1045
895 -12.8049 93.8535 1.1045
896 95.0864 47.4256 1.1045
897 45.4526 36.1210 1.1045
898 46.5537 103.4177 1.1045
899 53.9150 28.4629 1.1045
900 102.5430 45.6081 1.1045
901 27.0312 22.0371 1.1045
Continued on next page
671
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
902 72.2401 34.2889 1.1045
903 54.4331 -6.2551 1.1045
904 76.4125 46.9810 1.1045
905 69.1565 53.3430 1.1045
906 67.8488 53.6384 1.1045
907 93.9684 87.8762 1.1045
908 73.2116 57.7970 1.1045
909 50.3352 41.2014 1.1045
910 60.2628 6.0605 1.1045
911 9.1569 61.6426 1.1045
912 50.9668 1.7170 1.1045
913 8.0611 104.0930 1.1045
914 98.2004 50.3921 1.1045
915 55.7669 1.6852 1.1045
916 99.3434 90.9979 1.1045
917 96.0238 29.4057 1.1045
918 8.1477 101.1634 1.1045
919 58.1260 35.2400 1.1045
920 52.0607 4.6851 1.1045
921 67.7991 50.1342 1.1045
922 22.4003 2.9895 1.1045
923 51.7623 34.8081 1.1045
924 44.5689 9.7500 1.1045
925 69.2681 55.3133 1.1045
926 22.6268 64.3936 1.1045
927 7.6803 61.1857 1.1045
928 11.4442 66.9869 1.1045
929 52.3291 3.6705 1.1045
930 91.9756 47.4725 1.1045
931 85.5250 32.0217 1.1045
932 9.1707 70.0865 1.1045
933 47.7428 26.4380 1.1045
934 52.8937 1.3390 1.1045
935 72.0723 49.2863 1.1045
936 47.1015 12.1757 1.1045
937 96.2521 73.5638 1.1045
938 60.1802 30.6710 1.1045
939 25.3366 76.5380 1.1045
940 76.3790 48.6237 1.1045
941 17.3215 22.8150 1.1045
942 91.1291 78.4897 1.1045
Continued on next page
672
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
943 65.3289 43.5846 1.1045
944 75.7300 42.7229 1.1045
945 32.6009 89.9531 1.1045
946 4.9579 99.4405 1.1045
947 51.8363 2.0767 1.1045
948 62.4640 33.4003 1.1045
949 47.7789 92.5461 1.1045
950 43.7175 13.3612 1.1045
951 63.2951 31.2899 1.1045
952 94.8477 58.3247 1.1045
953 89.3520 47.1855 1.1045
954 24.5729 19.8583 1.1045
955 51.0819 30.8837 1.1045
956 51.7765 0.7553 1.1045
957 35.7859 98.3251 1.1045
958 66.7482 27.6121 1.1045
959 98.3726 88.4744 1.1045
960 31.3011 106.2109 1.1045
961 -7.5489 96.9207 1.1045
962 44.3034 16.6265 1.1045
963 31.6916 96.8159 1.1045
964 98.4228 65.0226 1.1045
965 77.5882 39.4219 1.1045
966 53.1154 7.9184 1.1045
967 99.3413 60.5080 1.1045
968 42.4139 3.5597 1.1045
969 21.3934 72.6127 1.1045
970 97.5011 28.0267 1.1045
971 100.3439 52.2486 1.1045
972 31.7064 96.9880 1.1045
973 33.0573 97.9271 1.1045
974 75.2757 50.6388 1.1045
975 11.4886 67.7219 1.1045
976 44.3651 39.5082 1.1045
977 86.5120 33.4131 1.1045
978 51.4730 33.7115 1.1045
979 97.1838 29.5842 1.1045
980 105.0575 26.2706 1.1045
981 39.3246 101.8921 1.1045
982 69.4154 51.8752 1.1045
983 54.5841 1.3000 1.1045
Continued on next page
673
Table D.7 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
984 23.7960 77.2181 1.1045
985 50.2911 5.2466 1.1045
986 89.5631 83.3752 1.1045
987 89.1249 38.0318 1.1045
988 95.5040 96.3510 1.1045
989 70.9160 53.3608 1.1045
990 72.9378 43.4347 1.1045
991 79.7169 32.9378 1.1045
992 89.0134 41.3658 1.1045
993 23.3217 16.9506 1.1045
994 95.8598 39.2349 1.1045
995 75.9853 41.4015 1.1045
996 90.7200 30.0490 1.1045
997 95.1396 47.3596 1.1045
998 46.0030 37.4534 1.1045
999 54.3108 6.5803 1.1045
Depot 47.1287 11.9659 N.A.
674
Table D.8: CETSP instance team1 100rdmRad
Customer index x-coordinate y-coordinate Service range
1 78.2140 79.2180 2.9020
2 74.4470 77.3820 2.9020
3 76.1540 71.7630 2.9020
4 77.9190 74.0570 2.9020
5 54.0320 12.1970 2.9020
6 53.7540 0.1480 2.9020
7 46.1540 2.0830 2.9020
8 53.4050 3.0410 2.9020
9 40.8680 2.9810 2.9020
10 45.2930 9.0570 2.9020
11 27.2190 44.5100 2.9020
12 19.8810 93.1810 2.9020
13 1.5270 46.5990 2.9020
14 74.6790 41.8650 2.9020
15 36.9240 96.6360 2.9020
16 30.5030 90.0560 2.9020
17 24.0530 94.1890 2.9020
18 33.4430 88.5780 2.9020
19 36.7620 86.0920 2.9020
20 20.3930 83.7930 2.9020
21 33.6260 83.8690 2.9020
22 27.5900 93.6440 2.9020
23 19.5690 24.4490 2.9020
24 25.5420 20.5060 2.9020
25 15.7720 12.5490 2.9020
26 29.4470 11.2430 2.9020
27 21.4590 12.5300 2.9020
28 33.5000 17.3520 2.9020
29 33.3410 22.1780 2.9020
30 26.8390 11.7320 2.9020
31 12.4140 20.9620 2.9020
32 22.4940 14.2020 2.9020
33 20.5410 9.2600 2.9020
34 16.1230 17.5680 2.9020
35 49.5710 48.1400 2.9020
36 47.2320 45.2700 2.9020
37 52.9750 65.5600 2.9020
38 51.2900 49.5800 2.9020
39 55.2810 51.8710 2.9020
40 59.0070 60.2130 2.9020
41 49.0200 51.5410 2.9020
Continued on next page
675
Table D.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 57.2430 55.7920 2.9020
43 40.9780 46.4900 2.9020
44 59.5340 67.7320 2.9020
45 43.2430 58.4040 2.9020
46 42.8040 54.7400 2.9020
47 57.1420 56.8570 2.9020
48 53.9580 52.6810 2.9020
49 89.3590 10.8390 2.9020
50 85.8410 12.6530 2.9020
51 91.8570 16.5020 2.9020
52 94.9260 4.0060 2.9020
53 91.0070 13.2490 2.9020
54 92.8890 3.8550 2.9020
55 85.5540 10.0610 2.9020
56 88.4570 8.1850 2.9020
57 95.3170 17.8640 2.9020
58 93.5740 3.2550 2.9020
59 20.7350 74.6590 2.9020
60 26.2130 68.9770 2.9020
61 26.7320 55.6120 2.9020
62 21.2990 57.5930 2.9020
63 11.8440 68.3940 2.9020
64 13.4540 69.0070 2.9020
65 5.7770 62.0030 2.9020
66 17.3740 67.5290 2.9020
67 8.6410 64.1880 2.9020
68 25.9230 53.1850 2.9020
69 19.6190 52.7340 2.9020
70 11.1230 60.4420 2.9020
71 20.1030 52.3470 2.9020
72 7.2350 62.3670 2.9020
73 11.8780 70.4440 2.9020
74 25.2010 54.5070 2.9020
75 18.4500 52.9540 2.9020
76 5.7390 68.5350 2.9020
77 93.6940 56.9250 2.9020
78 87.1730 60.9980 2.9020
79 87.1800 60.8600 2.9020
80 89.0910 59.8860 2.9020
81 93.4560 57.6900 2.9020
82 87.6330 63.4320 2.9020
Continued on next page
676
Table D.8 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 91.0430 63.6910 2.9020
84 93.9460 64.0030 2.9020
85 94.8940 61.2620 2.9020
86 94.6190 62.1030 2.9020
87 63.6310 81.2240 2.9020
88 73.5230 67.7270 2.9020
89 81.4760 87.3160 2.9020
90 86.7850 67.2170 2.9020
91 68.1930 67.1240 2.9020
92 67.6430 91.8290 2.9020
93 85.9680 75.1940 2.9020
94 66.9710 72.2010 2.9020
95 84.1460 71.4270 2.9020
96 87.2520 72.9520 2.9020
97 66.9570 73.7970 2.9020
98 67.1790 79.7460 2.9020
99 61.4930 65.5920 2.9020
100 62.3520 63.1440 2.9020
Depot 50.0000 10.0000 N.A.
677
Table D.9: CETSP instance team 200rdmRad
Customer index x-coordinate y-coordinate Service range
1 70.5547 53.3424 6.3030
2 57.9519 28.9562 6.3030
3 30.1948 77.4740 6.3030
4 1.4018 76.0724 6.3030
5 81.4490 70.9038 6.3030
6 4.5353 41.4033 6.3030
7 86.2619 79.0480 6.3030
8 37.3536 96.1953 6.3030
9 87.1446 5.6237 6.3030
10 94.9557 36.4019 6.3030
11 52.4868 76.7112 6.3030
12 5.3505 59.2458 6.3030
13 46.8700 29.8165 6.3030
14 62.2697 64.7821 6.3030
15 26.3793 27.9342 6.3030
16 82.9802 82.4602 6.3030
17 58.9163 98.6093 6.3030
18 91.0964 22.6866 6.3030
19 69.5115 98.0003 6.3030
20 24.3931 53.3873 6.3030
21 10.6370 99.9415 6.3030
22 67.6176 1.5704 6.3030
23 57.5184 10.0052 6.3030
24 10.3023 79.8884 6.3030
25 28.4480 4.5649 6.3030
26 29.5773 38.2011 6.3030
27 30.0970 94.8571 6.3030
28 97.9829 40.1374 6.3030
29 27.8280 16.0441 6.3030
30 16.2822 64.6587 6.3030
31 41.0073 41.2767 6.3030
32 71.2730 32.6206 6.3030
33 63.3179 20.7561 6.3030
34 18.6014 58.3359 6.3030
35 8.0715 45.7971 6.3030
36 90.5730 26.1368 6.3030
37 78.5212 37.8903 6.3030
38 28.9665 91.9377 6.3030
39 63.1742 62.7642 6.3030
40 42.8456 9.7974 6.3030
41 56.1040 69.4485 6.3030
Continued on next page
678
Table D.9 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 91.3718 83.4817 6.3030
43 2.2629 54.3361 6.3030
44 91.6164 43.0261 6.3030
45 67.7948 0.2454 6.3030
46 51.3738 46.2980 6.3030
47 35.3473 40.4834 6.3030
48 26.9732 5.5594 6.3030
49 24.3845 97.9078 6.3030
50 6.0916 39.0291 6.3030
51 36.4995 48.9895 6.3030
52 15.5663 47.4459 6.3030
53 25.7268 62.8752 6.3030
54 54.2070 15.6302 6.3030
55 93.8545 65.4499 6.3030
56 50.6087 39.0471 6.3030
57 10.7375 78.3995 6.3030
58 45.9641 75.3688 6.3030
59 59.6095 83.2730 6.3030
60 1.8758 21.0369 6.3030
61 7.3953 10.5453 6.3030
62 33.1694 12.8250 6.3030
63 0.0241 3.6794 6.3030
64 65.7055 54.4014 6.3030
65 82.7412 8.1894 6.3030
66 19.1923 67.8913 6.3030
67 45.4208 35.7023 6.3030
68 14.9981 70.4396 6.3030
69 92.8786 53.0213 6.3030
70 8.9641 75.7729 6.3030
71 40.1842 46.1874 6.3030
72 49.2166 20.7627 6.3030
73 32.9736 9.5429 6.3030
74 58.9793 16.9873 6.3030
75 92.7617 9.7930 6.3030
76 44.3862 27.2947 6.3030
77 87.2547 75.0688 6.3030
78 27.2942 67.3647 6.3030
79 25.6629 8.9897 6.3030
80 3.0951 32.2718 6.3030
81 79.0129 29.7258 6.3030
82 23.5282 48.0475 6.3030
Continued on next page
679
Table D.9 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 25.4602 34.0607 6.3030
84 4.4934 48.2428 6.3030
85 20.6017 86.4535 6.3030
86 58.8629 75.4908 6.3030
87 92.7883 33.1017 6.3030
88 54.2941 8.0691 6.3030
89 63.4372 41.0037 6.3030
90 96.0423 11.4623 6.3030
91 92.3445 62.0210 6.3030
92 34.7726 14.9246 6.3030
93 47.9978 21.9409 6.3030
94 99.3731 13.0420 6.3030
95 2.8886 34.5392 6.3030
96 54.7669 92.2955 6.3030
97 53.8246 40.6421 6.3030
98 84.7245 82.6226 6.3030
99 67.2428 72.1895 6.3030
100 99.6771 33.9806 6.3030
101 49.5211 41.2968 6.3030
102 69.5282 17.9089 6.3030
103 42.2918 54.3177 6.3030
104 81.4664 54.0914 6.3030
105 42.7533 50.9068 6.3030
106 22.7782 61.9188 6.3030
107 48.9830 68.0819 6.3030
108 88.6600 37.0515 6.3030
109 30.2498 29.2867 6.3030
110 15.0311 2.9821 6.3030
111 22.3262 58.4529 6.3030
112 36.3459 87.5975 6.3030
113 47.8014 19.0633 6.3030
114 68.4062 74.7416 6.3030
115 61.3935 78.2139 6.3030
116 16.1744 80.7780 6.3030
117 20.2618 95.6762 6.3030
118 6.5851 6.1522 6.3030
119 79.3198 37.9605 6.3030
120 46.3584 11.9544 6.3030
121 11.5470 17.3773 6.3030
122 4.8119 71.4816 6.3030
123 53.3022 56.1009 6.3030
Continued on next page
680
Table D.9 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 21.6734 6.8006 6.3030
125 74.6355 75.2311 6.3030
126 39.8932 90.3099 6.3030
127 74.6007 8.8559 6.3030
128 63.4571 71.3028 6.3030
129 1.5682 43.1144 6.3030
130 40.1983 27.5296 6.3030
131 98.5374 80.2587 6.3030
132 69.6101 41.7599 6.3030
133 73.4488 27.7168 6.3030
134 35.6586 43.3457 6.3030
135 94.4971 12.1550 6.3030
136 64.5951 34.7833 6.3030
137 10.4432 18.5403 6.3030
138 7.7685 43.2760 6.3030
139 95.9271 54.2029 6.3030
140 49.4377 97.2967 6.3030
141 21.7800 37.8991 6.3030
142 39.5844 28.1503 6.3030
143 50.3371 13.8732 6.3030
144 51.7256 96.5364 6.3030
145 55.7501 90.9204 6.3030
146 65.7256 44.1115 6.3030
147 69.2995 6.4491 6.3030
148 75.6093 70.0514 6.3030
149 49.7071 15.5436 6.3030
150 22.3738 32.6144 6.3030
151 78.4489 5.0263 6.3030
152 51.8016 75.7030 6.3030
153 80.0670 32.5205 6.3030
154 97.2729 80.4267 6.3030
155 67.4826 90.5129 6.3030
156 87.5780 41.6648 6.3030
157 12.3083 95.4158 6.3030
158 79.7297 69.6285 6.3030
159 40.1605 1.6298 6.3030
160 16.7763 16.4234 6.3030
161 50.9720 40.6063 6.3030
162 10.6134 27.6123 6.3030
163 64.3047 84.9100 6.3030
164 49.7969 18.7775 6.3030
Continued on next page
681
Table D.9 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 89.6617 37.2814 6.3030
166 32.3555 77.0833 6.3030
167 21.8000 44.6993 6.3030
168 23.6028 87.8385 6.3030
169 61.0433 37.4432 6.3030
170 38.9502 86.0589 6.3030
171 58.5938 93.1559 6.3030
172 51.7192 33.0301 6.3030
173 86.8454 25.9061 6.3030
174 25.9541 17.8694 6.3030
175 34.6957 0.2506 6.3030
176 74.2342 84.0887 6.3030
177 27.8589 70.2970 6.3030
178 40.4865 81.1571 6.3030
179 74.1781 43.7664 6.3030
180 7.7981 41.0632 6.3030
181 33.9375 71.0554 6.3030
182 31.2288 79.8774 6.3030
183 15.1756 59.2991 6.3030
184 95.6237 24.3148 6.3030
185 93.9971 11.4333 6.3030
186 98.4253 63.2976 6.3030
187 59.8856 90.2570 6.3030
188 57.4865 24.5174 6.3030
189 86.0162 7.4950 6.3030
190 43.8826 75.9979 6.3030
191 24.5679 37.8606 6.3030
192 39.7244 52.6573 6.3030
193 27.0359 58.1176 6.3030
194 20.9699 7.8709 6.3030
195 89.5446 11.1433 6.3030
196 65.2377 90.0334 6.3030
197 23.1597 94.9905 6.3030
198 84.6187 44.1216 6.3030
199 49.2006 76.9507 6.3030
200 83.4893 38.2569 6.3030
Depot 19.5535 32.6157 N.A.
