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An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems
Author(s) -
Feillet Dominique,
Dejax Pierre,
Gendreau Michel,
Gueguen Cyrille
Publication year - 2004
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20033
Subject(s) - column generation , shortest path problem , path (computing) , routing (electronic design automation) , vehicle routing problem , computer science , mathematical optimization , computation , k shortest path routing , longest path problem , constrained shortest path first , algorithm , mathematics , theoretical computer science , graph , computer network , programming language
In this article, we propose a solution procedure for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). A relaxed version of this problem in which the path does not have to be elementary has been the backbone of a number of solution procedures based on column generation for several important problems, such as vehicle routing and crew pairing. In many cases relaxing the restriction of an elementary path resulted in optimal solutions in a reasonable computation time. However, for a number of other problems, the elementary path restriction has too much impact on the solution to be relaxed or might even be necessary. We propose an exact solution procedure for the ESPPRC, which extends the classical label correcting algorithm originally developed for the relaxed (nonelementary) path version of this problem. We present computational experiments of this algorithm for our specific problem and embedded in a column generation scheme for the classical Vehicle Routing Problem with Time Windows. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 216–229 2004