New dynamic programming algorithms for the resource constrained elementary shortest path problem

The resource constrained elementary shortest path problem (RCESPP) arises as a pricing subproblem in branch‐and‐price algorithms for vehicle‐routing problems with additional constraints. We address the optimization of the RCESPP and we present and compare three methods. The first method is a well‐kn...

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Bibliographic Details
Published in:Networks Vol. 51; no. 3; pp. 155 - 170
Main Authors: Righini, Giovanni, Salani, Matteo
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.05.2008
John Wiley & Sons
Subjects:
Applied sciences
branch-and-bound
column generation
dynamic-programming
Exact sciences and technology
Logistics
Operational research and scientific management
Operational research. Management science
shortest path
vehicle-routing
Branching
Lower bound
Fleet
Branch and bound method
Vehicle routing problem
Shortest path
Routing
State space
Hybridization
State space method
Optimization
Column generation
Time window
branch-and-bound
vehicle-routing
Pricing
Capacity constraint
Dynamic programming
Resource management
dynamic-programming
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:The resource constrained elementary shortest path problem (RCESPP) arises as a pricing subproblem in branch‐and‐price algorithms for vehicle‐routing problems with additional constraints. We address the optimization of the RCESPP and we present and compare three methods. The first method is a well‐known exact dynamic‐programming algorithm improved by new ideas, such as bidirectional search with resource‐based bounding. The second method consists in a branch‐and‐bound algorithm, where lower bounds are computed by dynamic‐programming with state‐space relaxation; we show how bounded bidirectional search can be adapted to state‐space relaxation and we present different branching strategies and their hybridization. The third method, called decremental state‐space relaxation, is a new one; exact dynamic‐programming and state‐space relaxation are two special cases of this new method. The experimental comparison of the three methods is definitely favorable to decrement state‐space relaxation. Computational results are given for different kinds of resources, arising from the capacitated vehicle‐routing problem, the vehicle‐routing problem with distribution and collection, and the vehicle‐routing problem with capacities and time windows. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008
Bibliography:istex:4866757EF79C38F1F9909B4CD892F15D0A7B1114
ACSU
ArticleID:NET20212
ark:/67375/WNG-LLC3PF15-H
ISSN:0028-3045
1097-0037
DOI:10.1002/net.20212