车辆路径问题

list of contributors

preface

1 an overview of vehicle routing problems

1.1 introduction

1.2 problem definition and basic notation

1.2.1 capacitated and distance-constrained vrp

1.2.2 vrp with time windows

1.2.3 vrp with backhauls

1.2.4 vrp with pickup and delivery

1.3 basic models for the vrp

1.3.1 vehicle flow models

1.3.2 extensions of vehicle flow models

1.3.3 commodity flow models

1.3.4 set-partitioning models

1.4 test instances for the cvrp and other vrps

bibliography

ⅰ capacitated vehicle routing problem

2 branch-and-bound algorithms for the capacitated vrp

2.1 introduction

2.2 basic relaxations

2.2.1 bounds based on assignment and matching

2.2.2 bounds based on arborescences and trees

2.2.3 comparison of the basic relaxations

2.3 better relaxations

2.3.1 additive bounds for acvrp

2.3.2 further lower bounds for acvrp

2.3.3 lagrangian lower bounds for scvrp

2.3.4 lower bounds from a set-partitioning formulation

2.3.5 comparison of the improved lower bounds

2.4 structure of the branch-and-bound algorithms for cvrp

2.4.1 branching schemes and search strategies

2.4.2 reduction, dominance rules, and other features

2.4.3 performance of the branch-and-bound algorithms

2.5 distance-constrained vrp

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3 branch-and-cut algorithms for the capacitated vrp

3.1 introduction and two-index flow model

3.2 branch-and-cut

3.3 polyhedral studies

3.3.1 capacity constraints

3.3.2 generalized capacity constraints

3.3.3 framed capacity constraints

3.3.4 valid inequalities from stsp

?　　3.3.5 valid inequalities combining bin packing and stsp

3.3.6 valid inequalities from the stable set problem

3.4 separation procedures

3.4.1 exact separation of capacity constraints

3.4.2 heuristics for capacity and related constraints

3.4.3 stsp constraints

3.5 branching strategies

3.6 computational results

3.7 conclusions

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4 set-covering-based algorithms for the capacitated vrp

4.1 introduction

4.2 solving the linear programming relaxation of p

4.3 set-covering-based solution methods

4.3.1 branch-and-bound algorithm for problem cg

4.3.2 polyhedral branch-and-bound algorithm

4.3.3 pseudo-polynomial lower bound on cmin

4.3.4 solving pa via dual-ascent and branch-and-bound

4.4 solving the set-covering integer program

4.4.1 a cutting plane method

4.4.2 branch-and-price

4.4.3 additional comments on computational approaches

4.5 computational results

4.6 effectiveness of the set-covering formulation

4.6.1 worst-case analysis

4.6.2 average-case analysis

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5 classical heuristics for the capacitated vrp

5.1 introduction

5.2 constructive methods

5.2.1 clarke and wright savings algorithm

5.2.2 enhancements of the clarke and wright algorithm

5.2.3 matching-based savings algorithms

5.2.4 sequential insertion heuristics

5.3 two-phase methods

5.3.1 elementary clustering methods

5.3.2 truncated branch-and-bound

5.3.3 petal algorithms

5.3.4 route-first, cluster-second methods

5.4 improvement heuristics

5.4.1 single-route improvements

5.4.2 multiroute improvements

5.5 conclusions

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6 metaheuristics for the capacitated vrp

6.1 introduction

6.2 simulated annealing

6.2.1 two early simulated annealing algorithms

6.2.2 osman's simulated annealing algorithms

6.2.3 van breedam's experiments

6.3 deterministic annealing

6.4 tabu search

6.4.1 two early tabu search algorithms

6.4.2 osman's tabu search algorithm

6.4.3 taburoute

6.4.4 taillard's algorithm

6.4.5 xu and kelly's algorithm

6.4.6 rego and roucairol's algorithms

6.4.7 barbarosoglu and ozgur's algorithm

6.4.8 adaptive memory procedure of rochat and taillard

6.4.9 granular tabu search of toth and vigo

6.4.10 computational comparison

6.5 genetic algorithms

6.5.1 simple genetic algorithm

6.5.2 application to sequencing problems

6.5.3 application to the vrp

6.6 ant algorithms

6.7 neural networks

6.8 conclusions

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ⅱ important variants of the vehicle routing problem

