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The vehicle routing problem

Author: Paolo Toth; Daniele Vigo
Publisher: Philadelphia : Society for Industrial and Applied Mathematics, ©2002.
Series: SIAM monographs on discrete mathematics and applications.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This text covers the state-of-the-art solution methods developed at the end of the 20th century for the Vechicle Routing Problem (VRP) and some of its main variants, while also devoting a large part  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Paolo Toth; Daniele Vigo
ISBN: 0898714982 9780898714982 9780898715798 0898715792
OCLC Number: 47126854
Description: xviii, 367 pages : illustrations ; 27 cm.
Contents: 1 An Overview of Vehicle Routing Problems / P. Toth, D. Vigo 1 --
1.2 Problem Definition and Basic Notation 5 --
1.2.1 Capacitated and Distance-Constrained VRP 5 --
1.2.2 VRP with Time Windows 8 --
1.2.3 VRP with Backhauls 9 --
1.2.4 VRP with Pickup and Delivery 10 --
1.3 Basic Models for the VRP 11 --
1.3.1 Vehicle Flow Models 11 --
1.3.2 Extensions of Vehicle Flow Models 17 --
1.3.3 Commodity Flow Models 19 --
1.3.4 Set-Partitioning Models 21 --
1.4 Test Instances for the CVRP and Other VRPs 22 --
I Capacitated Vehicle Routing Problem 27 --
2 Branch-and-Bound Algorithms for the Capacitated VRP / P. Toth, D. Vigo 29 --
2.2 Basic Relaxations 30 --
2.2.1 Bounds Based on Assignment and Matching 30 --
2.2.2 Bounds Based on Arborescences and Trees 32 --
2.2.3 Comparison of the Basic Relaxations 33 --
2.3 Better Relaxations 35 --
2.3.1 Additive Bounds for ACVRP 35 --
2.3.2 Further Lower Bounds for ACVRP 39 --
2.3.3 Lagrangian Lower Bounds for SCVRP 40 --
2.3.4 Lower Bounds from a Set-Partitiong Formulation 41 --
2.3.5 Comparison of the Improved Lower Bounds 42 --
2.4 Structure of the Branch-and-Bound Algorithms for CVRP 44 --
2.4.1 Branching Schemes and Search Strategies 44 --
2.4.2 Reduction, Dominance Rules, and Other Features 46 --
2.4.3 Performance of the Branch-and-Bound Algorithms 47 --
2.5 Distance-Constrained VRP 48 --
3 Branch-and-Cut Algorithms for the Capacitated VRP / D. Naddef, G. Rinaldi 53 --
3.1 Introduction and Two-Index Flow Model 53 --
3.2 Branch-and-Cut 55 --
3.3 Polyhedral Studies 58 --
3.3.1 Capacity Constraints 59 --
3.3.2 Generalized Capacity Constraints 61 --
3.3.3 Framed Capacity Constraints 62 --
3.3.4 Valid Inequalities from STSP 62 --
3.3.5 Valid Inequalities Combining Bin Packing and STSP 67 --
3.3.6 Valid Inequalities from the Stable Set Problem 69 --
3.4 Separation Procedures 71 --
3.4.1 Exact Separation of Capacity Constraints 71 --
3.4.2 Heuristics for Capacity and Related Constraints 72 --
3.4.3 STSP Constraints 75 --
3.5 Branching Strategies 75 --
3.6 Computational Results 78 --
4 Set-Covering-Based Algorithms for the Capacitated VRP / J. Bramel, D. Simchi-Levi 85 --
4.2 Solving the Linear Programming Relaxation of P 87 --
4.3 Set-Covering-Based Solution Methods 89 --
4.3.1 Branch-and-Bound Algorithm for Problem CG 89 --
4.3.2 Polyhedral Branch-and-Bound Algorithm 91 --
4.3.3 Pseudo-Polynomial Lower Bound on cmin 92 --
4.3.4 Solving P[subscript D] via Dual-Ascent and Branch-and-Bound 94 --
4.4 Solving the Set-Covering Integer Program 96 --
4.4.1 A Cutting Plane Method 97 --
4.4.2 Branch-and-Price 99 --
4.4.3 Additional Comments on Computational Approaches 100 --
4.5 Computational Results 100 --
