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The Edge Set Cost of the Vehicle Routing Problem with Time Windows

Author

Listed:
  • Line Blander Reinhardt

    (Department of Management Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark)

  • Mads Kehlet Jepsen

    (Department of Management Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark)

  • David Pisinger

    (Department of Management Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark)

Abstract

We consider an important generalization of the vehicle routing problem with time windows in which a fixed cost must be paid for accessing a set of edges. This fixed cost could reflect payment for toll roads, investment in new facilities, the need for certifications, and other costly investments. The certifications and investments impose a cost for the company while they also give unlimited usage of a set of roads to all vehicles belonging to the company.This violates the traditional assumption that the path between two destinations is well defined and independent of other choices. Different versions for defining the edge sets are discussed and formulated. Both the multigraph case and the direct path case are described, and mixed-integer-programming formulations of the problem are presented for both cases. A solution method based on branch-price-and-cut is applied to the direct path case. The computational results show that instances with up to 40 customers can be solved in a reasonable time, and that the branch-cut-and-price algorithm generally outperforms CPLEX.

Suggested Citation

  • Line Blander Reinhardt & Mads Kehlet Jepsen & David Pisinger, 2016. "The Edge Set Cost of the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 50(2), pages 694-707, May.
    • Handle: RePEc:inm:ortrsc:v:50:y:2016:i:2:p:694-707
    DOI: 10.1287/trsc.2015.0620
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    References listed on IDEAS

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    Cited by:

    1. 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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