682
Table D.10: CETSP instance team3 300rdmRad
Customer index x-coordinate y-coordinate Service range
1 44.7500 90.0800 11.2700
2 82.4200 49.9900 11.2700
3 2.0100 79.0100 11.2700
4 25.8400 61.0900 11.2700
5 88.2100 3.6100 11.2700
6 24.4700 65.2400 11.2700
7 5.0700 73.1500 11.2700
8 85.7600 19.2700 11.2700
9 64.8700 11.3600 11.2700
10 43.2100 42.6100 11.2700
11 49.7800 61.4800 11.2700
12 51.3800 10.5100 11.2700
13 23.5500 20.8300 11.2700
14 27.7400 25.6300 11.2700
15 40.1400 85.4700 11.2700
16 39.2800 92.9900 11.2700
17 46.8000 93.4300 11.2700
18 48.9800 92.0300 11.2700
19 37.9300 93.9200 11.2700
20 39.3100 87.1400 11.2700
21 42.3700 92.4500 11.2700
22 40.1400 88.2500 11.2700
23 47.6700 92.5900 11.2700
24 47.5600 92.0300 11.2700
25 37.8800 93.1600 11.2700
26 49.1100 94.3100 11.2700
27 49.9100 91.9000 11.2700
28 48.8900 93.1000 11.2700
29 39.7000 88.7300 11.2700
30 41.1100 92.5500 11.2700
31 47.0800 88.2600 11.2700
32 45.5700 93.7100 11.2700
33 46.8900 94.8500 11.2700
34 47.4800 94.9000 11.2700
35 46.9200 92.9400 11.2700
36 42.9300 88.7800 11.2700
37 39.1800 94.8600 11.2700
38 38.9900 86.4200 11.2700
39 41.1100 86.3300 11.2700
40 38.3600 90.4300 11.2700
41 48.4200 91.5300 11.2700
Continued on next page
683
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 48.2500 85.2600 11.2700
43 48.6800 92.5500 11.2700
44 42.7800 91.8700 11.2700
45 38.0800 89.4800 11.2700
46 40.1300 86.4800 11.2700
47 50.9100 90.3000 11.2700
48 44.3300 87.3000 11.2700
49 51.7500 85.8100 11.2700
50 85.7800 45.3700 11.2700
51 86.8800 55.3400 11.2700
52 92.8200 43.5000 11.2700
53 90.9300 51.7800 11.2700
54 89.3300 46.2300 11.2700
55 84.4700 44.9100 11.2700
56 85.4300 53.0000 11.2700
57 91.0800 56.3200 11.2700
58 89.5900 51.8800 11.2700
59 85.2100 44.3500 11.2700
60 92.9200 45.3000 11.2700
61 92.5900 46.1600 11.2700
62 87.2600 54.5300 11.2700
63 92.0000 48.8000 11.2700
64 93.8600 49.1100 11.2700
65 92.0900 44.0800 11.2700
66 85.0200 48.7500 11.2700
67 89.3600 56.0300 11.2700
68 84.4700 48.1600 11.2700
69 89.1100 45.9400 11.2700
70 88.9200 43.6200 11.2700
71 87.5600 46.9900 11.2700
72 87.9200 47.4600 11.2700
73 85.8500 46.4900 11.2700
74 8.9500 75.4300 11.2700
75 3.4400 75.5800 11.2700
76 0.7600 80.9700 11.2700
77 2.9900 72.0900 11.2700
78 6.6200 72.9600 11.2700
79 6.3600 80.4400 11.2700
80 1.2100 81.9700 11.2700
81 4.1500 75.9200 11.2700
82 1.3600 82.4100 11.2700
Continued on next page
684
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 0.9700 75.7800 11.2700
84 10.6600 76.4400 11.2700
85 8.2900 81.4500 11.2700
86 2.1900 82.1300 11.2700
87 4.7500 76.3700 11.2700
88 8.0600 78.3600 11.2700
89 8.6000 80.5600 11.2700
90 0.9100 72.4300 11.2700
91 11.2300 82.6000 11.2700
92 21.7500 55.1900 11.2700
93 30.8500 54.3900 11.2700
94 23.7800 67.3700 11.2700
95 23.5000 55.8400 11.2700
96 23.1900 66.2200 11.2700
97 30.3600 58.1400 11.2700
98 19.6500 58.2000 11.2700
99 86.4600 7.1500 11.2700
100 90.7100 5.3500 11.2700
101 90.1400 0.7400 11.2700
102 86.7100 7.9000 11.2700
103 84.2100 1.1500 11.2700
104 84.5700 2.1900 11.2700
105 90.4500 0.1800 11.2700
106 84.2200 4.2500 11.2700
107 84.8500 7.4900 11.2700
108 85.1800 6.8100 11.2700
109 91.8600 5.0900 11.2700
110 83.5000 4.8300 11.2700
111 89.8100 1.3300 11.2700
112 83.9800 4.2400 11.2700
113 86.4900 3.9700 11.2700
114 87.0600 2.8900 11.2700
115 90.7900 7.2700 11.2700
116 83.0800 5.9000 11.2700
117 83.6300 6.6100 11.2700
118 85.3400 3.1300 11.2700
119 83.0800 6.8500 11.2700
120 24.0300 65.5600 11.2700
121 20.6400 65.0000 11.2700
122 28.7700 62.0500 11.2700
123 23.5200 71.0500 11.2700
Continued on next page
685
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 26.5000 63.4400 11.2700
125 20.8800 59.5100 11.2700
126 25.8600 63.8500 11.2700
127 25.2400 60.7700 11.2700
128 27.6400 62.7800 11.2700
129 27.4000 59.8400 11.2700
130 25.0100 63.1200 11.2700
131 27.6200 60.6100 11.2700
132 22.1700 64.9400 11.2700
133 22.5100 60.1500 11.2700
134 27.2800 65.4700 11.2700
135 28.8600 67.8400 11.2700
136 27.3600 59.9400 11.2700
137 24.4900 66.2700 11.2700
138 26.1500 61.9600 11.2700
139 21.3900 62.7100 11.2700
140 20.5600 61.4400 11.2700
141 25.6200 68.9800 11.2700
142 24.8600 66.0500 11.2700
143 22.6500 62.2000 11.2700
144 20.3500 68.7500 11.2700
145 8.6700 72.7700 11.2700
146 21.4900 69.2000 11.2700
147 19.8600 66.1100 11.2700
148 4.8000 88.5100 11.2700
149 28.9500 69.7200 11.2700
150 1.0100 87.8300 11.2700
151 21.9900 57.1500 11.2700
152 24.2500 76.6600 11.2700
153 4.2100 66.5300 11.2700
154 28.8200 81.7800 11.2700
155 35.5800 76.0600 11.2700
156 30.8300 54.4200 11.2700
157 37.8500 53.7600 11.2700
158 12.8200 66.4900 11.2700
159 27.1800 54.0400 11.2700
160 39.4200 71.5400 11.2700
161 36.6000 82.9400 11.2700
162 23.4700 70.4900 11.2700
163 16.7900 62.6700 11.2700
164 35.4600 90.5000 11.2700
Continued on next page
686
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 21.1000 78.1200 11.2700
166 13.3600 65.0000 11.2700
167 24.2000 92.4200 11.2700
168 35.3700 65.9900 11.2700
169 11.7400 69.1700 11.2700
170 16.9900 78.3600 11.2700
171 12.1400 56.7600 11.2700
172 12.0700 80.1400 11.2700
173 34.7900 81.5700 11.2700
174 31.9900 67.7400 11.2700
175 27.3500 82.2400 11.2700
176 11.1800 57.9200 11.2700
177 58.7500 56.6300 11.2700
178 92.9200 88.4600 11.2700
179 2.5700 49.6700 11.2700
180 70.7000 73.7000 11.2700
181 72.9300 73.7000 11.2700
182 24.6700 93.3400 11.2700
183 33.0100 55.5500 11.2700
184 31.2200 0.1800 11.2700
185 90.6500 58.2600 11.2700
186 60.9400 57.5600 11.2700
187 68.1700 79.2100 11.2700
188 51.1200 47.5400 11.2700
189 19.4800 4.7500 11.2700
190 53.7300 28.3700 11.2700
191 16.0700 82.1400 11.2700
192 5.5400 99.2900 11.2700
193 48.2600 14.5800 11.2700
194 9.4100 84.3800 11.2700
195 74.4900 84.4600 11.2700
196 47.3000 55.2500 11.2700
197 98.4100 37.6400 11.2700
198 54.0500 68.3900 11.2700
199 63.2600 50.7700 11.2700
200 57.5700 78.4400 11.2700
201 65.1600 40.7800 11.2700
202 3.2100 36.3500 11.2700
203 32.4200 78.2700 11.2700
204 1.2400 99.0100 11.2700
205 60.1200 71.0500 11.2700
Continued on next page
687
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 53.3500 83.1400 11.2700
207 3.3600 12.5400 11.2700
208 78.9800 97.8300 11.2700
209 22.6000 70.1000 11.2700
210 54.8300 99.8800 11.2700
211 5.5800 22.9000 11.2700
212 24.6600 9.1300 11.2700
213 15.5400 52.8300 11.2700
214 4.0100 20.5000 11.2700
215 96.4300 49.7300 11.2700
216 60.8900 11.9900 11.2700
217 61.2700 24.4100 11.2700
218 78.0100 26.1900 11.2700
219 44.5300 2.7200 11.2700
220 54.2200 8.1800 11.2700
221 71.3300 32.2300 11.2700
222 50.2100 0.8200 11.2700
223 63.3500 21.4900 11.2700
224 55.5000 8.8600 11.2700
225 73.6300 17.0700 11.2700
226 47.3400 38.2500 11.2700
227 45.5700 28.2600 11.2700
228 58.0200 32.4600 11.2700
229 79.7900 30.3200 11.2700
230 56.3100 21.3100 11.2700
231 62.1600 16.8800 11.2700
232 43.2300 11.5400 11.2700
233 75.9800 28.2600 11.2700
234 45.6300 23.7600 11.2700
235 74.9300 38.6300 11.2700
236 50.3000 13.2800 11.2700
237 77.9400 16.7300 11.2700
238 40.0000 38.7700 11.2700
239 66.8700 17.1000 11.2700
240 41.4700 31.6900 11.2700
241 67.0000 3.9400 11.2700
242 63.8800 23.8100 11.2700
243 76.8100 16.4000 11.2700
244 41.4900 2.2900 11.2700
245 78.4100 15.8800 11.2700
246 49.8500 30.5600 11.2700
Continued on next page
688
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 44.1500 32.6400 11.2700
248 42.7200 42.8400 11.2700
249 42.9500 44.7400 11.2700
250 42.6900 39.7800 11.2700
251 45.6000 43.9300 11.2700
252 43.2100 42.3500 11.2700
253 42.6200 44.8100 11.2700
254 42.5900 39.1600 11.2700
255 41.0700 43.9800 11.2700
256 41.9700 43.2200 11.2700
257 40.1100 39.6000 11.2700
258 45.4200 39.9100 11.2700
259 40.4000 40.1900 11.2700
260 45.6000 41.8100 11.2700
261 42.5600 42.2800 11.2700
262 43.9600 42.1000 11.2700
263 45.7100 40.8000 11.2700
264 64.3000 1.0300 11.2700
265 30.6900 95.9800 11.2700
266 11.4600 53.0700 11.2700
267 0.6200 84.9500 11.2700
268 34.2400 70.4600 11.2700
269 85.6000 88.6500 11.2700
270 66.2600 99.0700 11.2700
271 25.6500 24.5300 11.2700
272 70.2300 90.7300 11.2700
273 9.0700 51.9200 11.2700
274 53.8700 15.5100 11.2700
275 57.6600 15.5100 11.2700
276 52.1200 16.8400 11.2700
277 47.4500 7.4900 11.2700
278 48.0000 4.0000 11.2700
279 50.9700 4.5900 11.2700
280 55.4000 11.1700 11.2700
281 54.5000 15.9100 11.2700
282 52.6700 8.8800 11.2700
283 52.9600 3.7500 11.2700
284 44.7200 11.8700 11.2700
285 55.3800 10.1300 11.2700
286 45.5700 12.7600 11.2700
287 56.9400 12.1800 11.2700
Continued on next page
689
Table D.10 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 53.8500 15.0800 11.2700
289 56.3800 14.3200 11.2700
290 54.1500 15.5400 11.2700
291 56.2600 10.3400 11.2700
292 46.3800 12.3100 11.2700
293 50.5200 8.6800 11.2700
294 56.8500 15.4900 11.2700
295 55.2400 13.3700 11.2700
296 51.9800 10.9900 11.2700
297 45.0900 11.7000 11.2700
298 52.6700 4.6500 11.2700
299 51.8600 7.7000 11.2700
300 52.0300 16.0400 11.2700
Depot 23.5500 20.8300 N.A.
