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The vehicle routing problem with hard time windows and stochastic service times

Author

Listed:
  • F. Errico

    (CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, GERAD Group for Research in Decision Analysis
    École de Technologie Supérieure de Montréal)

  • G. Desaulniers

    (GERAD Group for Research in Decision Analysis
    École Polytechnique de Montréal)

  • M. Gendreau

    (École Polytechnique de Montréal
    CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation)

  • W. Rei

    (CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation
    Université du Québec à Montréal)

  • L.-M. Rousseau

    (École Polytechnique de Montréal
    CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation)

Abstract

In this paper we consider the vehicle routing problem with hard time windows and stochastic service times (VRPTW-ST); in this variant of the classic VRPTW the service times are random variables. In particular, given a set of vehicle routes, some of the actual service times might not lead to a feasible solution, given the customer time windows. We consider a chance-constrained program to model the VRPTW-ST and provide a new set partitioning formulation that includes a constraint on the minimum success probability of the set of vehicle routes. Under some mild conditions, we develop a method to exactly compute the success probability of the routes. We then solve the VRPTW-ST by a branch-price-and-cut algorithm, where the main challenges are in the solution of the subproblems of the column generation procedure. We adapt the dynamic programming algorithm to account for the probabilistic resource consumption by extending the label dimension and by providing new dominance rules. Extensive computational experiments prove the effectiveness of both the solution method and the stochastic model.

Suggested Citation

  • F. Errico & G. Desaulniers & M. Gendreau & W. Rei & L.-M. Rousseau, 2018. "The vehicle routing problem with hard time windows and stochastic service times," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 223-251, September.
    • Handle: RePEc:spr:eurjtl:v:7:y:2018:i:3:d:10.1007_s13676-016-0101-4
    DOI: 10.1007/s13676-016-0101-4
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    References listed on IDEAS

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    4. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
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    8. Sebastián Dávila & Miguel Alfaro & Guillermo Fuertes & Manuel Vargas & Mauricio Camargo, 2021. "Vehicle Routing Problem with Deadline and Stochastic Service Times: Case of the Ice Cream Industry in Santiago City of Chile," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
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    10. Alexandre M. Florio & Richard F. Hartl & Stefan Minner & Juan-José Salazar-González, 2021. "A Branch-and-Price Algorithm for the Vehicle Routing Problem with Stochastic Demands and Probabilistic Duration Constraints," Transportation Science, INFORMS, vol. 55(1), pages 122-138, 1-2.
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    12. Julio C. Londoño & Rafael D. Tordecilla & Leandro do C. Martins & Angel A. Juan, 2021. "A biased-randomized iterated local search for the vehicle routing problem with optional backhauls," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 387-416, July.
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