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The Vehicle Routing Problem with Transhipment Facilities

Author

Listed:
  • Roberto Baldacci

    (Department of Electrical, Electronic, and Information Engineering, University of Bologna, 47521 Cesena, Italy)

  • Sandra Ulrich Ngueveu

    (LAAS–CNRS, Université de Toulouse, CNRS, INP, F-31400 Toulouse, France)

  • Roberto Wolfler Calvo

    (Laboratoire d’Informatique de Paris Nord, Université de Paris 13, 93430 Villetaneuse, France; and Sorbonne Paris Cité, CNRS (UMR 7030), 93430 Villetaneuse, France)

Abstract

This paper proposes an exact method for solving an optimization problem arising in several distribution networks where customers can be served directly, using vehicle routes from a central depot, or through transhipment facilities. The problem consists of optimizing the following inter-dependent decisions: selecting transhipment facilities, allocating customers to these facilities, and designing vehicle routes emanating from a central depot to minimize the total distribution cost. This problem is called the Vehicle Routing Problem with Transhipment Facilities ( vrptf ). The paper describes two integer-programming formulations for the vrptf , i.e., an edge-flow based formulation and a Set Partitioning (SP) based formulation. The LP-relaxation of the two formulations are further strengthened by the addition of different valid inequalities. We also describe two new route relaxations used by dual ascent heuristics to find near-optimal dual solutions of LP-relaxation of the SP model. The valid inequalities and the route relaxations are used in a branch-and-cut-and-price approach to solve the problem to optimality. The proposed method is tested on a large family of instances, including real-world examples. The computational results obtained indicate the effectiveness of the proposed method.

Suggested Citation

  • Roberto Baldacci & Sandra Ulrich Ngueveu & Roberto Wolfler Calvo, 2017. "The Vehicle Routing Problem with Transhipment Facilities," Transportation Science, INFORMS, vol. 51(2), pages 592-606, May.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:2:p:592-606
    DOI: 10.1287/trsc.2016.0711
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    References listed on IDEAS

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    1. Van Belle, Jan & Valckenaers, Paul & Cattrysse, Dirk, 2012. "Cross-docking: State of the art," Omega, Elsevier, vol. 40(6), pages 827-846.
    2. Michael Drexl, 2012. "Synchronization in Vehicle Routing---A Survey of VRPs with Multiple Synchronization Constraints," Transportation Science, INFORMS, vol. 46(3), pages 297-316, August.
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    4. Mads Jepsen & Simon Spoorendonk & Stefan Ropke, 2013. "A Branch-and-Cut Algorithm for the Symmetric Two-Echelon Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 47(1), pages 23-37, February.
    5. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti & Roberto Wolfler Calvo, 2013. "An Exact Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem," Operations Research, INFORMS, vol. 61(2), pages 298-314, April.
    6. Roberto Baldacci & Aristide Mingozzi & Roberto Wolfler Calvo, 2011. "An Exact Method for the Capacitated Location-Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1284-1296, October.
    7. Hà, Minh Hoàng & Bostel, Nathalie & Langevin, André & Rousseau, Louis-Martin, 2013. "An exact algorithm and a metaheuristic for the multi-vehicle covering tour problem with a constraint on the number of vertices," European Journal of Operational Research, Elsevier, vol. 226(2), pages 211-220.
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    Cited by:

    1. Guo, Chaojie & Thompson, Russell G. & Foliente, Greg & Kong, Xiang T.R., 2021. "An auction-enabled collaborative routing mechanism for omnichannel on-demand logistics through transshipment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 146(C).
    2. Chen, Cheng & Demir, Emrah & Huang, Yuan, 2021. "An adaptive large neighborhood search heuristic for the vehicle routing problem with time windows and delivery robots," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1164-1180.

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