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

EURO Journal on Transportation and Logistics volume 7, pages 223–251 (2018)Cite this article

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.

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Authors and Affiliations

  1. CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, GERAD Group for Research in Decision Analysis, Montreal, Canada

    F. Errico

  2. Département de génie de la construction, École de Technologie Supérieure de Montréal, Montreal, Canada

    F. Errico

  3. GERAD Group for Research in Decision Analysis, Montreal, Canada

    G. Desaulniers

  4. Département de mathématiques et génie industriel, École Polytechnique de Montréal, Montreal, Canada

    G. Desaulniers, M. Gendreau & L.-M. Rousseau

  5. CIRRELT Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montreal, Canada

    M. Gendreau, W. Rei & L.-M. Rousseau

  6. Département de management et de technologie, Université du Québec à Montréal, Montreal, Canada

    W. Rei

Authors
  1. F. Errico
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  2. G. Desaulniers
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  3. M. Gendreau
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  4. W. Rei
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  5. L.-M. Rousseau
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Correspondence to F. Errico.

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Errico, F., Desaulniers, G., Gendreau, M. et al. The vehicle routing problem with hard time windows and stochastic service times. EURO J Transp Logist 7, 223–251 (2018). https://doi.org/10.1007/s13676-016-0101-4

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  • DOI: https://doi.org/10.1007/s13676-016-0101-4

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