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A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem

Author

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  • Ahmed Hadjar

    (Département de mathématiques et génie industriel, École Polytechnique de Montréal, C.P. 6079, succursale Centre-ville, Montréal, Québec, Canada H3C 3A7)

  • Odile Marcotte

    (Département d’informatique, Université du Québec à Montréal, C.P. 8888, succursale Centre-ville, Montréal, Québec, Canada H3C 3P8)

  • François Soumis

    (Département de mathématiques et génie industriel, École Polytechnique de Montréal, C.P. 6079, succursale Centre-ville, Montréal, Québec, Canada H3C 3A7)

Abstract

We consider the multiple depot vehicle scheduling problem (MDVSP) and propose a branch-and-bound algorithm for solving it that combines column generation, variable fixing, and cutting planes. We show that the solutions of the linear relaxation of the MDVSP contain many “odd cycles.” We derive a class of valid inequalities by extending the notion of odd cycle and describe a lifting procedure for these inequalities. We prove that the lifted inequalities represent, under certain conditions, facets of the underlying polytope. Finally, we present the results of a computational study comparing several strategies (variable fixing, cutting planes, mixed branching, and tree search) for solving the MDVSP.

Suggested Citation

  • Ahmed Hadjar & Odile Marcotte & François Soumis, 2006. "A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 54(1), pages 130-149, February.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:1:p:130-149
    DOI: 10.1287/opre.1050.0240
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    References listed on IDEAS

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    1. Matteo Fischetti & Andrea Lodi & Silvano Martello & Paolo Toth, 2001. "A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems," Management Science, INFORMS, vol. 47(6), pages 833-850, June.
    2. Celso C. Ribeiro & François Soumis, 1994. "A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 42(1), pages 41-52, February.
    3. Forbes, M. A. & Holt, J. N. & Watts, A. M., 1994. "An exact algorithm for multiple depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 72(1), pages 115-124, January.
    4. Desaulniers, Guy & Lavigne, June & Soumis, Francois, 1998. "Multi-depot vehicle scheduling problems with time windows and waiting costs," European Journal of Operational Research, Elsevier, vol. 111(3), pages 479-494, December.
    5. Niklas Kohl & Jacques Desrosiers & Oli B. G. Madsen & Marius M. Solomon & François Soumis, 1999. "2-Path Cuts for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 33(1), pages 101-116, February.
    Full references (including those not matched with items on IDEAS)

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