690
Table D.11: CETSP instance team4 400rdmRad
Customer index x-coordinate y-coordinate Service range
1 68.7924 27.9017 3.9464
2 17.2729 64.9732 3.9464
3 77.7502 18.7938 3.9464
4 0.0015 79.2564 3.9464
5 54.8709 48.0989 3.9464
6 91.0810 71.6915 3.9464
7 36.1103 75.9600 3.9464
8 22.2764 97.9200 3.9464
9 76.1173 11.8321 3.9464
10 92.4806 84.1266 3.9464
11 33.3240 88.8623 3.9464
12 92.0500 40.0562 3.9464
13 2.1250 13.8908 3.9464
14 2.4043 62.3745 3.9464
15 91.0375 80.9252 3.9464
16 16.4015 79.8607 3.9464
17 83.1155 24.6903 3.9464
18 80.0039 44.2789 3.9464
19 14.3588 25.8838 3.9464
20 55.5813 65.9389 3.9464
21 74.4430 98.0205 3.9464
22 34.0987 26.4840 3.9464
23 72.8895 91.5533 3.9464
24 33.2403 8.1602 3.9464
25 40.4237 12.9471 3.9464
26 39.6583 53.3929 3.9464
27 94.4040 75.1851 3.9464
28 40.2902 96.6895 3.9464
29 28.2020 68.6988 3.9464
30 87.3023 11.9374 3.9464
31 14.2410 46.1101 3.9464
32 18.4766 32.5001 3.9464
33 2.3493 1.7072 3.9464
34 90.7256 70.4444 3.9464
35 64.4698 94.9116 3.9464
36 56.4281 90.2054 3.9464
37 27.6568 28.0813 3.9464
38 98.6909 7.7236 3.9464
39 76.2706 23.4637 3.9464
40 31.8731 36.0461 3.9464
41 27.4824 83.1530 3.9464
Continued on next page
691
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 12.5519 14.7340 3.9464
43 75.8385 89.3970 3.9464
44 76.5389 22.0861 3.9464
45 43.0542 52.0799 3.9464
46 75.5897 88.7076 3.9464
47 74.9194 66.3328 3.9464
48 56.7601 13.3255 3.9464
49 10.7326 2.4910 3.9464
50 20.9401 75.2051 3.9464
51 71.8295 5.8557 3.9464
52 99.8277 8.4995 3.9464
53 67.6795 96.8283 3.9464
54 95.4862 52.7465 3.9464
55 77.3352 0.0095 3.9464
56 23.8316 88.2043 3.9464
57 82.1504 71.4598 3.9464
58 96.9141 16.7463 3.9464
59 84.9479 97.5133 3.9464
60 62.9449 12.9098 3.9464
61 20.6862 21.9667 3.9464
62 72.1063 71.5136 3.9464
63 54.0981 10.2091 3.9464
64 39.2436 59.3441 3.9464
65 59.3606 77.3659 3.9464
66 70.1631 48.5955 3.9464
67 40.9139 82.7298 3.9464
68 86.1930 99.2032 3.9464
69 44.8986 41.3810 3.9464
70 61.4918 51.7088 3.9464
71 57.2413 42.4061 3.9464
72 37.3237 47.1648 3.9464
73 28.8727 55.2137 3.9464
74 84.2511 92.6645 3.9464
75 12.1212 83.5253 3.9464
76 32.7339 86.4767 3.9464
77 61.3321 47.8180 3.9464
78 76.5757 39.1932 3.9464
79 42.3184 87.3475 3.9464
80 60.2356 81.9564 3.9464
81 69.3496 77.5166 3.9464
82 8.3478 79.0334 3.9464
Continued on next page
692
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 98.9377 68.3223 3.9464
84 91.8252 77.1235 3.9464
85 80.1284 42.2928 3.9464
86 44.6523 7.1683 3.9464
87 49.1001 97.0702 3.9464
88 13.3837 46.0323 3.9464
89 30.7328 57.7810 3.9464
90 59.8276 37.2156 3.9464
91 9.3526 52.2461 3.9464
92 2.3079 97.4497 3.9464
93 43.3124 33.0226 3.9464
94 51.0767 59.9316 3.9464
95 95.9689 41.8080 3.9464
96 47.9977 20.6394 3.9464
97 61.7325 60.2897 3.9464
98 45.1100 59.2193 3.9464
99 53.0851 32.1161 3.9464
100 89.0595 90.2910 3.9464
101 34.8220 51.0418 3.9464
102 58.9807 40.3692 3.9464
103 95.6406 28.6846 3.9464
104 19.0289 48.6519 3.9464
105 30.4635 78.6539 3.9464
106 19.9845 27.4016 3.9464
107 87.8583 88.3340 3.9464
108 72.4200 34.9981 3.9464
109 77.4640 15.6282 3.9464
110 90.1952 89.0370 3.9464
111 1.6920 67.9044 3.9464
112 37.4986 37.9479 3.9464
113 24.1584 82.4956 3.9464
114 54.0177 81.8894 3.9464
115 67.9702 74.9438 3.9464
116 67.6624 58.9604 3.9464
117 38.1230 58.9120 3.9464
118 18.7791 36.0166 3.9464
119 69.8176 1.3068 3.9464
120 46.5921 4.2476 3.9464
121 5.2982 16.1674 3.9464
122 94.8080 43.2514 3.9464
123 59.9265 35.2070 3.9464
Continued on next page
693
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 26.6212 98.8512 3.9464
125 81.5208 13.6878 3.9464
126 74.4851 34.7013 3.9464
127 82.3362 2.4203 3.9464
128 40.4153 76.3084 3.9464
129 64.1813 8.8859 3.9464
130 28.4719 7.1244 3.9464
131 94.3772 57.5521 3.9464
132 58.6675 14.4559 3.9464
133 66.5081 91.3032 3.9464
134 91.5733 68.7250 3.9464
135 94.8136 7.1370 3.9464
136 71.3065 97.9771 3.9464
137 42.3445 27.2316 3.9464
138 73.9755 66.7195 3.9464
139 48.9905 98.5583 3.9464
140 40.7182 8.4509 3.9464
141 59.2576 30.0921 3.9464
142 77.4727 18.0575 3.9464
143 92.6853 90.3106 3.9464
144 32.2238 93.2863 3.9464
145 83.8356 49.2214 3.9464
146 84.7755 95.2831 3.9464
147 68.7842 11.8632 3.9464
148 84.7108 44.2604 3.9464
149 53.6864 15.1982 3.9464
150 17.1382 10.2546 3.9464
151 0.3310 69.3032 3.9464
152 34.7277 67.4825 3.9464
153 13.0118 10.0758 3.9464
154 0.6110 22.3311 3.9464
155 15.4511 94.4715 3.9464
156 68.0334 62.5790 3.9464
157 39.2178 28.4875 3.9464
158 21.6688 63.7323 3.9464
159 75.1239 56.3550 3.9464
160 67.8084 64.8800 3.9464
161 59.2050 55.7600 3.9464
162 43.9034 88.3872 3.9464
163 29.4659 31.2299 3.9464
164 2.2063 60.7249 3.9464
Continued on next page
694
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 40.2054 70.4585 3.9464
166 56.1365 83.4511 3.9464
167 71.9668 79.2858 3.9464
168 59.6668 17.1521 3.9464
169 94.0901 9.3589 3.9464
170 32.6364 9.7190 3.9464
171 15.2685 27.3870 3.9464
172 21.1268 22.9892 3.9464
173 12.3430 3.7208 3.9464
174 60.7709 76.3761 3.9464
175 79.6523 4.1446 3.9464
176 35.7766 45.5234 3.9464
177 49.8213 32.0888 3.9464
178 72.2221 99.2555 3.9464
179 84.7303 97.6119 3.9464
180 77.8827 4.1124 3.9464
181 53.2499 71.4317 3.9464
182 16.5338 6.3140 3.9464
183 13.1154 76.2785 3.9464
184 72.3747 95.9811 3.9464
185 75.3053 17.7805 3.9464
186 8.8531 66.0938 3.9464
187 75.9403 77.0935 3.9464
188 31.5835 68.6781 3.9464
189 4.7291 38.2206 3.9464
190 15.8066 40.8770 3.9464
191 74.0184 45.6925 3.9464
192 22.6094 83.2183 3.9464
193 60.8141 45.8650 3.9464
194 48.8252 33.4678 3.9464
195 44.5494 51.8385 3.9464
196 47.8105 52.5088 3.9464
197 25.0904 4.2535 3.9464
198 90.3145 71.6626 3.9464
199 85.8230 42.2536 3.9464
200 45.8847 65.7157 3.9464
201 36.3513 83.6870 3.9464
202 30.8045 50.3614 3.9464
203 49.4347 86.0537 3.9464
204 41.3239 57.0652 3.9464
205 63.1063 74.4484 3.9464
Continued on next page
695
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 56.6801 15.8457 3.9464
207 36.3460 45.5586 3.9464
208 86.3064 44.0864 3.9464
209 57.8987 27.0669 3.9464
210 61.6925 66.4791 3.9464
211 41.3638 51.8118 3.9464
212 59.6161 30.5374 3.9464
213 35.0570 38.8871 3.9464
214 12.5480 14.2955 3.9464
215 66.0957 55.8768 3.9464
216 55.8945 37.2993 3.9464
217 90.9219 35.3086 3.9464
218 70.3859 48.2898 3.9464
219 74.1862 37.6646 3.9464
220 8.7059 46.6269 3.9464
221 62.1382 61.2182 3.9464
222 27.2520 44.4723 3.9464
223 76.3481 68.0516 3.9464
224 11.1344 51.5807 3.9464
225 65.7573 28.4960 3.9464
226 92.1248 61.7917 3.9464
227 38.0514 44.2529 3.9464
228 46.7183 46.7951 3.9464
229 82.4553 37.9749 3.9464
230 53.1029 58.7135 3.9464
231 30.1798 54.1346 3.9464
232 40.7033 55.5378 3.9464
233 56.7074 20.9848 3.9464
234 27.2796 90.9405 3.9464
235 61.7514 53.5726 3.9464
236 31.7652 39.5927 3.9464
237 69.4258 42.6618 3.9464
238 63.0662 46.0732 3.9464
239 41.6832 67.2999 3.9464
240 30.2641 36.1150 3.9464
241 75.4200 23.3656 3.9464
242 22.7932 31.8095 3.9464
243 24.4446 63.1281 3.9464
244 57.7680 55.4125 3.9464
245 56.7084 61.0847 3.9464
246 19.3226 41.0610 3.9464
Continued on next page
696
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 74.9758 51.8098 3.9464
248 46.2289 65.5692 3.9464
249 35.6091 81.9958 3.9464
250 75.7060 48.3543 3.9464
251 78.8975 61.3791 3.9464
252 44.5420 62.0002 3.9464
253 32.8006 59.1862 3.9464
254 83.2473 46.4582 3.9464
255 45.0155 41.5840 3.9464
256 62.8697 20.9291 3.9464
257 52.0729 45.6617 3.9464
258 55.9361 51.8971 3.9464
259 28.2160 27.2877 3.9464
260 40.4688 56.3576 3.9464
261 62.1796 60.0916 3.9464
262 63.9561 69.9443 3.9464
263 87.3495 37.1432 3.9464
264 67.0963 78.4071 3.9464
265 63.5648 58.6141 3.9464
266 52.7263 74.9715 3.9464
267 66.2734 16.5814 3.9464
268 50.5204 51.7746 3.9464
269 39.7753 66.1984 3.9464
270 53.5198 31.6109 3.9464
271 33.2761 49.6482 3.9464
272 31.9169 49.6313 3.9464
273 40.5297 53.2312 3.9464
274 38.9665 52.1661 3.9464
275 29.5312 77.7594 3.9464
276 64.2971 80.8087 3.9464
277 60.9642 55.7678 3.9464
278 43.5222 45.0811 3.9464
279 65.0247 48.4739 3.9464
280 58.5988 48.8076 3.9464
281 79.5563 49.1563 3.9464
282 32.5307 9.6036 3.9464
283 64.0451 44.9107 3.9464
284 61.5062 10.2838 3.9464
285 26.5978 58.3008 3.9464
286 17.0957 43.1770 3.9464
287 58.5251 25.3352 3.9464
Continued on next page
697
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 94.9979 34.8510 3.9464
289 85.3769 55.4160 3.9464
290 49.5023 72.1454 3.9464
291 76.0468 40.8299 3.9464
292 32.2946 34.1886 3.9464
293 53.4297 29.2302 3.9464
294 37.6153 65.2627 3.9464
295 26.5142 33.5758 3.9464
296 19.2930 43.8704 3.9464
297 46.1191 55.3112 3.9464
298 44.8988 67.7847 3.9464
299 67.6691 30.5870 3.9464
300 56.4631 20.9863 3.9464
301 47.3591 48.0710 3.9464
302 45.6168 55.3496 3.9464
303 44.4217 64.7039 3.9464
304 49.0147 34.9475 3.9464
305 47.8029 54.5327 3.9464
306 64.4826 39.6275 3.9464
307 22.4677 76.0271 3.9464
308 18.3822 65.7727 3.9464
309 30.6886 60.6373 3.9464
310 21.4066 50.2747 3.9464
311 28.2316 43.8665 3.9464
312 51.3323 47.3944 3.9464
313 39.4302 70.4283 3.9464
314 51.8225 53.8510 3.9464
315 58.9625 15.5492 3.9464
316 54.0993 51.1211 3.9464
317 68.0484 58.4864 3.9464
318 26.5492 47.5983 3.9464
319 42.1145 60.8719 3.9464
320 43.1088 48.2723 3.9464
321 37.0745 51.1465 3.9464
322 53.6353 62.5864 3.9464
323 49.0937 40.0849 3.9464
324 66.6863 83.4025 3.9464
325 56.7604 48.0907 3.9464
326 75.0516 36.4713 3.9464
327 34.2418 45.0413 3.9464
328 10.7151 57.1828 3.9464
Continued on next page
698
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 54.7913 22.7911 3.9464
330 42.8852 65.0999 3.9464
331 43.7645 63.1864 3.9464
332 36.8297 55.6905 3.9464
333 51.4644 46.2734 3.9464
334 56.4549 49.1402 3.9464
335 22.8912 56.1225 3.9464
336 52.7031 49.5684 3.9464
337 52.9024 64.8021 3.9464
338 19.4145 76.0326 3.9464
339 60.3132 36.9078 3.9464
340 85.7270 46.8848 3.9464
341 43.4796 52.4779 3.9464
342 29.2116 52.6250 3.9464
343 77.2673 35.3236 3.9464
344 20.9892 20.7572 3.9464
345 41.8965 53.7976 3.9464
346 21.0091 68.3516 3.9464
347 13.9285 83.1657 3.9464
348 50.0755 49.5260 3.9464
349 56.1453 18.9705 3.9464
350 56.1848 25.5187 3.9464
351 74.7548 56.6636 3.9464
352 50.9611 51.5263 3.9464
353 20.9956 24.2822 3.9464
354 70.2027 51.2646 3.9464
355 64.8811 21.1972 3.9464
356 48.8014 47.1117 3.9464
357 25.4986 33.4547 3.9464
358 53.3194 62.8710 3.9464
359 12.5031 65.2026 3.9464
360 43.2425 40.8624 3.9464
361 55.4605 43.2139 3.9464
362 56.2811 43.4068 3.9464
363 44.4130 51.8214 3.9464
364 51.7318 54.0640 3.9464
365 39.4736 37.6722 3.9464
366 59.0369 52.1624 3.9464
367 62.4817 64.7784 3.9464
368 33.9891 25.3104 3.9464
369 82.1660 45.3840 3.9464
Continued on next page
699
Table D.11 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 11.4589 55.4068 3.9464
371 52.7275 27.0565 3.9464
372 17.2193 51.7951 3.9464
373 31.6019 76.5275 3.9464
374 42.8060 50.9693 3.9464
375 64.6270 39.5987 3.9464
376 41.7658 57.6063 3.9464
377 8.9679 51.4227 3.9464
378 50.0329 71.6923 3.9464
379 40.7628 47.3901 3.9464
380 43.2503 8.7931 3.9464
381 54.1254 38.6935 3.9464
382 65.7892 19.5599 3.9464
383 50.3420 58.1772 3.9464
384 27.2689 42.1855 3.9464
385 74.7580 68.7651 3.9464
386 31.2464 46.9846 3.9464
387 42.3891 68.3790 3.9464
388 63.2317 61.3780 3.9464
389 65.7214 76.7065 3.9464
390 75.3204 66.3381 3.9464
391 83.9818 43.9587 3.9464
392 55.2899 75.9977 3.9464
393 36.0198 39.3899 3.9464
394 37.4906 38.7355 3.9464
395 49.4834 26.9493 3.9464
396 29.2380 80.0224 3.9464
397 55.2621 52.9866 3.9464
398 77.7363 41.2571 3.9464
399 14.2590 13.4288 3.9464
400 30.8960 84.8684 3.9464
Depot 0.0000 0.0000 N.A.