4.6 Effectiveness of the Set-Covering Formulation 102 --
4.6.1 Worst-Case Analysis 103 --
4.6.2 Average-Case Analysis 103 --
5 Classical Heuristics for the Capacitated VRP / G. Laporte, F. Semet 109 --
5.2 Constructive Methods 110 --
5.2.1 Clarke and Wright Savings Algorithm 110 --
5.2.2 Enhancements of the Clarke and Wright Algorithm 111 --
5.2.3 Matching-Based Savings Algorithms 113 --
5.2.4 Sequential Insertion Heuristics 114 --
5.3 Two-Phase Methods 116 --
5.3.1 Elementary Clustering Methods 116 --
5.3.2 Truncated Branch-and-Bound 118 --
5.3.3 Petal Algorithms 120 --
5.3.4 Route-First, Cluster-Second Methods 120 --
5.4 Improvement Heuristics 121 --
5.4.1 Single-Route Improvements 121 --
5.4.2 Multiroute Improvements 122 --
6 Metaheuristics for the Capacitated VRP / M. Gendreau, G. Laporte, J.-Y. Potvin 129 --
6.2 Simulated Annealing 130 --
6.2.1 Two Early Simulated Annealing Algorithms 130 --
6.2.2 Osman's Simulated Annealing Algorithms 131 --
6.2.3 Van Breedam's Experiments 133 --
6.3 Deterministic Annealing 133 --
6.4 Tabu Search 134 --
6.4.1 Two Early Tabu Search Algorithms 134 --
6.4.2 Osman's Tabu Search Algorithm 134 --
6.4.3 Taburoute 135 --
6.4.4 Taillard's Algorithm 137 --
6.4.5 Xu and Kelly's Algorithm 137 --
6.4.6 Rego and Roucairol's Algorithms 137 --
6.4.7 Barbarosoglu and Ozgur's Algorithm 138 --
6.4.8 Adaptive Memory Procedure of Rochat and Taillard 138 --
6.4.9 Granular Tabu Search of Toth and Vigo 138 --
6.4.10 Computational Comparison 140 --
6.5 Genetic Algorithms 140 --
6.5.1 Simple Genetic Algorithm 140 --
6.5.2 Application to Sequencing Problems 141 --
6.5.3 Application to the VRP 142 --
6.6 Ant Algorithms 144 --
6.7 Neural Networks 146 --
II Important Variants of the Vehicle Routing Problem 155 --
7 VRP with Time Windows / J.-F. Cordeau, G. Desaulniers, J. Desrosiers, M.M. Solomon, F. Soumis 157 --
7.2 Problem Formulation 158 --
7.2.1 Formulation 158 --
7.2.2 Network Lower Bound 159 --
7.2.3 Linear Programming Lower Bound 159 --
7.2.4 Algorithms 160 --
7.3 Upper Bounds: Heuristic Approaches 160 --
7.3.1 Route Construction 160 --
7.3.2 Route Improvement 161 --
7.3.3 Composite Heuristics 161 --
7.3.4 Metaheuristics 162 --
7.3.5 Parallel Implementations 165 --
7.3.6 Optimization-Based Heuristics 165 --
7.3.7 Asymptotically Optimal Heuristics 165 --
7.4 Lower Bounds from Decomposition Approaches 166 --
7.4.1 Lagrangian Relaxation 166 --
7.4.2 Capacity and Time-Constrained Shortest-Path Problem 167 --
7.4.3 Variable Splitting 168 --
7.4.4 Column Generation 169 --
7.4.5 Set-Partitioning Formulation 169 --
7.4.6 Lower Bound 170 --
7.4.7 Commodity Aggregation 171 --
7.4.8 Hybrid Approach 172 --
7.5 Integer Solutions 173 --
7.5.1 Binary Decisions on Arc Flow Variables 173 --
7.5.2 Integer Decisions on Arc Flow Variables 173 --
7.5.3 Binary Decisions on Path Flow Variables 174 --
7.5.4 Subtour Elimination and 2-Path Cuts 175 --
7.5.5 k-Path Cuts and Parallelism 176 --
7.5.6 Integer Decisions on (Fractional and Integer) Time Variables 176 --
7.6 Special Cases 177 --
7.6.1 Multiple TSP with Time Windows 177 --
7.6.2 VRP with Backhauls and Time Windows 177 --
7.7 Extensions 178 --
7.7.1 Heterogeneous Fleet, Multiple-Depot, and Initial Conditions 178 --
7.7.2 Fleet Size 179 --
7.7.3 Multiple Time Windows 179 --
7.7.4 Soft Time Windows 179 --
7.7.5 Time- and Load-Dependent Costs 180 --
7.7.6 Driver Considerations 180 --