7 vrp with time windows

7.1 introduction

7.2 problem formulation

7.2.1 formulation

7.2.2 network lower bound

7.2.3 linear programming lower bound

7.2.4 algorithms

7.3 upper bounds: heuristic approaches

7.3.1 route construction

7.3.2 route improvement

?　7.3.3 composite heuristics

7.3.4 metaheuristics

7.3.5 parallel implementations

7.3.6 optimization-based heuristics

7.3.7 asymptotically optimal heuristics

7.4 lower bounds from decomposition approaches

7.4.1 lagrangian relaxation

7.4.2 capacity and time-constrained shortest-path problem.

7.4.3 variable splitting

7.4.4 column generation

7.4.5 set-partitioning formulation

7.4.6 lower bound

7.4.7 commodity aggregation

7.4.8 hybrid approach

7.5 integer solutions

7.5.1 binary decisions on arc flow variables

7.5.2 integer decisions on arc flow variables

7.5.3 binary decisions on path flow variables

7.5.4 subtour elimination and 2-path cuts

7.5.5 k-path cuts and parallelism

7.5.6 integer decisions on (fractional and integer) time variables

7.6 special cases

7.6.1 multiple tsp with time windows

7.6.2 vrp with backhauls and time windows

7.7 extensions

7.7.1 heterogeneous fleet, multiple-depot, and initial conditions

7.7.2 fleet size

7.7.3 multiple time windows

7.7.4 soft time windows

7.7.5 time- and load-dependent costs

7.7.6 driver considerations

7.8 computational results for vrptw.

7.9 conclusions

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8 vrp with backhauls

8.1 introduction

8.1.1 benchmark instances

8.2 integer linear programming models

8.2.1 formulation of toth and vigo

8.2.2 formulation of mingozzi, giorgi, and baldacci

8.3 relaxations

8.3.1 relaxation obtained by dropping the cccs

8.3.2 relaxation based on projection

8.3.3 lagrangian relaxation

8.3.4 overall additive lower bound

8.3.5 relaxation based on the set-partitioning model

8.4 exact algorithms

8.4. i algorithm of toth and vigo

8.4.2 algorithm of mingozzi, giorgi, and baldacci

8.4.3 computational results for the exact algorithms

8.5 heuristic algorithms

8.5.1 algorithm of deif and bodin

8.5.2 algorithms of goetschalckx and jacobs-blecha

8.5.3 algorithm of toth and vigo

8.5.4 computational results for the heuristics

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9 vrp with pickup and delivery

9.1 introduction

9.2 mathematical formulation

9.2.1 construction of the networks

9.2.2 formulation

9.2.3 service quality

9.2.4 reduction of the network size

9.3 heuristics

9.3.1 construction and improvement

9.3.2 clustering algorithms

9.3.3 metaheuristics

9.3.4 neural network heuristics

9.3.5 theoretical analysis of algorithms

9.4 optimization-based approaches

9.4.1 single vehicle cases

9.4.2 multiple vehicle cases

9.5 applications

9.6 computational results

9.7 conclusions

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ⅲ applications and case studies