700
Table D.12: CETSP instance team5 499rdmRad
Customer index x-coordinate y-coordinate Service range
1 10.5260 3.7790 20.8200
2 8.4009 11.7989 20.8200
3 11.3126 12.1774 20.8200
4 9.2095 19.5087 20.8200
5 9.7281 5.4172 20.8200
6 11.1690 1.5527 20.8200
7 19.7672 14.9362 20.8200
8 2.2625 16.1551 20.8200
9 11.8636 12.6991 20.8200
10 13.2666 12.9678 20.8200
11 5.0355 11.9367 20.8200
12 8.6382 10.3371 20.8200
13 14.5843 15.7568 20.8200
14 3.5607 15.7968 20.8200
15 15.4200 17.0914 20.8200
16 17.8934 15.1905 20.8200
17 1.2192 5.9144 20.8200
18 15.5961 8.5134 20.8200
19 2.4773 0.0520 20.8200
20 16.5052 19.9903 20.8200
21 4.0240 17.3232 20.8200
22 13.8628 4.3052 20.8200
23 1.7290 2.5191 20.8200
24 4.8686 17.5054 20.8200
25 18.8587 8.5087 20.8200
26 9.9074 11.0867 20.8200
27 8.0267 2.1019 20.8200
28 8.6500 19.7295 20.8200
29 13.9396 19.5452 20.8200
30 4.0211 5.0495 20.8200
31 5.3173 19.9696 20.8200
32 4.1301 7.1548 20.8200
33 9.4253 3.1222 20.8200
34 18.0470 6.7045 20.8200
35 19.0819 14.2893 20.8200
36 19.3111 17.5672 20.8200
37 14.7151 17.4542 20.8200
38 16.6256 12.3206 20.8200
39 18.6523 3.9117 20.8200
40 16.2452 9.3220 20.8200
41 15.7685 10.3669 20.8200
Continued on next page
701
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 4.2430 12.8676 20.8200
43 15.4595 7.4752 20.8200
44 18.2952 1.0836 20.8200
45 2.6723 10.4123 20.8200
46 1.5116 19.0597 20.8200
47 1.2522 5.4022 20.8200
48 0.7828 19.7397 20.8200
49 14.7479 11.7757 20.8200
50 19.5822 17.4941 20.8200
51 13.7484 0.7577 20.8200
52 9.9632 1.8111 20.8200
53 13.2084 1.5682 20.8200
54 2.7850 16.9995 20.8200
55 10.3100 1.5005 20.8200
56 3.6086 13.0876 20.8200
57 15.3812 8.8682 20.8200
58 0.4211 5.2548 20.8200
59 16.1355 6.6685 20.8200
60 18.0288 10.2093 20.8200
61 5.4781 9.3534 20.8200
62 11.5459 0.8736 20.8200
63 10.6256 1.7583 20.8200
64 12.9432 8.6486 20.8200
65 12.2950 19.9912 20.8200
66 2.3396 12.8751 20.8200
67 12.5256 4.7007 20.8200
68 12.3192 17.7013 20.8200
69 2.8757 1.3778 20.8200
70 3.7626 17.1174 20.8200
71 5.2006 6.8919 20.8200
72 3.9756 4.3104 20.8200
73 2.7247 6.6491 20.8200
74 8.8668 5.4121 20.8200
75 6.6930 16.2603 20.8200
76 3.8933 3.6617 20.8200
77 2.4532 11.1564 20.8200
78 3.9473 4.1638 20.8200
79 8.0980 10.1576 20.8200
80 15.3264 12.7877 20.8200
81 17.3372 11.1211 20.8200
82 15.9493 16.7531 20.8200
Continued on next page
702
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 11.5168 3.2870 20.8200
84 5.4981 6.1028 20.8200
85 1.4037 6.1535 20.8200
86 9.0075 17.4052 20.8200
87 8.9599 2.5066 20.8200
88 5.6082 3.0104 20.8200
89 12.8565 9.4609 20.8200
90 4.7530 19.8404 20.8200
91 5.6246 7.2770 20.8200
92 14.8098 1.8409 20.8200
93 10.2894 7.4847 20.8200
94 12.6858 19.6571 20.8200
95 12.1595 5.1953 20.8200
96 2.5621 10.2967 20.8200
97 19.0824 1.0940 20.8200
98 1.2646 1.8964 20.8200
99 2.4914 14.4710 20.8200
100 45.5527 26.8832 20.8200
101 49.5874 32.9921 20.8200
102 20.8210 23.0825 20.8200
103 32.0319 48.7602 20.8200
104 31.0932 49.2942 20.8200
105 28.4876 46.0461 20.8200
106 44.3864 36.3116 20.8200
107 38.8284 23.4703 20.8200
108 25.1657 24.0751 20.8200
109 40.4113 32.0356 20.8200
110 20.1897 48.2132 20.8200
111 32.1965 21.5710 20.8200
112 43.5486 39.6053 20.8200
113 27.0476 34.4285 20.8200
114 24.2607 34.0424 20.8200
115 47.2249 31.4694 20.8200
116 24.5672 24.4137 20.8200
117 47.2998 37.9687 20.8200
118 30.1704 30.5441 20.8200
119 27.0718 22.4926 20.8200
120 32.0569 46.2162 20.8200
121 20.1974 25.6106 20.8200
122 23.8984 35.8981 20.8200
123 24.5323 49.8988 20.8200
Continued on next page
703
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 29.0027 23.8765 20.8200
125 35.1494 28.8106 20.8200
126 37.8149 25.8690 20.8200
127 22.5985 27.2784 20.8200
128 32.7117 42.3778 20.8200
129 30.9136 43.9894 20.8200
130 41.7938 26.8087 20.8200
131 23.4201 21.9457 20.8200
132 37.7223 44.0563 20.8200
133 33.6715 23.2449 20.8200
134 33.7228 34.6090 20.8200
135 44.5785 34.1629 20.8200
136 25.9644 23.2030 20.8200
137 27.7157 24.2487 20.8200
138 45.8348 38.3992 20.8200
139 44.6412 21.1681 20.8200
140 45.8095 43.1051 20.8200
141 36.3020 43.7274 20.8200
142 44.7377 48.2657 20.8200
143 20.5677 31.0115 20.8200
144 20.4824 37.2243 20.8200
145 42.0622 41.0674 20.8200
146 47.3120 20.1150 20.8200
147 36.9556 37.1182 20.8200
148 24.4655 29.9184 20.8200
149 30.3241 25.8121 20.8200
150 29.6006 20.2054 20.8200
151 23.4789 26.9268 20.8200
152 48.0614 30.3792 20.8200
153 49.2796 22.4102 20.8200
154 22.8416 32.9746 20.8200
155 47.7847 28.4345 20.8200
156 22.4944 48.7727 20.8200
157 48.8851 33.6728 20.8200
158 33.9160 28.6484 20.8200
159 48.2875 25.5427 20.8200
160 31.0534 27.3935 20.8200
161 35.5448 24.2684 20.8200
162 26.5855 26.5008 20.8200
163 43.0635 31.4686 20.8200
164 30.4469 21.4825 20.8200
Continued on next page
704
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 33.3877 38.8388 20.8200
166 20.8616 31.8567 20.8200
167 20.9805 20.9752 20.8200
168 30.5550 31.3009 20.8200
169 41.9344 32.8635 20.8200
170 32.6566 40.0511 20.8200
171 38.1953 36.0490 20.8200
172 37.4163 24.6203 20.8200
173 29.5705 36.6700 20.8200
174 23.5397 47.0618 20.8200
175 44.7486 39.7162 20.8200
176 42.5333 36.3249 20.8200
177 28.8128 30.4765 20.8200
178 25.2216 48.8368 20.8200
179 32.6554 40.5505 20.8200
180 45.8434 28.1097 20.8200
181 21.3330 28.4534 20.8200
182 23.8226 36.8408 20.8200
183 41.3150 20.0800 20.8200
184 21.8127 22.4456 20.8200
185 37.6461 42.0792 20.8200
186 47.0840 47.7144 20.8200
187 22.2385 33.2025 20.8200
188 36.1356 35.5262 20.8200
189 49.7446 26.3767 20.8200
190 35.3466 47.2689 20.8200
191 28.3920 21.3903 20.8200
192 37.9243 23.9119 20.8200
193 41.4412 38.9568 20.8200
194 26.8183 32.6012 20.8200
195 22.5313 48.1754 20.8200
196 47.3754 37.9401 20.8200
197 22.0871 33.2260 20.8200
198 23.1185 40.5549 20.8200
199 29.0396 36.1372 20.8200
200 73.1002 79.4037 20.8200
201 84.7887 79.7551 20.8200
202 81.7913 86.2239 20.8200
203 73.6863 74.2382 20.8200
204 75.4182 80.1750 20.8200
205 74.9451 88.4605 20.8200
Continued on next page
705
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 78.0272 82.0721 20.8200
207 89.7033 80.1502 20.8200
208 81.6179 74.1421 20.8200
209 74.3211 82.1244 20.8200
210 89.2994 73.1482 20.8200
211 78.4966 80.8407 20.8200
212 77.1908 76.3248 20.8200
213 70.0787 86.0551 20.8200
214 87.8356 87.4643 20.8200
215 89.6546 85.2790 20.8200
216 87.2864 89.2526 20.8200
217 76.9521 88.5890 20.8200
218 75.5773 80.7384 20.8200
219 85.3838 89.3565 20.8200
220 82.4808 71.6064 20.8200
221 70.5598 83.7819 20.8200
222 87.4850 79.3312 20.8200
223 85.2200 71.0885 20.8200
224 70.8021 79.2974 20.8200
225 72.5273 88.3137 20.8200
226 79.7775 80.2960 20.8200
227 77.3640 70.7565 20.8200
228 70.8501 86.3243 20.8200
229 79.4150 85.2350 20.8200
230 84.4928 76.9707 20.8200
231 83.5177 79.6473 20.8200
232 88.5666 89.9178 20.8200
233 85.7193 87.9646 20.8200
234 73.5126 71.3248 20.8200
235 88.3919 89.4210 20.8200
236 82.7904 89.3622 20.8200
237 85.5265 86.4226 20.8200
238 72.3356 86.1550 20.8200
239 80.7173 88.9602 20.8200
240 84.8025 72.2361 20.8200
241 78.8402 71.1237 20.8200
242 81.0772 83.8409 20.8200
243 77.9819 77.7483 20.8200
244 73.6161 81.1388 20.8200
245 89.4354 80.1567 20.8200
246 83.3441 85.5151 20.8200
Continued on next page
706
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 75.6074 70.2776 20.8200
248 77.1151 89.3423 20.8200
249 78.4301 80.0876 20.8200
250 80.2922 75.8098 20.8200
251 87.5661 81.6563 20.8200
252 79.6279 80.9538 20.8200
253 77.4087 74.0915 20.8200
254 75.9291 73.9471 20.8200
255 71.0504 85.2637 20.8200
256 76.8895 78.6378 20.8200
257 79.7296 78.3022 20.8200
258 79.3747 83.7664 20.8200
259 76.1087 74.9228 20.8200
260 79.3483 75.3688 20.8200
261 85.8335 84.6274 20.8200
262 76.3867 80.9989 20.8200
263 72.6803 81.9225 20.8200
264 76.1847 74.2911 20.8200
265 87.8874 83.7559 20.8200
266 85.5459 86.1581 20.8200
267 89.4099 75.3847 20.8200
268 77.4302 82.5606 20.8200
269 82.7718 81.5009 20.8200
270 87.3140 87.2617 20.8200
271 85.4655 89.4614 20.8200
272 82.0065 75.6791 20.8200
273 82.7574 74.2926 20.8200
274 84.1657 89.6201 20.8200
275 70.0314 77.1275 20.8200
276 83.0689 84.7397 20.8200
277 84.0326 80.9470 20.8200
278 78.9268 79.6337 20.8200
279 80.5183 71.0301 20.8200
280 71.0080 83.9726 20.8200
281 75.2812 79.5319 20.8200
282 73.5352 77.8165 20.8200
283 87.0156 79.9660 20.8200
284 73.8575 87.6690 20.8200
285 79.9937 73.4457 20.8200
286 80.0260 88.4312 20.8200
287 76.4126 75.5480 20.8200
Continued on next page
707
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 85.8774 87.3240 20.8200
289 89.0638 74.5581 20.8200
290 84.6626 79.7388 20.8200
291 71.4242 75.4202 20.8200
292 79.4655 74.4467 20.8200
293 76.7822 82.9894 20.8200
294 85.6153 86.7737 20.8200
295 86.8222 80.0693 20.8200
296 80.1131 82.5047 20.8200
297 89.3790 76.0987 20.8200
298 81.9035 87.9149 20.8200
299 88.9513 72.6403 20.8200
300 92.5909 80.0433 20.8200
301 86.7862 83.7110 20.8200
302 83.1514 91.3190 20.8200
303 87.6085 88.0524 20.8200
304 92.7639 86.5161 20.8200
305 94.6937 81.2040 20.8200
306 99.1691 80.9928 20.8200
307 94.4375 89.8165 20.8200
308 83.6163 95.4960 20.8200
309 83.3685 88.3604 20.8200
310 92.0809 99.3222 20.8200
311 95.3031 91.4204 20.8200
312 99.0472 85.7396 20.8200
313 95.4796 96.1290 20.8200
314 87.1273 84.0324 20.8200
315 81.0134 86.4250 20.8200
316 97.0785 86.7219 20.8200
317 90.2560 83.0105 20.8200
318 98.1513 96.3450 20.8200
319 86.8895 84.3247 20.8200
320 82.0258 98.9707 20.8200
321 89.0000 83.7031 20.8200
322 80.4141 88.4668 20.8200
323 88.3602 93.5594 20.8200
324 95.9324 92.1458 20.8200
325 80.5965 92.0964 20.8200
326 91.4519 94.5103 20.8200
327 94.4683 90.0421 20.8200
328 92.8113 98.2407 20.8200
Continued on next page
708
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 88.7272 81.0174 20.8200
330 89.9310 94.5372 20.8200
331 89.3359 93.6392 20.8200
332 85.1326 93.3031 20.8200
333 84.3334 97.0716 20.8200
334 83.3686 96.8014 20.8200
335 96.0605 94.4950 20.8200
336 93.3103 99.0843 20.8200
337 99.7949 88.8243 20.8200
338 84.0572 98.2927 20.8200
339 86.9940 98.1050 20.8200
340 91.1620 99.9650 20.8200
341 88.1669 82.2879 20.8200
342 85.9222 83.4369 20.8200
343 90.7381 99.8897 20.8200
344 89.9830 98.6224 20.8200
345 94.5090 92.4532 20.8200
346 83.9295 97.9734 20.8200
347 84.3608 92.1480 20.8200
348 87.8518 83.2273 20.8200
349 99.2920 98.0492 20.8200
350 96.6710 90.7145 20.8200
351 87.7484 83.7546 20.8200
352 86.0867 81.5330 20.8200
353 82.5335 87.3296 20.8200
354 80.7551 80.6861 20.8200
355 96.5452 93.1720 20.8200
356 88.3323 91.5035 20.8200
357 89.0976 96.4455 20.8200
358 82.1226 91.9552 20.8200
359 88.1760 88.8141 20.8200
360 89.6970 88.1654 20.8200
361 89.5983 91.5249 20.8200
362 80.3025 81.1115 20.8200
363 92.0930 98.3621 20.8200
364 97.9735 93.9042 20.8200
365 94.7529 81.9671 20.8200
366 84.7929 84.8117 20.8200
367 87.3294 86.7915 20.8200
368 81.9044 86.7930 20.8200
369 83.1803 86.2205 20.8200
Continued on next page
709
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 89.9071 81.4441 20.8200
371 90.3741 83.7882 20.8200
372 84.4799 87.8799 20.8200
373 93.0738 84.8753 20.8200
374 96.6476 96.9796 20.8200
375 90.1019 83.4860 20.8200
376 90.6972 96.9626 20.8200
377 96.6676 92.6743 20.8200
378 88.0059 90.7740 20.8200
379 94.2258 98.7848 20.8200
380 97.4362 85.8361 20.8200
381 81.2522 99.2612 20.8200
382 92.1839 88.8237 20.8200
383 94.7976 88.4491 20.8200
384 93.4254 97.8126 20.8200
385 80.2014 81.5949 20.8200
386 97.0965 81.0307 20.8200
387 88.2817 96.3510 20.8200
388 98.6006 82.3388 20.8200
389 99.7041 87.1751 20.8200
390 84.2824 83.9445 20.8200
391 96.8090 92.5136 20.8200
392 93.2550 98.1789 20.8200
393 96.8293 85.3988 20.8200
394 84.7850 93.3953 20.8200
395 84.5701 92.5098 20.8200
396 96.1791 97.5552 20.8200
397 86.6750 81.8002 20.8200
398 94.8083 91.5304 20.8200
399 85.8291 89.3215 20.8200
400 1.5647 88.8122 20.8200
401 1.8225 87.7760 20.8200
402 16.0720 81.5553 20.8200
403 19.5543 89.8549 20.8200
404 2.0599 86.0050 20.8200
405 9.9966 85.8576 20.8200
406 13.6279 83.3943 20.8200
407 13.8296 81.5783 20.8200
408 0.7751 88.6342 20.8200
409 4.4842 86.5445 20.8200
410 13.6170 84.1913 20.8200
Continued on next page
710
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
411 16.4864 81.6235 20.8200
412 17.8246 84.0918 20.8200
413 11.8372 87.4011 20.8200
414 1.1933 81.8445 20.8200
415 16.2773 81.3093 20.8200
416 6.7503 86.8120 20.8200
417 1.9830 86.3665 20.8200
418 5.0910 83.7862 20.8200
419 2.6250 81.2761 20.8200
420 19.4915 88.9148 20.8200
421 15.9151 82.9337 20.8200
422 2.6960 85.7661 20.8200
423 0.0290 82.9455 20.8200
424 17.8311 84.5721 20.8200
425 17.0206 82.7787 20.8200
426 14.2245 83.0966 20.8200
427 0.2473 82.0871 20.8200
428 11.6247 87.7046 20.8200
429 5.1015 81.8103 20.8200
430 10.6041 85.0219 20.8200
431 8.8756 85.3213 20.8200
432 15.4215 81.5375 20.8200
433 9.5220 88.7288 20.8200
434 18.7876 82.3448 20.8200
435 13.2856 89.4879 20.8200
436 19.7188 83.0222 20.8200
437 14.2132 82.4414 20.8200
438 7.6764 88.6806 20.8200
439 17.1642 87.7833 20.8200
440 17.0519 88.8308 20.8200
441 12.6448 83.0865 20.8200
442 6.0677 84.3942 20.8200
443 3.3964 83.4982 20.8200
444 16.8870 83.4344 20.8200
445 9.2565 85.6186 20.8200
446 5.1953 87.1361 20.8200
447 2.5389 82.9669 20.8200
448 5.3870 87.7604 20.8200
449 7.4797 86.7529 20.8200
450 94.4757 9.4701 20.8200
451 29.7505 96.6210 20.8200
Continued on next page
711
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
452 17.7167 97.5636 20.8200
453 1.0919 90.7016 20.8200
454 25.0595 61.5431 20.8200
455 97.0848 81.6578 20.8200
456 78.1743 38.6355 20.8200
457 22.1476 14.8515 20.8200
458 28.6149 8.2266 20.8200
459 73.6361 68.0431 20.8200
460 84.5964 57.5663 20.8200
461 73.1545 60.0435 20.8200
462 84.9979 3.9891 20.8200
463 27.0169 46.6583 20.8200
464 26.3736 85.6358 20.8200
465 91.1956 46.5873 20.8200
466 59.4827 70.1321 20.8200
467 28.4031 32.2444 20.8200
468 52.9148 12.3625 20.8200
469 97.6128 23.6668 20.8200
470 7.7403 89.8119 20.8200
471 39.3354 89.6580 20.8200
472 92.0943 24.6880 20.8200
473 93.0930 71.3467 20.8200
474 30.7692 16.7931 20.8200
475 64.9540 37.3090 20.8200
476 47.0351 69.5204 20.8200
477 84.8772 45.0654 20.8200
478 4.1027 5.9391 20.8200
479 44.1821 62.8241 20.8200
480 73.9225 9.6395 20.8200
481 44.9743 74.4953 20.8200
482 43.1416 9.2079 20.8200
483 25.8602 58.6207 20.8200
484 72.5026 72.4828 20.8200
485 49.5234 55.0957 20.8200
486 54.1532 48.4548 20.8200
487 99.2739 52.0431 20.8200
488 57.0413 9.9678 20.8200
489 92.9329 22.8145 20.8200
490 84.7658 77.8153 20.8200
491 63.7544 71.2264 20.8200
492 19.3715 86.9483 20.8200
Continued on next page
712
Table D.12 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
493 80.2520 96.9762 20.8200
494 88.2673 94.5543 20.8200
495 27.2789 43.4795 20.8200
496 77.6803 63.0066 20.8200
497 23.9463 67.9458 20.8200
498 49.2766 27.3707 20.8200
499 10.8331 85.8288 20.8200
Depot 70.0000 40.0000 N.A.