7.8 Computational Results for VRPTW 181 --
8 VRP with Backhauls / P. Toth, D. Vigo 195 --
8.1.1 Benchmark Instances 197 --
8.2 Integer Linear Programming Models 198 --
8.2.1 Formulation of Toth and Vigo 198 --
8.2.2 Formulation of Mingozzi, Giorgi, and Baldacci 200 --
8.3 Relaxations 201 --
8.3.1 Relaxation Obtained by Dropping the CCCs 202 --
8.3.2 Relaxation Based on Projection 202 --
8.3.3 Lagrangian Relaxation 203 --
8.3.4 Overall Additive Lower Bound 204 --
8.3.5 Relaxation Based on the Set-Partitioning Model 204 --
8.4 Exact Algorithms 208 --
8.4.1 Algorithm of Toth and Vigo 208 --
8.4.2 Algorithm of Mingozzi, Giorgi, and Baldacci 209 --
8.4.3 Computational Results for the Exact Algorithms 210 --
8.5 Heuristic Algorithms 214 --
8.5.1 Algorithm of Deif and Bodin 214 --
8.5.2 Algorithms of Goetschalckx and Jacobs-Blecha 215 --
8.5.3 Algorithm of Toth and Vigo 216 --
8.5.4 Computational Results for the Heuristics 217 --
9 VRP with Pickup and Delivery / G. Desaulniers, J. Desrosiers, A. Erdmann, M.M. Solomon, F. Soumis 225 --
9.2 Mathematical Formulation 226 --
9.2.1 Construction of the Networks 226 --
9.2.2 Formulation 227 --
9.2.3 Service Quality 228 --
9.2.4 Reduction of the Network Size 228 --
9.3 Heuristics 229 --
9.3.1 Construction and Improvement 229 --
9.3.2 Clustering Algorithms 230 --
9.3.3 Metaheuristics 230 --
9.3.4 Neural Network Heuristics 231 --
9.3.5 Theoretical Analysis of Algorithms 231 --
9.4 Optimization-Based Approaches 232 --
9.4.1 Single Vehicle Cases 232 --
9.4.2 Multiple Vehicle Cases 234 --
9.5 Applications 236 --
9.6 Computational Results 236 --
III Applications and Case Studies 243 --
10 Routing Vehicles in the Real World: Applications in the Solid Waste, Beverage, Food, Dairy, and Newspaper Industries / B.L. Golden, A.A. Assad, E.A. Wasil 245 --
10.2 Computerized Vehicle Routing in the Solid Waste Industry 247 --
10.2.1 History 247 --
10.2.3 Commercial Collection 249 --
10.2.4 Residential Collection 250 --
10.2.6 Roll-on-Roll-off 252 --
10.2.7 Further Remarks 254 --
10.3 Vehicle Routing in the Beverage, Food, and Dairy Industries 254 --
10.3.2 Beverage Industry 255 --
10.3.3 Food Industry 259 --
10.3.4 Dairy Industry 260 --
10.4 Distribution and Routing in the Newspaper Industry 266 --
10.4.1 Industry Background 266 --
10.4.2 Newspaper Distribution Problem 268 --
10.4.3 Vehicle Routing Algorithms for NDP 271 --
10.4.4 Three Case Studies 276 --
11 Capacitated Arc Routing Problem with Vehicle-Site Dependencies: The Philadelphia Experience / J. Sniezek, L. Bodin, L. Levy, M. Ball 287 --
11.2 Networks, Assumptions, and Goals of the CARP-VSD 288 --
11.2.1 Travel Network 288 --
11.2.2 Service Network 289 --
11.2.3 Vehicle Classes 290 --
11.2.4 Travel Network and Service Network for a Vehicle Class 291 --
11.2.5 Vehicle Preference List 291 --
11.2.6 Other Assumptions 292 --
11.2.7 Goals and Constraints of the CARP-VSD 292 --
11.3 Vehicle Decomposition Algorithm (VDA) 293 --
11.3.1 Step A. Create and Verify Vehicle Class Networks 293 --
11.3.2 Step B. Estimate Total Work and Determine Initial Fleet Mix 294 --
11.3.3 Step C. Partition the Service Network 301 --
11.3.4 Step D. Determine Travel Path and Balance the Partitions 304.
Series Title: SIAM monographs on discrete mathematics and applications.
Responsibility: edited by Paolo Toth, Daniele Vigo.
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