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Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows

Author

Listed:
  • Stefan Ropke

    (Department of Transport, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

  • Jean-François Cordeau

    (HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal H3T 2A7, Canada)

Abstract

In the pickup and delivery problem with time windows vehicle routes must be designed to satisfy a set of transportation requests, each involving a pickup and delivery location, under capacity, time window, and precedence constraints. This paper introduces a new branch-and-cut-and-price algorithm in which lower bounds are computed by solving through column generation the linear programming relaxation of a set partitioning formulation. Two pricing subproblems are considered in the column generation algorithm: an elementary and nonelementary shortest path problem. Valid inequalities are added dynamically to strengthen the relaxations. Some of the previously proposed inequalities for the pickup and delivery problem with time windows are also shown to be implied by the set partitioning formulation. Computational experiments indicate that the proposed algorithm outperforms a recent branch-and-cut algorithm.

Suggested Citation

  • Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
    • Handle: RePEc:inm:ortrsc:v:43:y:2009:i:3:p:267-286
    DOI: 10.1287/trsc.1090.0272
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    References listed on IDEAS

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