713
Table D.13: CETSP instance team6 500rdmRad
Customer index x-coordinate y-coordinate Service range
1 9.8270 6.8843 6.8651
2 2.4254 44.8523 6.8651
3 53.0251 68.7919 6.8651
4 0.2763 64.7360 6.8651
5 4.9443 50.7874 6.8651
6 20.5127 86.7994 6.8651
7 58.4293 38.9397 6.8651
8 53.3341 54.2742 6.8651
9 57.0337 24.3926 6.8651
10 41.2500 12.6932 6.8651
11 30.2787 8.2280 6.8651
12 46.3730 74.0499 6.8651
13 21.4284 90.1196 6.8651
14 55.0654 81.2340 6.8651
15 25.6409 32.9850 6.8651
16 47.9098 77.7960 6.8651
17 37.4598 44.2188 6.8651
18 23.2467 53.1537 6.8651
19 3.9184 46.6239 6.8651
20 56.0822 62.8731 6.8651
21 57.4377 71.1536 6.8651
22 15.5277 59.9412 6.8651
23 26.8042 95.3391 6.8651
24 7.3492 35.5012 6.8651
25 3.4981 86.0326 6.8651
26 79.8029 56.0883 6.8651
27 72.2470 39.7077 6.8651
28 9.2264 90.0125 6.8651
29 9.4077 50.7341 6.8651
30 2.4096 76.5677 6.8651
31 29.6717 65.8678 6.8651
32 16.1988 59.3188 6.8651
33 1.4411 27.5670 6.8651
34 43.8196 68.1614 6.8651
35 72.0758 18.0334 6.8651
36 20.1950 67.6818 6.8651
37 40.5650 30.2351 6.8651
38 64.1034 11.1965 6.8651
39 46.8229 71.8444 6.8651
40 74.2228 38.6100 6.8651
41 75.8802 29.7113 6.8651
Continued on next page
714
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 2.7334 77.6754 6.8651
43 37.6481 47.8813 6.8651
44 50.8239 67.1806 6.8651
45 74.4568 73.8914 6.8651
46 38.4714 30.1542 6.8651
47 16.5565 18.5576 6.8651
48 75.0689 72.4744 6.8651
49 48.3602 34.0465 6.8651
50 33.7089 9.9712 6.8651
51 46.0567 72.0198 6.8651
52 45.8973 89.1189 6.8651
53 33.8270 93.4853 6.8651
54 36.9546 32.1019 6.8651
55 51.6263 32.9510 6.8651
56 77.3467 92.4222 6.8651
57 51.5218 39.5765 6.8651
58 4.5207 34.7763 6.8651
59 31.6461 7.3586 6.8651
60 54.2236 56.2655 6.8651
61 55.5353 38.1752 6.8651
62 23.3331 67.4298 6.8651
63 23.1077 77.6166 6.8651
64 76.8304 30.6899 6.8651
65 34.6178 91.6565 6.8651
66 77.1266 88.6843 6.8651
67 23.2602 19.1726 6.8651
68 69.2934 49.5143 6.8651
69 39.4220 48.1564 6.8651
70 70.9135 14.8762 6.8651
71 57.0800 64.0173 6.8651
72 28.9098 26.1469 6.8651
73 75.0360 91.1497 6.8651
74 38.2308 97.9754 6.8651
75 77.6410 49.4044 6.8651
76 6.8207 39.0714 6.8651
77 15.6672 41.9038 6.8651
78 48.6879 60.2173 6.8651
79 61.4066 99.6333 6.8651
80 64.1367 44.5156 6.8651
81 63.6802 81.8267 6.8651
82 44.2724 24.1530 6.8651
Continued on next page
715
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 57.9600 34.4090 6.8651
84 78.4066 56.8223 6.8651
85 63.7722 68.1837 6.8651
86 1.1893 3.3623 6.8651
87 70.2766 21.7580 6.8651
88 71.3344 25.5496 6.8651
89 31.6419 23.7354 6.8651
90 41.5242 2.2495 6.8651
91 11.0263 80.6461 6.8651
92 33.1471 60.1559 6.8651
93 50.7479 74.0551 6.8651
94 36.1244 41.0243 6.8651
95 14.9649 8.2570 6.8651
96 39.6569 80.0064 6.8651
97 70.4834 96.1071 6.8651
98 62.5782 94.8346 6.8651
99 2.7731 90.8552 6.8651
100 4.0095 79.3775 6.8651
101 10.0346 20.0551 6.8651
102 24.2845 53.5119 6.8651
103 13.6478 21.6503 6.8651
104 5.6520 82.6769 6.8651
105 58.3586 20.3359 6.8651
106 4.4183 14.4468 6.8651
107 13.5199 39.2703 6.8651
108 9.1420 20.9819 6.8651
109 0.9336 72.1660 6.8651
110 2.2886 93.0946 6.8651
111 78.3682 28.4149 6.8651
112 5.9393 95.2324 6.8651
113 70.7490 60.5658 6.8651
114 11.1949 32.5348 6.8651
115 22.9057 97.6297 6.8651
116 44.6442 33.1240 6.8651
117 6.1458 57.4553 6.8651
118 20.6501 50.1791 6.8651
119 40.3911 90.9327 6.8651
120 68.9038 16.8105 6.8651
121 57.8812 36.8910 6.8651
122 78.4107 73.5258 6.8651
123 39.0652 2.4238 6.8651
Continued on next page
716
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 64.3381 93.7227 6.8651
125 62.3574 96.1600 6.8651
126 38.9702 21.3779 6.8651
127 38.9618 51.3998 6.8651
128 73.6484 37.1698 6.8651
129 45.1706 33.2151 6.8651
130 49.7031 90.8228 6.8651
131 39.7157 22.5518 6.8651
132 43.0003 59.9693 6.8651
133 32.0337 81.0046 6.8651
134 55.2537 1.3429 6.8651
135 40.9380 91.8871 6.8651
136 25.1363 82.5967 6.8651
137 44.7688 34.8472 6.8651
138 76.9821 94.8107 6.8651
139 79.9522 98.0359 6.8651
140 57.8284 65.6998 6.8651
141 20.1050 16.8211 6.8651
142 17.0586 58.0717 6.8651
143 38.9768 28.6596 6.8651
144 30.5118 74.0434 6.8651
145 2.1730 46.8604 6.8651
146 56.9850 36.3051 6.8651
147 39.5709 52.0192 6.8651
148 64.9777 99.8573 6.8651
149 52.3761 17.3067 6.8651
150 64.0122 92.7907 6.8651
151 73.9903 3.2091 6.8651
152 45.3946 79.9114 6.8651
153 7.7653 6.1676 6.8651
154 47.2237 11.5266 6.8651
155 56.5515 98.5201 6.8651
156 62.0390 27.7697 6.8651
157 64.4755 95.6952 6.8651
158 13.0553 35.1491 6.8651
159 26.7897 74.3958 6.8651
160 65.8846 36.2104 6.8651
161 17.9199 62.5969 6.8651
162 31.9711 13.1659 6.8651
163 69.6306 57.4600 6.8651
164 6.0949 74.0865 6.8651
Continued on next page
717
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 4.9451 53.7480 6.8651
166 45.3796 10.2394 6.8651
167 11.2137 2.0282 6.8651
168 58.9987 45.7674 6.8651
169 66.3729 97.9005 6.8651
170 3.7969 1.0311 6.8651
171 72.4289 91.8837 6.8651
172 3.9505 53.4738 6.8651
173 33.7700 15.2532 6.8651
174 65.5339 33.2996 6.8651
175 79.9571 14.1068 6.8651
176 62.1997 26.9323 6.8651
177 51.8847 57.7017 6.8651
178 12.2845 12.8434 6.8651
179 64.4880 60.4855 6.8651
180 68.3856 35.3493 6.8651
181 25.7941 5.0229 6.8651
182 78.2121 82.5216 6.8651
183 9.6122 63.4754 6.8651
184 10.2957 4.6843 6.8651
185 33.6743 16.0148 6.8651
186 61.6782 59.4733 6.8651
187 15.8202 13.1438 6.8651
188 0.0138 97.6201 6.8651
189 2.2794 46.9159 6.8651
190 16.0956 47.1990 6.8651
191 31.0050 87.5127 6.8651
192 65.7365 88.9695 6.8651
193 67.7946 81.6778 6.8651
194 33.8398 32.0377 6.8651
195 6.7702 28.6398 6.8651
196 51.7497 79.9145 6.8651
197 29.1113 69.2428 6.8651
198 8.4509 92.4898 6.8651
199 24.4888 25.3300 6.8651
200 68.5238 98.3882 6.8651
201 15.7168 72.1076 6.8651
202 3.2029 51.0422 6.8651
203 67.4655 12.1137 6.8651
204 41.3355 82.7797 6.8651
205 63.3054 48.8331 6.8651
Continued on next page
718
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 17.2034 24.1028 6.8651
207 9.5622 88.5032 6.8651
208 22.4747 48.1041 6.8651
209 16.9544 52.9271 6.8651
210 20.3908 60.0437 6.8651
211 45.4130 71.2677 6.8651
212 53.5581 47.7414 6.8651
213 37.7594 72.4638 6.8651
214 67.7687 50.9424 6.8651
215 2.2118 78.3384 6.8651
216 37.6570 81.9317 6.8651
217 5.3361 49.6057 6.8651
218 72.3203 3.8463 6.8651
219 27.0999 87.1794 6.8651
220 73.9542 35.1681 6.8651
221 58.1838 68.9986 6.8651
222 23.0786 38.1228 6.8651
223 20.3278 46.5707 6.8651
224 61.0867 94.7583 6.8651
225 51.3584 31.1839 6.8651
226 45.3765 76.9955 6.8651
227 25.3534 42.3963 6.8651
228 70.8086 11.5810 6.8651
229 32.3710 53.6854 6.8651
230 70.2908 10.4186 6.8651
231 71.2869 13.7572 6.8651
232 51.2079 35.5792 6.8651
233 12.7058 46.3942 6.8651
234 72.4567 79.8069 6.8651
235 77.5185 26.3493 6.8651
236 37.1302 34.1671 6.8651
237 20.4275 84.2678 6.8651
238 75.4923 99.8090 6.8651
239 68.4103 6.9404 6.8651
240 2.3000 55.3764 6.8651
241 30.6527 22.7083 6.8651
242 13.1892 88.2939 6.8651
243 72.9487 9.0752 6.8651
244 0.7950 63.4583 6.8651
245 3.1063 26.7804 6.8651
246 21.2206 30.6756 6.8651
Continued on next page
719
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 43.3710 79.9296 6.8651
248 59.1397 81.6064 6.8651
249 60.5483 13.7851 6.8651
250 40.8800 90.9920 6.8651
251 38.0621 81.3957 6.8651
252 74.3686 61.1798 6.8651
253 3.2443 74.1559 6.8651
254 79.1559 54.6404 6.8651
255 2.8109 93.7321 6.8651
256 49.4510 19.2329 6.8651
257 45.0927 13.5451 6.8651
258 34.7674 23.4201 6.8651
259 5.5712 90.2338 6.8651
260 53.1447 48.4278 6.8651
261 2.4228 13.8762 6.8651
262 14.6393 26.7492 6.8651
263 66.5762 96.7049 6.8651
264 41.3951 34.6025 6.8651
265 65.5436 56.9924 6.8651
266 54.8329 43.6672 6.8651
267 19.7736 66.4248 6.8651
268 13.4476 91.4294 6.8651
269 55.1301 40.0588 6.8651
270 69.1127 61.5738 6.8651
271 24.4057 14.8195 6.8651
272 66.8428 74.9419 6.8651
273 16.5956 19.4929 6.8651
274 54.1004 16.0525 6.8651
275 6.9414 77.9429 6.8651
276 16.6662 74.8364 6.8651
277 43.0965 49.2871 6.8651
278 31.5096 51.0685 6.8651
279 75.4040 79.0607 6.8651
280 6.5131 96.1439 6.8651
281 49.7681 46.8278 6.8651
282 27.9226 21.7643 6.8651
283 48.2550 40.2376 6.8651
284 71.8743 17.8343 6.8651
285 28.2512 43.1797 6.8651
286 44.8729 51.9811 6.8651
287 47.6524 52.2250 6.8651
Continued on next page
720
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 78.2443 33.2915 6.8651
289 63.2522 99.6147 6.8651
290 73.6394 37.6931 6.8651
291 2.2068 85.9728 6.8651
292 15.1928 63.8864 6.8651
293 49.3213 48.3120 6.8651
294 54.9749 31.6899 6.8651
295 14.7546 14.6103 6.8651
296 66.7265 28.6242 6.8651
297 4.0390 87.3303 6.8651
298 4.8022 64.3438 6.8651
299 37.4895 92.2139 6.8651
300 6.4322 5.6038 6.8651
301 18.0420 31.0088 6.8651
302 2.5747 43.4684 6.8651
303 48.3895 84.8379 6.8651
304 34.2378 1.7695 6.8651
305 63.7966 99.8650 6.8651
306 30.1525 91.7060 6.8651
307 19.6070 87.5156 6.8651
308 20.7475 95.7593 6.8651
309 18.5593 70.8498 6.8651
310 68.0410 93.0677 6.8651
311 26.1535 60.2417 6.8651
312 28.9981 9.3107 6.8651
313 42.9598 72.0705 6.8651
314 44.2907 51.8898 6.8651
315 19.9583 6.5164 6.8651
316 16.4820 98.2716 6.8651
317 77.1619 52.0527 6.8651
318 66.0988 58.3516 6.8651
319 68.5427 70.6500 6.8651
320 8.7489 58.9073 6.8651
321 43.6827 74.1879 6.8651
322 56.9482 35.7189 6.8651
323 17.6447 95.7025 6.8651
324 67.3901 74.1747 6.8651
325 6.2197 67.2192 6.8651
326 20.4304 56.6156 6.8651
327 36.6689 15.3803 6.8651
328 55.3537 50.0230 6.8651
Continued on next page
721
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 26.2176 40.5221 6.8651
330 54.3750 73.4717 6.8651
331 46.3459 54.8709 6.8651
332 40.9923 81.1407 6.8651
333 50.0180 68.4527 6.8651
334 13.6467 56.6412 6.8651
335 78.8734 30.5074 6.8651
336 31.5116 30.4350 6.8651
337 23.9069 59.9122 6.8651
338 42.5831 37.1399 6.8651
339 25.3621 2.9418 6.8651
340 1.9078 84.1439 6.8651
341 28.8395 85.6979 6.8651
342 42.0439 1.2746 6.8651
343 38.5585 8.9239 6.8651
344 22.4809 75.2844 6.8651
345 57.9146 37.4787 6.8651
346 21.5800 71.4487 6.8651
347 14.3875 98.8261 6.8651
348 7.2094 55.9097 6.8651
349 72.8918 2.6850 6.8651
350 46.2315 17.3070 6.8651
351 15.2276 8.2482 6.8651
352 9.4518 0.0818 6.8651
353 57.1362 5.5136 6.8651
354 64.9436 1.6864 6.8651
355 61.0701 98.8684 6.8651
356 65.5247 34.4820 6.8651
357 11.5513 26.7284 6.8651
358 21.6218 70.9165 6.8651
359 57.7425 53.0432 6.8651
360 67.1669 49.4372 6.8651
361 38.1284 50.9907 6.8651
362 17.3929 9.8303 6.8651
363 7.5281 85.6801 6.8651
364 41.0252 15.6289 6.8651
365 39.7052 20.7341 6.8651
366 23.9937 92.6752 6.8651
367 21.5005 1.4444 6.8651
368 14.7300 38.6202 6.8651
369 9.8143 65.8912 6.8651
Continued on next page
722
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 23.2410 69.6046 6.8651
371 4.2645 75.4569 6.8651
372 9.7861 28.4045 6.8651
373 33.6894 8.5224 6.8651
374 21.4467 69.0185 6.8651
375 21.0217 51.8703 6.8651
376 15.3635 8.9465 6.8651
377 34.4982 43.6098 6.8651
378 77.8566 47.3210 6.8651
379 19.7990 26.8560 6.8651
380 11.9840 90.8471 6.8651
381 10.2639 16.7344 6.8651
382 75.6464 86.4518 6.8651
383 18.1201 57.6123 6.8651
384 45.5119 65.9533 6.8651
385 52.4413 6.2568 6.8651
386 56.7398 71.0931 6.8651
387 59.7400 37.5402 6.8651
388 62.9728 48.2611 6.8651
389 54.6678 5.1971 6.8651
390 67.3269 96.0070 6.8651
391 34.0987 23.3047 6.8651
392 67.0620 97.8078 6.8651
393 13.9199 46.2671 6.8651
394 77.5651 71.0149 6.8651
395 1.2957 73.7881 6.8651