10 routing vehicles in the real world: applications in the solid waste,

10.1 introduction

10.2 computerized vehicle routing in the solid waste industry

10.2.1 history

10.2.2 background

10.2.3 commercial collection

10.2.4 residential collection

10.2.5 case studies

10.2.6 roll-on-roll-off

10.2.7 further remarks

10.3 vehicle routing in the beverage, food, and dairy industries

10.3.1 introduction

10.3.2 beverage industry

10.3.3 food industry

10.3.4 dairy industry

10.4 distribution and routing in the newspaper industry

10.4.1 industry background

10.4.2 newspaper distribution problem

10.4.3 vehicle routing algorithms for ndp

10.4.4 three case studies

10.4.5 further remarks

10.5 conclusions

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11 capacitated arc routing problem with vehicle-site dependencies: the philadelphia experience

11.1 introduction

11.2 networks, assumptions, and goals of the carp-vsd

11.2.1 travel network

11.2.2 service network

11.2.3 vehicle classes

11.2.4 travel network and service network for a vehicle class

11.2.5 vehicle preference list

11.2.6 other assumptions

11.2.7 goals and constraints of the carp-vsd

11.3 vehicle decomposition algorithm (vda)

11.3.1 step a. create and verify vehicle class networks

11.3.2 step b. estimate total work and determine initial fleet mix

11.3.3 step c. partition the service network

11.3.4 step d. determine travel path and balance the partitions

11.3.5 step e. revise estimate of total work and adjust fleet mix

11.4 implementation of the vda in philadelphia

11.5 enhancements and extensions

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12 inventory routing in practice

12.1 introduction

12.2 problem definition

12.3 literature review

12.4 solution approach

12.4.1 phase i: integer programming model

12.4.2 phase i: solving the integer programming model

12.4.3 phase ii: scheduling

12.5 computational experience

12.5.1 instances

12.5.2 solution quality

12.5.3 alternate heuristic

12.5.4 computational experiments

12.6 conclusion

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13 routing under uncertainty: an application in the scheduling of field service engineers

13.1 introduction

13.2 vrpsst with variable costs of recourse

13.3 literature review

13.3.1 vrpst

13.3.2 vrpsd

13.4 stochastic integer vrpsst formulation

13.4.1 first-stage problem

13.4.2 second-stage problem

13.5 paired tree search algorithm (ptsa)

13.5.1 linked trees

13.5.2 lower bounds

13.5.3 computational implementation

13.6 applied maintenance scheduling problem

13.6.1 maintenance scheduling system in practice

13.6.2 stochastic problem setting

13.7 modeling the applied problem as a vrpsst

13.8 model input

13.8.1 job locations and the road network

13.8.2 service times

13.9 model output: computational considerations

13.9.1 framework for the analysis of results

13.9.2 reoptimization

13.10 example scenario

13.11 overall computational results

13.12 conclusion

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14 evolution of microcomputer-based vehicle routing software: case studies in the united states

14.1 introduction

14.2 definition of the vrp

14.2.1 customer specification

14.2.2 product specification

14.2.3 vehicle specification

14.3 algorithms

14.4 future trends in vehicle routing software

14.5 summary and conclusions

bibliography

index

in the field of combinatorial optimization problems, the vehicle routing problem (vrp) is one of the most challenging. defined more than 40 years ago, the problem involves designing the optimal set of routes for fleets of vehicles for the purpose of serving a given set of customers . interest in vrp is motivated by its practical relevance as well as its considerable difficulty. 　　the vehicle routing problem covers both exact and heuristic methods developed for the vrp and some of its main variants, emphasizing the practical issues common to vrp. the book is composed of three parts containing contributions from well-known experts. the first part covers basic vrp, known more commonly as capacitated vrp. the second part covers three main variants of vrp: with time windows, backhauls, and pickup and delivery. the third part covers issues arising in real-world vrp applications and includes both case studies and references to software packages. 　　this book will be of interest to both researchers and graduate-level students in the communities of operations research and mathematical sciences. it focuses on a specific family of problems while offering a complete overview of the effective use of the most important techniques proposed for the solution of hard combinatorial problems. practitioners will find this book particularly useful. 　　reader need a basic knowledge of the main methods for the solution of combinatorial optimization problems.