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The Shortest Path Problem with Time Windows and Linear Waiting Costs

Author

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  • Guy Desaulniers

    (Groupe d'Études et de Recherche en Analyse des Décisions and École Polytechnique, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec H3T 2A7, Canada)

  • Daniel Villeneuve

    (Groupe d'Études et de Recherche en Analyse des Décisions and École Polytechnique, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec H3T 2A7, Canada)

Abstract

This paper considers the shortest path problem with waiting costs (SPWC) as an extension to the shortest path problem with time windows. The problem consists of finding the minimum cost path in a network, where cost and time are two independent quantities associated with a path. Path feasibility is constrained by time windows at each node and a linear cost penalty is imposed for each unit of time spent waiting along the path. Starting from a known, nonlinear, integer programming formulation, we propose two alternative formulations for which algorithms already exist. First, we indicate how to transform the SPWC into a shortest path problem with time windows and linear node costs. Second, we prove that the SPWC can also be formulated as a two-resource generalized shortest path problem with resource constraints. Computational results used to compare these alternative formulations are presented.

Suggested Citation

  • Guy Desaulniers & Daniel Villeneuve, 2000. "The Shortest Path Problem with Time Windows and Linear Waiting Costs," Transportation Science, INFORMS, vol. 34(3), pages 312-319, August.
    • Handle: RePEc:inm:ortrsc:v:34:y:2000:i:3:p:312-319
    DOI: 10.1287/trsc.34.3.312.12298
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    References listed on IDEAS

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    1. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. 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.
    4. Moshe Dror, 1994. "Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW," Operations Research, INFORMS, vol. 42(5), pages 977-978, October.
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    Cited by:

    1. Nagih, Anass & Soumis, Francois, 2006. "Nodal aggregation of resource constraints in a shortest path problem," European Journal of Operational Research, Elsevier, vol. 172(2), pages 500-514, July.
    2. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    3. Arslan, Okan & Yıldız, Barış & Karaşan, Oya Ekin, 2015. "Minimum cost path problem for Plug-in Hybrid Electric Vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 123-141.
    4. G Ioannou & M N Kritikos, 2004. "A synthesis of assignment and heuristic solutions for vehicle routing with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 2-11, January.
    5. Y-L Chen & L-J Hsiao & K Tang, 2003. "Time analysis for planning a path in a time-window network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 860-870, August.
    6. Albiach, José & Sanchis, José Marí­a & Soler, David, 2008. "An asymmetric TSP with time windows and with time-dependent travel times and costs: An exact solution through a graph transformation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 789-802, September.
    7. Katrin Heßler & Stefan Irnich, 2023. "Partial Dominance in Branch-Price-and-Cut for the Basic Multicompartment Vehicle-Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 50-65, January.
    8. Katrin Heßler & Stefan Irnich, 2021. "Partial Dominance in Branch-Price-and-Cut for the Basic Multi-Compartment Vehicle-Routing Problem," Working Papers 2115, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

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