396 37.7929 6.0601 6.8651
397 21.5695 0.9568 6.8651
398 6.1363 48.8675 6.8651
399 43.6411 3.9331 6.8651
400 40.4353 45.1451 6.8651
401 32.8303 42.2310 6.8651
402 24.3319 37.4284 6.8651
403 76.1613 37.0440 6.8651
404 44.3711 67.9206 6.8651
405 2.9296 91.7762 6.8651
406 61.0630 98.6998 6.8651
407 77.2293 82.6694 6.8651
408 73.3690 50.7129 6.8651
409 32.3079 45.1141 6.8651
410 1.8948 99.1556 6.8651
Continued on next page
723
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
411 73.7932 65.1929 6.8651
412 6.5220 46.8393 6.8651
413 0.6046 98.8714 6.8651
414 32.5069 76.0168 6.8651
415 65.8501 46.5185 6.8651
416 30.8820 13.4627 6.8651
417 50.0447 86.3511 6.8651
418 30.0938 44.3309 6.8651
419 12.1928 37.3703 6.8651
420 5.3401 99.7769 6.8651
421 26.3324 9.9110 6.8651
422 67.7861 18.0441 6.8651
423 60.7744 89.6482 6.8651
424 18.0605 3.6101 6.8651
425 21.8833 32.2702 6.8651
426 49.4828 84.8462 6.8651
427 34.4830 80.3653 6.8651
428 32.7632 61.4479 6.8651
429 25.8247 62.4300 6.8651
430 19.6994 87.7216 6.8651
431 57.0033 47.9295 6.8651
432 28.0185 49.9258 6.8651
433 63.3831 45.6708 6.8651
434 75.1791 28.4357 6.8651
435 56.1389 85.5616 6.8651
436 64.4544 70.2655 6.8651
437 62.4720 86.6470 6.8651
438 61.3812 10.1841 6.8651
439 35.4564 78.9241 6.8651
440 9.4154 53.1681 6.8651
441 75.4423 46.5496 6.8651
442 63.9530 87.4245 6.8651
443 33.5301 3.5427 6.8651
444 61.1690 94.8861 6.8651
445 10.8813 21.2221 6.8651
446 8.8712 13.2955 6.8651
447 11.8542 36.7134 6.8651
448 70.5957 27.6007 6.8651
449 28.3265 80.6515 6.8651
450 75.2340 1.1053 6.8651
451 49.7784 78.4397 6.8651
Continued on next page
724
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
452 47.2434 72.8349 6.8651
453 73.2291 73.9763 6.8651
454 1.0904 26.3845 6.8651
455 13.5790 86.3111 6.8651
456 1.1696 7.0254 6.8651
457 15.0420 3.4633 6.8651
458 35.1926 70.9963 6.8651
459 44.6810 94.9895 6.8651
460 73.2927 7.8306 6.8651
461 71.5875 94.5400 6.8651
462 71.4910 88.8238 6.8651
463 4.4920 30.1971 6.8651
464 67.7344 45.7338 6.8651
465 35.0134 33.6653 6.8651
466 56.2067 40.2418 6.8651
467 67.6345 29.9025 6.8651
468 12.9149 73.6814 6.8651
469 25.8175 47.2716 6.8651
470 19.3271 51.9549 6.8651
471 14.8230 72.6203 6.8651
472 6.6502 63.3599 6.8651
473 69.7655 86.0200 6.8651
474 74.8496 95.8479 6.8651
475 18.6254 45.1800 6.8651
476 1.3892 56.8496 6.8651
477 18.4742 58.4012 6.8651
478 35.4890 25.3753 6.8651
479 37.3850 18.6566 6.8651
480 45.6990 60.3070 6.8651
481 22.9209 53.7234 6.8651
482 61.6425 72.8564 6.8651
483 25.4341 30.3643 6.8651
484 56.0728 23.8687 6.8651
485 61.8021 40.7858 6.8651
486 52.8784 80.2957 6.8651
487 61.0936 52.6920 6.8651
488 39.2148 31.0796 6.8651
489 64.6627 65.3996 6.8651
490 37.4152 67.1119 6.8651
491 56.5346 68.6367 6.8651
492 69.6772 28.9704 6.8651
Continued on next page
725
Table D.13 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
493 29.8399 3.7319 6.8651
494 25.8820 79.9487 6.8651
495 62.1748 23.5386 6.8651
496 6.6484 67.6725 6.8651
497 58.3317 48.8465 6.8651
498 62.6983 97.3779 6.8651
499 18.3784 57.1027 6.8651
500 34.2887 41.9043 6.8651
Depot 95.0000 50.0000 N.A.
726
Table D.14: CETSP instance bonus1000rdmRad
Customer index x-coordinate y-coordinate Service range
1 8.8424 89.8918 9.2489
2 32.7799 83.2523 9.2489
3 10.3686 64.9958 9.2489
4 3.4302 27.3978 9.2489
5 45.3407 99.2752 9.2489
6 59.1160 27.8960 9.2489
7 35.1725 39.3614 9.2489
8 20.1985 8.6278 9.2489
9 56.7681 74.9360 9.2489
10 12.6505 38.2099 9.2489
11 27.0631 42.6427 9.2489
12 55.9910 83.6015 9.2489
13 17.2588 95.6994 9.2489
14 3.9727 68.4310 9.2489
15 18.1027 98.2919 9.2489
16 27.4650 78.5652 9.2489
17 16.8508 91.4539 9.2489
18 63.6804 79.2999 9.2489
19 50.3298 35.4364 9.2489
20 28.6920 99.3457 9.2489
21 33.8581 68.2147 9.2489
22 36.8668 93.0634 9.2489
23 53.6999 99.8116 9.2489
24 66.1742 21.1575 9.2489
25 94.7589 85.8354 9.2489
26 39.0793 20.5735 9.2489
27 55.9549 32.8020 9.2489
28 27.3246 98.0804 9.2489
29 74.5573 43.4874 9.2489
30 36.6564 59.2725 9.2489
31 10.0815 81.4641 9.2489
32 19.7751 38.5893 9.2489
33 86.5066 33.3392 9.2489
34 22.8444 60.0141 9.2489
35 56.7361 58.8782 9.2489
36 25.5882 94.6226 9.2489
37 24.7778 44.0408 9.2489
38 30.3319 43.7550 9.2489
39 3.2126 94.5139 9.2489
40 53.8745 88.1645 9.2489
41 25.4736 81.9426 9.2489
Continued on next page
727
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
42 64.9653 93.9823 9.2489
43 59.2804 42.0297 9.2489
44 23.1086 93.4653 9.2489
45 63.7656 37.4523 9.2489
46 6.3025 40.0086 9.2489
47 5.2830 51.8958 9.2489
48 12.6386 82.4267 9.2489
49 35.4087 49.3338 9.2489
50 20.7513 88.7330 9.2489
51 67.6930 75.2440 9.2489
52 66.6720 95.9202 9.2489
53 39.8494 96.2279 9.2489
54 38.8733 61.9742 9.2489
55 55.0732 28.8544 9.2489
56 38.0529 66.4334 9.2489
57 7.3422 50.3657 9.2489
58 20.4748 85.6818 9.2489
59 25.6525 56.5792 9.2489
60 29.7776 79.3797 9.2489
61 2.1978 16.1644 9.2489
62 51.9854 93.0331 9.2489
63 51.6551 43.8565 9.2489
64 28.8226 20.3671 9.2489
65 19.6423 34.9921 9.2489
66 51.3358 40.3066 9.2489
67 65.5557 66.5833 9.2489
68 65.3379 63.7280 9.2489
69 48.3583 45.6967 9.2489
70 64.6614 51.5825 9.2489
71 70.6175 78.6546 9.2489
72 36.3196 94.1542 9.2489
73 29.0317 90.5330 9.2489
74 3.8151 26.6511 9.2489
75 1.8378 81.0681 9.2489
76 26.4999 86.4966 9.2489
77 2.7664 66.0955 9.2489
78 19.4021 41.6602 9.2489
79 24.6849 59.8520 9.2489
80 39.7518 71.5148 9.2489
81 15.7783 66.1941 9.2489
82 44.6693 80.7972 9.2489
Continued on next page
728
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
83 70.8337 78.2109 9.2489
84 54.1510 63.8943 9.2489
85 56.3608 54.4387 9.2489
86 1.3542 31.3159 9.2489
87 11.0047 35.1418 9.2489
88 17.2016 81.6953 9.2489
89 32.8349 54.5053 9.2489
90 0.8488 80.8042 9.2489
91 51.1775 73.3951 9.2489
92 32.8781 90.1018 9.2489
93 15.0640 86.4956 9.2489
94 52.2458 74.9856 9.2489
95 11.2816 86.8372 9.2489
96 30.5161 92.2095 9.2489
97 11.7365 68.8238 9.2489
98 94.1781 30.5898 9.2489
99 22.6819 72.9081 9.2489
100 8.0785 52.1247 9.2489
101 48.0135 55.6763 9.2489
102 68.5202 55.6901 9.2489
103 63.2492 4.0157 9.2489
104 36.9912 62.0965 9.2489
105 47.3158 98.1370 9.2489
106 4.4401 94.8769 9.2489
107 91.1933 55.0935 9.2489
108 6.3593 87.0647 9.2489
109 53.6024 70.8029 9.2489
110 72.8429 65.6705 9.2489
111 35.8599 20.9040 9.2489
112 55.7200 71.9192 9.2489
113 16.8097 72.8482 9.2489
114 14.0606 63.9325 9.2489
115 17.2263 94.0864 9.2489
116 0.0736 50.2029 9.2489
117 63.5921 50.3481 9.2489
118 56.3040 89.7292 9.2489
119 11.5453 68.9331 9.2489
120 30.1834 92.1548 9.2489
121 22.3390 31.6024 9.2489
122 0.1023 55.0565 9.2489
123 9.7553 43.1833 9.2489
Continued on next page
729
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
124 31.3418 77.8679 9.2489
125 18.6946 36.2655 9.2489
126 49.5565 80.8162 9.2489
127 40.3266 53.6266 9.2489
128 1.7756 46.3840 9.2489
129 40.1668 89.0974 9.2489
130 16.7366 65.2661 9.2489
131 11.7116 63.2315 9.2489
132 19.9269 66.4829 9.2489
133 8.0266 29.1706 9.2489
134 43.5910 70.7565 9.2489
135 78.1811 99.7924 9.2489
136 85.7141 51.6725 9.2489
137 31.7830 62.7455 9.2489
138 10.3544 93.6186 9.2489
139 36.4950 99.8776 9.2489
140 51.9156 83.2415 9.2489
141 31.9235 85.9644 9.2489
142 20.7225 50.2905 9.2489
143 66.6570 47.7723 9.2489
144 42.5877 73.9463 9.2489
145 67.8999 88.1232 9.2489
146 36.2672 91.8152 9.2489
147 33.4598 51.4764 9.2489
148 17.9309 43.3009 9.2489
149 69.3830 98.1867 9.2489
150 30.4651 92.1055 9.2489
151 30.4145 39.5532 9.2489
152 72.7038 66.7065 9.2489
153 5.7931 87.7203 9.2489
154 10.7162 46.6229 9.2489
155 43.1138 45.0009 9.2489
156 76.6865 13.8696 9.2489
157 47.9675 95.1452 9.2489
158 1.2508 48.7403 9.2489
159 71.1705 92.9623 9.2489
160 77.1133 85.3156 9.2489
161 36.7712 29.7051 9.2489
162 52.5936 61.8708 9.2489
163 13.3420 71.1511 9.2489
164 39.8369 68.0599 9.2489
Continued on next page
730
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
165 50.2067 26.4023 9.2489
166 45.0121 95.4797 9.2489
167 3.2007 54.9040 9.2489
168 28.3496 82.6684 9.2489
169 18.4668 77.2930 9.2489
170 4.3777 84.9846 9.2489
171 90.5069 55.4383 9.2489
172 90.8182 18.2159 9.2489
173 39.1205 68.7577 9.2489
174 36.9079 88.7829 9.2489
175 63.4832 69.3620 9.2489
176 16.4753 49.4456 9.2489
177 38.1894 65.5461 9.2489
178 65.5150 11.6864 9.2489
179 62.0368 91.4278 9.2489
180 3.3803 80.9989 9.2489
181 51.4966 83.1106 9.2489
182 39.6715 49.4413 9.2489
183 39.4705 98.0104 9.2489
184 14.8123 50.2913 9.2489
185 20.0396 90.8383 9.2489
186 18.1581 79.4001 9.2489
187 61.0960 95.3880 9.2489
188 52.5789 54.1620 9.2489
189 0.8673 18.0482 9.2489
190 55.1648 55.4235 9.2489
191 36.1781 80.1310 9.2489
192 65.9828 56.0226 9.2489
193 37.5175 33.0911 9.2489
194 12.0030 63.9467 9.2489
195 45.1387 81.8637 9.2489
196 42.2598 46.8683 9.2489
197 77.7745 46.7226 9.2489
198 13.1791 60.0536 9.2489
199 48.2062 39.2479 9.2489
200 84.1408 54.4625 9.2489
201 7.1782 91.7684 9.2489
202 8.3764 96.8380 9.2489
203 76.0424 64.4500 9.2489
204 57.5342 91.7322 9.2489
205 5.7248 81.8072 9.2489
Continued on next page
731
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
206 86.7540 75.2393 9.2489
207 23.0673 35.0376 9.2489
208 42.5322 92.9240 9.2489
209 0.1552 73.1144 9.2489
210 56.8490 69.2710 9.2489
211 48.8881 29.6929 9.2489
212 41.8469 52.1516 9.2489
213 12.6368 12.9194 9.2489
214 8.0139 41.4146 9.2489
215 0.8464 97.1558 9.2489
216 3.6845 54.7535 9.2489
217 40.5842 81.5496 9.2489
218 50.3737 63.5418 9.2489
219 57.4844 43.2517 9.2489
220 5.3511 54.8790 9.2489
221 8.8809 67.1678 9.2489
222 20.1601 73.5531 9.2489
223 26.3792 28.3109 9.2489
224 10.2030 47.6234 9.2489
225 31.5452 79.1636 9.2489
226 1.0097 74.3220 9.2489
227 41.3077 70.0597 9.2489
228 75.0077 29.5014 9.2489
229 36.4421 76.1390 9.2489
230 18.5697 98.9341 9.2489
231 13.4875 42.2999 9.2489
232 57.8211 79.2461 9.2489
233 36.4314 90.4821 9.2489
234 33.9192 90.5224 9.2489
235 70.2466 43.4055 9.2489
236 22.0652 57.5055 9.2489
237 3.1646 61.6706 9.2489
238 47.8921 67.3947 9.2489
239 11.0495 95.3028 9.2489
240 37.5812 53.7047 9.2489
241 61.6409 64.7246 9.2489
242 45.3343 93.5861 9.2489
243 4.9615 81.5142 9.2489
244 38.2509 84.7019 9.2489
245 83.9165 55.6949 9.2489
246 93.5356 11.2495 9.2489
Continued on next page
732
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
247 17.3895 82.2317 9.2489
248 52.0534 85.8262 9.2489
249 77.0304 15.5107 9.2489
250 27.3907 19.1091 9.2489
251 10.7776 89.0099 9.2489
252 46.1161 79.1341 9.2489
253 20.1668 86.4556 9.2489
254 47.5277 30.5453 9.2489
255 69.9295 96.4281 9.2489
256 35.0366 76.3190 9.2489
257 28.9502 86.7983 9.2489
258 21.6587 17.9915 9.2489
259 3.7052 66.5975 9.2489
260 34.0333 85.0669 9.2489
261 41.0948 34.9251 9.2489
262 4.2814 24.7215 9.2489
263 55.1100 85.6861 9.2489
264 83.7550 5.8578 9.2489
265 39.2592 24.7878 9.2489
266 53.2221 50.8472 9.2489
267 3.1158 88.0003 9.2489
268 43.4029 59.6042 9.2489
269 37.8711 99.6748 9.2489
270 24.3753 73.1083 9.2489
271 29.8983 58.8839 9.2489
272 14.1488 27.9872 9.2489
273 31.5200 50.8923 9.2489
274 35.9608 77.3873 9.2489
275 33.8474 94.5283 9.2489
276 13.5052 67.7224 9.2489
277 63.8837 92.9887 9.2489
278 79.3060 40.2843 9.2489
279 21.5258 69.0574 9.2489
280 47.6501 45.5187 9.2489
281 6.3344 68.8547 9.2489
282 31.1795 31.4063 9.2489
283 16.5476 53.0979 9.2489
284 53.6161 80.9346 9.2489
285 45.4707 56.9681 9.2489
286 53.0462 62.5622 9.2489
287 9.8322 38.0869 9.2489
Continued on next page
733
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
288 25.8382 22.0380 9.2489
289 69.8234 93.1595 9.2489
290 55.4034 57.6117 9.2489
291 38.0740 11.0946 9.2489
292 21.4033 88.6570 9.2489
293 46.2689 26.5321 9.2489
294 68.3689 72.6148 9.2489
295 37.3674 64.7252 9.2489
296 38.0003 82.2020 9.2489
297 59.7727 58.0187 9.2489
298 43.1282 79.6322 9.2489
299 64.8890 21.5835 9.2489
300 29.4961 81.7774 9.2489
301 64.8850 82.9677 9.2489
302 2.5447 74.4584 9.2489
303 6.7194 25.7387 9.2489
304 0.5395 84.8134 9.2489
305 6.5792 89.2491 9.2489
306 30.1807 48.3203 9.2489
307 7.8809 53.6342 9.2489
308 10.4056 91.9690 9.2489
309 46.2582 91.1776 9.2489
310 25.6400 98.3359 9.2489
311 28.5901 24.8331 9.2489
312 34.3258 66.3110 9.2489
313 39.8688 93.4778 9.2489
314 38.4607 17.3367 9.2489
315 91.9033 76.1624 9.2489
316 5.6684 43.1478 9.2489
317 54.1005 92.2862 9.2489
318 63.5404 40.4791 9.2489
319 57.0628 74.9877 9.2489
320 9.9219 86.8722 9.2489
321 61.3001 82.6964 9.2489
322 70.0736 96.6102 9.2489
323 46.0304 83.7999 9.2489
324 48.4559 88.4082 9.2489
325 9.0186 78.0382 9.2489
326 86.1092 91.4688 9.2489
327 69.6792 40.7468 9.2489
328 24.6164 54.0112 9.2489
Continued on next page
734
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
329 10.8214 82.8932 9.2489
330 18.3152 76.2750 9.2489
331 24.3449 68.8989 9.2489
332 0.0942 39.9156 9.2489
333 19.2935 63.3423 9.2489
334 2.8858 40.6085 9.2489
335 6.7729 23.0443 9.2489
336 81.4769 70.9413 9.2489
337 24.8475 78.2190 9.2489
338 75.7563 60.0220 9.2489
339 55.7308 81.0587 9.2489
340 15.3645 54.9739 9.2489
341 38.3895 19.6567 9.2489
342 9.9641 69.0274 9.2489
343 18.7901 77.5417 9.2489
344 63.4789 68.7065 9.2489
345 9.2651 48.1015 9.2489
346 45.7851 48.7667 9.2489
347 45.1386 90.4706 9.2489
348 54.3000 99.8919 9.2489
349 94.1559 20.2227 9.2489
350 10.2850 75.4358 9.2489
351 1.2826 62.3927 9.2489
352 12.3671 15.9058 9.2489
353 25.2040 63.9864 9.2489
354 41.9538 74.6074 9.2489
355 32.1140 10.6301 9.2489
356 12.2498 50.9274 9.2489
357 71.2277 93.7757 9.2489
358 24.8796 27.0958 9.2489
359 56.1558 36.1072 9.2489
360 41.5744 43.1383 9.2489
361 63.4136 44.6967 9.2489
362 61.0186 37.8221 9.2489
363 32.1467 66.5742 9.2489
364 82.0189 31.5854 9.2489
365 18.1644 83.3220 9.2489
366 17.2441 73.1430 9.2489
367 5.7226 17.3865 9.2489
368 34.1572 12.8461 9.2489
369 6.2917 89.2710 9.2489
Continued on next page
735
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
370 36.8886 65.1176 9.2489
371 14.9958 14.5728 9.2489
372 54.4363 91.9279 9.2489
373 21.6112 90.1973 9.2489
374 56.6448 82.2468 9.2489
375 39.8616 55.5819 9.2489
376 2.5594 66.6071 9.2489
377 97.9906 82.8454 9.2489
378 8.9159 48.8311 9.2489
379 9.3605 76.6338 9.2489
380 44.5697 97.2286 9.2489
381 8.9336 64.1942 9.2489
382 58.1489 37.5502 9.2489
383 62.2017 80.9666 9.2489
384 36.2315 27.6071 9.2489
385 6.6251 98.7289 9.2489
386 1.0969 69.2006 9.2489
387 25.8459 61.1767 9.2489
388 78.2926 66.4599 9.2489
389 7.8717 40.3520 9.2489
390 78.8307 69.6727 9.2489
391 12.4877 90.9011 9.2489
392 79.8675 54.3542 9.2489
393 28.0833 42.0226 9.2489
394 43.0404 95.3704 9.2489
395 29.4788 65.0111 9.2489
396 22.0030 49.7744 9.2489
397 35.5590 90.8560 9.2489
398 63.5373 67.0341 9.2489
399 38.2193 86.8894 9.2489
400 62.0316 81.1662 9.2489
401 58.5050 53.8647 9.2489
402 25.7317 44.0261 9.2489
403 16.2943 68.6310 9.2489
404 12.4548 85.2999 9.2489
405 13.7854 72.7506 9.2489
406 3.3194 86.8534 9.2489
407 14.8681 22.1771 9.2489
408 22.6880 46.2853 9.2489
409 71.2950 19.8608 9.2489
410 37.4347 70.1459 9.2489
Continued on next page
736
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
411 5.2317 94.8857 9.2489
412 49.7727 84.1375 9.2489
413 35.6247 10.7390 9.2489
414 49.1951 89.4435 9.2489
415 25.3592 97.9393 9.2489
416 42.9516 64.8413 9.2489
417 18.9784 66.0993 9.2489
418 5.6772 18.0492 9.2489
419 30.5551 47.7311 9.2489
420 29.6591 42.1276 9.2489
421 52.8342 85.5012 9.2489
422 40.5584 87.8830 9.2489
423 75.2100 80.5663 9.2489
424 24.7916 85.7327 9.2489
425 50.5931 22.7572 9.2489
426 69.7040 60.5823 9.2489
427 44.2169 34.3977 9.2489
428 20.1671 56.2638 9.2489
429 14.4428 41.3582 9.2489
430 22.4643 85.8783 9.2489
431 76.5703 49.5551 9.2489
432 3.4374 82.3966 9.2489
433 6.0418 70.0172 9.2489
434 28.9461 87.0548 9.2489
435 15.8397 72.6074 9.2489
436 25.3455 99.2054 9.2489
437 20.1167 80.5667 9.2489
438 55.9054 73.5658 9.2489
439 5.0427 78.4005 9.2489
440 52.7157 99.4669 9.2489
441 7.8101 100.0000 9.2489
442 7.9924 82.0809 9.2489
443 39.5764 86.6960 9.2489
444 25.7182 44.0237 9.2489
445 24.0950 20.3829 9.2489
446 59.0135 66.3423 9.2489
447 22.0652 97.8097 9.2489
448 14.3064 91.7270 9.2489
449 21.0475 76.8460 9.2489
450 5.9027 84.5742 9.2489
451 2.8851 70.7878 9.2489
Continued on next page
737
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
452 9.5779 89.1192 9.2489
453 6.2564 90.6626 9.2489
454 37.8361 96.1337 9.2489
455 41.1412 94.6163 9.2489
456 91.6000 72.6788 9.2489
457 21.5614 60.0085 9.2489
458 43.7454 43.8763 9.2489
459 50.8699 67.1185 9.2489
460 29.8137 76.7788 9.2489
461 5.5844 23.8118 9.2489
462 21.9541 97.0823 9.2489
463 8.5952 76.7397 9.2489
464 54.6946 37.3209 9.2489
465 40.9133 65.0544 9.2489
466 60.7968 75.3337 9.2489
467 40.9242 52.5492 9.2489
468 16.1042 94.6221 9.2489
469 8.7360 47.8647 9.2489
470 64.6461 95.0926 9.2489
471 69.0955 84.0762 9.2489
472 73.1387 41.7141 9.2489
473 40.0504 28.8112 9.2489
474 54.0363 65.0230 9.2489
475 19.1660 83.5812 9.2489
476 34.2859 93.0132 9.2489
477 42.1091 58.0660 9.2489
478 47.2285 47.8990 9.2489
479 87.6341 89.7208 9.2489
480 18.3969 22.7252 9.2489
481 23.7365 45.2154 9.2489
482 17.4742 43.6042 9.2489
483 63.3224 89.2938 9.2489
484 65.8500 61.3779 9.2489
485 18.4943 75.1491 9.2489
486 38.9024 39.4555 9.2489
487 68.9689 80.5562 9.2489
488 14.1148 66.5849 9.2489
489 94.4318 8.7963 9.2489
490 45.5908 70.2145 9.2489
491 62.8170 55.9489 9.2489
492 25.4040 32.3205 9.2489
Continued on next page
738
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
493 18.1553 77.8065 9.2489
494 18.2095 6.6196 9.2489
495 6.8110 49.5276 9.2489
496 24.9396 85.1814 9.2489
497 22.0024 99.1260 9.2489
498 50.2604 48.9503 9.2489
499 32.4793 60.0995 9.2489
500 76.4839 93.8150 9.2489
501 15.2509 86.8517 9.2489
502 17.8009 46.6451 9.2489
503 95.7766 57.6822 9.2489
504 48.6505 56.2634 9.2489
505 0.2247 41.4361 9.2489
506 14.6745 73.2206 9.2489
507 28.7770 67.7567 9.2489
508 14.5195 70.4911 9.2489
509 11.5664 72.1085 9.2489
510 67.2662 20.0201 9.2489
511 10.8419 50.7478 9.2489
512 87.3408 59.3793 9.2489
513 24.5862 59.9258 9.2489
514 30.6280 46.7773 9.2489
515 61.6361 74.0341 9.2489
516 27.1302 56.0074 9.2489
517 50.6763 98.0842 9.2489
518 43.6656 47.7714 9.2489
519 47.3485 74.6343 9.2489
520 2.5183 30.4543 9.2489
521 59.1060 64.7262 9.2489
522 49.5943 92.5112 9.2489
523 2.7813 68.3563 9.2489
524 42.3435 5.7699 9.2489
525 54.4337 52.1289 9.2489
526 87.5675 36.2741 9.2489
527 23.2328 99.3790 9.2489
528 39.9695 49.4623 9.2489
529 42.1359 68.9460 9.2489
530 16.6338 64.7785 9.2489
531 27.3771 46.4362 9.2489
532 23.3969 71.4392 9.2489
533 3.8578 53.9352 9.2489
Continued on next page
739
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
534 83.7723 73.1421 9.2489
535 31.8061 35.4502 9.2489
536 46.9347 83.7530 9.2489
537 3.3910 60.3206 9.2489
538 48.8236 98.3784 9.2489
539 39.0031 58.9811 9.2489
540 12.7718 48.3340 9.2489
541 26.1244 44.9649 9.2489
542 49.0366 90.6550 9.2489
543 25.6386 75.5532 9.2489
544 61.5633 58.6359 9.2489
545 42.2320 88.9530 9.2489
546 41.1479 74.7573 9.2489
547 48.3993 99.0273 9.2489
548 11.9922 50.5282 9.2489
549 26.5677 46.7769 9.2489
550 68.0919 95.8552 9.2489
551 26.9747 54.6651 9.2489
552 5.7791 82.0132 9.2489
553 2.6430 87.4823 9.2489
554 36.7941 92.2553 9.2489
555 25.9946 34.3791 9.2489
556 22.9640 79.2458 9.2489
557 14.0986 77.6885 9.2489
558 21.2619 68.3111 9.2489
559 71.9975 50.8209 9.2489
560 0.7735 79.8166 9.2489
561 51.9928 27.9991 9.2489
562 5.8634 76.0617 9.2489
563 13.0135 89.5506 9.2489
564 45.6832 63.6499 9.2489
565 44.5324 98.5951 9.2489
566 14.9291 79.4206 9.2489
567 41.1483 82.1060 9.2489
568 44.5606 79.7732 9.2489
569 47.1417 77.8433 9.2489
570 44.4709 80.1731 9.2489
571 13.8911 56.9273 9.2489
572 39.5865 43.5529 9.2489
573 62.3526 88.4620 9.2489
574 8.9809 92.3092 9.2489
Continued on next page
740
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
575 39.4429 96.3803 9.2489
576 3.7954 81.2097 9.2489
577 30.0151 69.9383 9.2489
578 9.3207 27.0856 9.2489
579 36.5703 15.6211 9.2489
580 28.1737 71.9430 9.2489
581 58.4027 82.8929 9.2489
582 41.1055 60.7357 9.2489
583 53.7074 57.8078 9.2489
584 23.5396 80.4714 9.2489
585 73.7584 73.1167 9.2489
586 74.5797 99.8382 9.2489
587 62.6115 17.9582 9.2489
588 53.9008 74.5538 9.2489
589 72.7343 54.9502 9.2489
590 57.8401 97.2493 9.2489
591 1.7250 93.7370 9.2489
592 40.5704 31.3183 9.2489
593 26.0326 67.0519 9.2489
594 10.8989 16.0250 9.2489
595 10.8371 59.6538 9.2489
596 88.1307 33.9075 9.2489
597 31.9616 70.6094 9.2489
598 77.1443 45.2508 9.2489
599 21.5330 97.7661 9.2489
600 57.5617 41.9770 9.2489
601 65.0962 64.3263 9.2489
602 36.5325 65.8983 9.2489
603 46.1572 56.4070 9.2489
604 66.9226 21.4897 9.2489
605 26.4628 62.6113 9.2489
606 22.1400 72.3773 9.2489
607 21.6104 65.8368 9.2489
608 23.3198 27.3418 9.2489
609 31.1212 52.6168 9.2489
610 28.4433 74.9867 9.2489
611 58.2043 69.5052 9.2489
612 64.4724 44.0792 9.2489
613 2.8819 70.7873 9.2489
614 21.5192 80.7447 9.2489
615 74.7837 42.0509 9.2489
Continued on next page
741
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
616 26.2032 94.4570 9.2489
617 27.5007 99.7677 9.2489
618 23.9149 35.5045 9.2489
619 35.8500 97.2623 9.2489
620 38.2077 77.8974 9.2489
621 4.2975 80.7329 9.2489
622 12.3199 42.0729 9.2489
623 52.6846 66.6860 9.2489
624 53.2956 92.4745 9.2489
625 31.8059 45.6064 9.2489
626 66.9270 97.5057 9.2489
627 44.9876 56.9639 9.2489
628 66.5931 88.4188 9.2489
629 55.8048 50.3019 9.2489
630 52.6039 98.5105 9.2489
631 56.1230 60.7693 9.2489
632 30.9043 20.9678 9.2489
633 95.9948 18.1473 9.2489
634 6.8102 85.2019 9.2489
635 8.4659 8.8741 9.2489
636 14.5275 66.8215 9.2489
637 27.0370 98.9981 9.2489
638 51.9170 73.6960 9.2489
639 23.6843 51.4413 9.2489
640 58.4855 38.4928 9.2489
641 22.9522 73.2583 9.2489
642 49.2122 82.1868 9.2489
643 7.0854 88.7785 9.2489
644 32.2127 85.4506 9.2489
645 3.2523 73.9521 9.2489
646 28.3829 59.7022 9.2489
647 18.7192 25.1044 9.2489
648 48.2093 82.3031 9.2489
649 24.2349 17.9886 9.2489
650 63.2177 46.4808 9.2489
651 32.2890 63.3739 9.2489
652 3.1779 14.9780 9.2489
653 62.0129 62.7069 9.2489
654 81.4352 82.8976 9.2489
655 38.2458 80.9579 9.2489
656 67.8758 63.8911 9.2489
Continued on next page
742
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
657 22.6210 94.0370 9.2489
658 9.1968 46.1557 9.2489
659 44.4501 17.9136 9.2489
660 67.4546 72.8538 9.2489
661 22.7988 41.5963 9.2489
662 70.9437 58.1456 9.2489
663 6.9799 73.9164 9.2489
664 22.9592 75.8305 9.2489
665 45.3176 83.7902 9.2489
666 93.2952 74.8246 9.2489
667 17.1684 23.6552 9.2489
668 34.3097 75.9018 9.2489
669 17.4426 43.6837 9.2489
670 28.5440 40.1369 9.2489
671 5.0204 69.5880 9.2489
672 72.9138 91.5489 9.2489
673 1.8255 70.7813 9.2489
674 60.5976 67.4229 9.2489
675 29.1581 9.5187 9.2489
676 71.6163 44.9777 9.2489
677 58.2152 76.7746 9.2489
678 31.0391 88.8192 9.2489
679 10.6233 24.2907 9.2489
680 8.6800 15.2269 9.2489
681 63.1252 41.2494 9.2489
682 44.9684 64.0571 9.2489
683 11.8661 56.8305 9.2489
684 3.2986 92.2687 9.2489
685 30.8364 38.3521 9.2489
686 14.0192 69.2201 9.2489
687 53.4809 34.5743 9.2489
688 7.3200 15.3781 9.2489
689 41.9598 64.9444 9.2489
690 85.1609 60.4770 9.2489
691 93.1274 86.7071 9.2489
692 4.2036 71.2869 9.2489
693 32.0671 41.1282 9.2489
694 28.9427 52.0186 9.2489
695 32.4397 75.5288 9.2489
696 56.1557 89.4150 9.2489
697 17.4531 57.0203 9.2489
Continued on next page
743
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
698 38.7847 39.0691 9.2489
699 7.0090 89.8085 9.2489
700 1.8346 71.1520 9.2489
701 18.8550 86.6147 9.2489
702 24.9239 92.0800 9.2489
703 24.5764 79.5754 9.2489
704 18.1048 51.4832 9.2489
705 12.0343 87.7882 9.2489
706 14.5063 38.1657 9.2489
707 19.1790 72.4898 9.2489
708 23.6494 19.8099 9.2489
709 10.6386 61.6451 9.2489
710 35.5398 15.9920 9.2489
711 87.0390 21.0955 9.2489
712 23.2926 57.3444 9.2489
713 34.0637 42.7709 9.2489
714 35.6019 93.1465 9.2489
715 3.1666 54.3858 9.2489
716 29.5659 24.5787 9.2489
717 9.4424 27.3202 9.2489
718 8.3279 95.9796 9.2489
719 18.2173 92.4873 9.2489
720 46.2073 94.8222 9.2489
721 22.1996 99.8400 9.2489
722 39.7386 66.9252 9.2489
723 49.9058 41.0723 9.2489
724 3.7026 67.5597 9.2489
725 6.6640 86.9327 9.2489
726 4.7243 85.8821 9.2489
727 26.3650 64.1039 9.2489
728 72.1571 9.1791 9.2489
729 3.0824 9.0439 9.2489
730 23.4079 43.6438 9.2489
731 38.1988 73.4530 9.2489
732 82.5399 88.8791 9.2489
733 19.4727 75.2589 9.2489
734 66.8109 72.1934 9.2489
735 3.7660 77.2812 9.2489
736 25.0801 60.4807 9.2489
737 29.0961 74.1868 9.2489
738 9.0204 42.8621 9.2489
Continued on next page
744
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
739 41.7217 60.3614 9.2489
740 25.6611 62.2794 9.2489
741 3.3366 66.3437 9.2489
742 24.0546 58.8274 9.2489
743 5.3337 86.8970 9.2489
744 58.0062 94.6472 9.2489
745 37.3556 97.3081 9.2489
746 14.3554 64.7100 9.2489
747 82.0902 81.3331 9.2489
748 10.7991 20.4204 9.2489
749 76.6853 86.4930 9.2489
750 50.2967 64.0758 9.2489
751 68.8428 76.0322 9.2489
752 75.1938 39.7539 9.2489
753 48.6909 94.6419 9.2489
754 8.0113 61.6922 9.2489
755 30.2819 43.7783 9.2489
756 6.9629 47.8774 9.2489
757 11.5133 99.9544 9.2489
758 54.0008 32.5022 9.2489
759 35.9208 99.0427 9.2489
760 19.5589 94.4852 9.2489
761 54.4897 89.3064 9.2489
762 45.3223 79.2675 9.2489
763 28.1720 56.5159 9.2489
764 24.6793 81.2170 9.2489
765 18.1343 49.1579 9.2489
766 3.0595 82.0560 9.2489
767 8.0771 60.5265 9.2489
768 25.2429 93.1818 9.2489
769 57.9733 65.3994 9.2489
770 43.9152 93.3979 9.2489
771 16.0716 60.0064 9.2489
772 38.5583 62.0328 9.2489
773 41.2395 98.4925 9.2489
774 66.6787 56.1352 9.2489
775 23.6527 99.4060 9.2489
776 53.9276 74.1265 9.2489
777 9.9545 42.5082 9.2489
778 18.2114 45.5866 9.2489
779 17.2560 61.6944 9.2489
Continued on next page
745
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
780 30.9617 84.9946 9.2489
781 51.9522 92.5799 9.2489
782 72.0901 81.4175 9.2489
783 17.8196 98.0177 9.2489
784 60.7167 14.8722 9.2489
785 34.1704 50.6373 9.2489
786 70.7195 19.5494 9.2489
787 44.4260 67.4520 9.2489
788 12.8762 80.5413 9.2489
789 59.4841 31.9800 9.2489
790 52.4099 76.9003 9.2489
791 34.3106 43.9536 9.2489
792 8.6898 62.8088 9.2489
793 51.1986 31.0981 9.2489
794 30.0885 94.0460 9.2489
795 30.3441 27.7443 9.2489
796 28.8603 61.8379 9.2489
797 25.3942 74.0149 9.2489
798 40.8101 38.7730 9.2489
799 52.6495 62.6853 9.2489
800 3.1055 84.7108 9.2489
801 53.5031 57.0494 9.2489
802 2.6944 27.6283 9.2489
803 32.3368 89.5627 9.2489
804 15.5069 76.4486 9.2489
805 19.1817 47.0577 9.2489
806 49.5272 60.8867 9.2489
807 2.8203 66.9401 9.2489
808 55.5809 76.5300 9.2489
809 60.7009 80.6445 9.2489
810 49.1367 77.1071 9.2489
811 5.8385 89.4611 9.2489
812 41.7271 62.5487 9.2489
813 9.8910 52.1661 9.2489
814 32.5694 80.9888 9.2489
815 40.7765 81.2371 9.2489
816 31.8981 95.6275 9.2489
817 37.6765 59.0182 9.2489
818 57.0948 60.4599 9.2489
819 29.9086 38.4851 9.2489
820 5.8013 5.2308 9.2489
Continued on next page
746
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
821 72.4880 89.5704 9.2489
822 46.0208 88.3362 9.2489
823 9.9401 86.9982 9.2489
824 59.0160 86.9927 9.2489
825 65.2673 95.8674 9.2489
826 74.4658 79.0435 9.2489
827 62.1759 23.5347 9.2489
828 79.3916 97.2659 9.2489
829 62.8346 32.3748 9.2489
830 34.8283 24.4509 9.2489
831 68.0145 90.2652 9.2489
832 27.2662 25.9020 9.2489
833 16.9340 77.9225 9.2489
834 47.9291 80.1113 9.2489
835 5.8197 97.5317 9.2489
836 58.0914 33.9778 9.2489
837 22.0736 33.0177 9.2489
838 1.6960 79.3379 9.2489
839 59.9771 27.0772 9.2489
840 58.8167 76.2826 9.2489
841 21.6338 90.7285 9.2489
842 37.0705 30.0448 9.2489
843 84.8598 39.8533 9.2489
844 16.7612 28.3125 9.2489
845 70.7717 73.8806 9.2489
846 83.1920 53.4864 9.2489
847 33.5083 58.4841 9.2489
848 38.7870 81.2074 9.2489
849 10.3039 47.8428 9.2489
850 64.7579 49.9210 9.2489
851 49.4895 49.4412 9.2489
852 49.8172 39.8995 9.2489
853 68.1156 90.2931 9.2489
854 22.5832 64.2388 9.2489
855 61.1490 72.7041 9.2489
856 45.9483 45.5070 9.2489
857 0.7151 54.3404 9.2489
858 72.1305 55.0307 9.2489
859 53.2731 89.6749 9.2489
860 74.8508 64.7465 9.2489
861 39.3557 35.0679 9.2489
Continued on next page
747
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
862 73.0497 93.6836 9.2489
863 49.3932 67.5706 9.2489
864 57.4325 97.9412 9.2489
865 51.9052 74.1053 9.2489
866 18.8095 50.6794 9.2489
867 24.6809 89.7145 9.2489
868 8.6752 76.1739 9.2489
869 51.1883 82.8098 9.2489
870 40.5774 42.4726 9.2489
871 7.9746 40.8370 9.2489
872 75.3828 84.8496 9.2489
873 49.4989 30.7347 9.2489
874 44.0124 95.5424 9.2489
875 69.1263 69.4594 9.2489
876 2.5102 94.8247 9.2489
877 27.4285 33.2762 9.2489
878 52.0310 42.5013 9.2489
879 20.4271 96.6926 9.2489
880 31.6797 78.2008 9.2489
881 51.0870 26.4204 9.2489
882 43.6316 99.6749 9.2489
883 53.7981 45.1618 9.2489
884 34.6877 48.2708 9.2489
885 37.6478 91.6093 9.2489
886 33.5730 70.5185 9.2489
887 9.8979 67.9400 9.2489
888 53.0876 83.0336 9.2489
889 8.9880 7.9259 9.2489
890 52.2624 99.8357 9.2489
891 35.9445 20.1240 9.2489
892 88.6056 53.6735 9.2489
893 23.9248 88.8528 9.2489
894 19.2915 80.5243 9.2489
895 55.7534 84.5659 9.2489
896 23.8691 73.8369 9.2489
897 91.0477 90.6018 9.2489
898 3.1000 78.6196 9.2489
899 33.4587 53.8592 9.2489
900 7.9364 83.6393 9.2489
901 79.1970 96.0601 9.2489
902 44.1366 71.3894 9.2489
Continued on next page
748
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
903 49.6284 78.6599 9.2489
904 54.0926 96.0479 9.2489
905 21.3065 61.8915 9.2489
906 0.4381 29.4254 9.2489
907 20.7321 24.2374 9.2489
908 73.0537 69.2663 9.2489
909 26.3675 61.2448 9.2489
910 21.7053 21.6002 9.2489
911 27.3610 64.8453 9.2489
912 65.3474 72.8039 9.2489
913 5.9124 83.1077 9.2489
914 51.1226 42.0525 9.2489
915 61.5967 60.8657 9.2489
916 22.8159 48.6759 9.2489
917 8.8117 48.5050 9.2489
918 38.5718 69.2997 9.2489
919 57.5832 98.5570 9.2489
920 35.3969 60.0156 9.2489
921 28.7236 49.0681 9.2489
922 5.2093 90.5033 9.2489
923 24.7044 26.1237 9.2489
924 16.2374 85.8701 9.2489
925 39.9123 41.2977 9.2489
926 30.7807 88.6774 9.2489
927 33.7199 84.5665 9.2489
928 78.9213 50.4135 9.2489
929 50.7844 76.1250 9.2489
930 36.9364 55.8048 9.2489
931 48.9135 54.7775 9.2489
932 20.7502 68.8208 9.2489
933 4.6928 58.0805 9.2489
934 67.1079 49.8065 9.2489
935 24.0084 69.2667 9.2489
936 86.3740 99.0292 9.2489
937 34.1513 57.3793 9.2489
938 55.5513 39.2153 9.2489
939 61.6783 82.5197 9.2489
940 78.8555 52.0414 9.2489
941 18.6594 93.9062 9.2489
942 42.4583 25.0181 9.2489
943 44.9441 36.2858 9.2489
Continued on next page
749
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
944 10.1680 51.0208 9.2489
945 69.8043 81.6082 9.2489
946 20.3745 52.9258 9.2489
947 0.7939 65.0080 9.2489
948 50.2039 81.9545 9.2489
949 71.8526 57.8562 9.2489
950 67.2781 56.7922 9.2489
951 18.7431 29.3024 9.2489
952 1.4520 80.8724 9.2489
953 47.3831 49.7186 9.2489
954 21.1655 75.9293 9.2489
955 51.4448 86.5947 9.2489
956 9.0889 70.5778 9.2489
957 18.2147 45.6508 9.2489
958 21.6088 73.6490 9.2489
959 86.5185 50.7156 9.2489
960 53.2647 92.1753 9.2489
961 2.8878 89.8019 9.2489
962 29.0554 78.8440 9.2489
963 9.7018 81.2314 9.2489
964 20.5309 55.6362 9.2489
965 28.6603 61.1318 9.2489
966 6.6689 38.8057 9.2489
967 63.0451 24.2986 9.2489
968 31.6550 99.4688 9.2489
969 48.8625 99.4418 9.2489
970 70.3628 70.3940 9.2489
971 4.9535 23.8151 9.2489
972 56.2033 63.0964 9.2489
973 26.6524 66.9167 9.2489
974 0.2999 68.5196 9.2489
975 77.8700 52.2111 9.2489
976 52.4538 66.1794 9.2489
977 3.5540 91.3872 9.2489
978 11.1781 66.0777 9.2489
979 24.6656 67.5861 9.2489
980 13.2177 55.1607 9.2489
981 14.0238 94.5577 9.2489
982 37.3514 99.5759 9.2489
983 74.0768 69.1633 9.2489
984 40.7698 74.9435 9.2489
Continued on next page
750
Table D.14 –Continued from previous page
Customer index x-coordinate y-coordinate Service range
985 83.5593 59.6475 9.2489
986 57.3566 43.7146 9.2489
987 85.2298 8.7159 9.2489
988 54.9097 93.3080 9.2489
989 20.9795 58.6686 9.2489
990 9.9848 87.6087 9.2489
991 80.8442 99.9885 9.2489
992 61.4907 91.4052 9.2489
993 10.7809 34.0837 9.2489
994 49.3815 71.8463 9.2489
995 59.0918 73.4479 9.2489
996 1.6629 98.2148 9.2489
997 38.7282 43.6440 9.2489
998 12.9785 40.6655 9.2489
999 5.0657 76.4183 9.2489
1000 62.6131 94.2939 9.2489
Depot 80.0000 20.0000 N.A.
751
−5 0 5 10 15 20 25 30 35 40 45
−5
0
5
10
15
20
25
kroD100rdmRad
Figure D.1: Solution to kroD100rdmRad produced by MMSZ
−30 −20 −10 0 10 20 30 40
−30
−20
−10
0
10
20
30
40
50
60
rat195rdmRad
Figure D.2: Solution to rat195rdmRad produced by MMSZ
752
−100 −50 0 50 100 150 200 250 300 350 400
−100
0
100
200
300
400
500
lin318rdmRad
Figure D.3: Solution to lin318rdmRad produced by MMSZ
−20 0 20 40 60 80 100 120
−20
0
20
40
60
80
100
120
rd400rdmRad
Figure D.4: Solution to rd400rdmRad produced by MMSZ
753
−5 0 5 10 15 20 25 30 35 40
−5
0
5
10
15
20
25
30
35
40
45
pcb442rdmRad
Figure D.5: Solution to pcb442rdmRad produced by MMSZ
0 5 10 15 20 25 30 35 40 45 50
0
5
10
15
20
25
30
35
40
d493rdmRad
Figure D.6: Solution to d493rdmRad produced by MMSZ
754
−40 −20 0 20 40 60 80 100 120 140
−40
−20
0
20
40
60
80
100
120
140
dsj1000rdmRad
Figure D.7: Solution to dsj1000rdmRad produced by MMSZ
−20 0 20 40 60 80 100 120
−20
0
20
40
60
80
100
120
team1100rdmRad
Figure D.8: Solution to team1 100rdmRad produced by MMSZ
755
−20 0 20 40 60 80 100 120
−20
0
20
40
60
80
100
120
team2200rdmRad
Figure D.9: Solution to team2 200rdmRad produced by MMSZ
−60 −40 −20 0 20 40 60 80 100 120 140
−50
0
50
100
150
team3300rdmRad
Figure D.10: Solution to team3 300rdmRad produced by MMSZ
756
−20 0 20 40 60 80 100 120
−20
0
20
40
60
80
100
120
team4400rdmRad
Figure D.11: Solution to team4 400rdmRad produced by MMSZ
−40 −20 0 20 40 60 80 100 120 140
−40
−20
0
20
40
60
80
100
120
140
team5499rdmRad
Figure D.12: Solution to team5 499rdmRad produced by MMSZ
757
−20 0 20 40 60 80 100
−20
0
20
40
60
80
100
120
team6500rdmRad
Figure D.13: Solution to team6 500rdmRad produced by MMSZ
−20 0 20 40 60 80 100 120
−20
0
20
40
60
80
100
120
bonus1000rdmRad
Figure D.14: Solution to bonus1000rdmRad produced by MMSZ
758
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