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A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes

Author

Listed:
  • Ibrahim Muter

    (Bahçeşehir University, İstanbul 34353, Turkey; and Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3C 3J7, Canada)

  • Jean-François Cordeau

    (Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3C 3J7, Canada; and HEC Montréal, Quebec H3T 2A7, Canada)

  • Gilbert Laporte

    (Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3C 3J7, Canada; and HEC Montréal, Quebec H3T 2A7, Canada)

Abstract

This paper proposes a column generation algorithm for the multidepot vehicle routing problem with interdepot routes. This problem is an extension of the multidepot vehicle routing problem in which the vehicles are allowed to stop at intermediate depots along their routes to replenish. The problem can be modeled as a set covering problem in which the variables are rotations corresponding to feasible combinations of routes. We consider two pricing subproblems to generate rotations. The first one generates rotations directly by solving an elementary shortest path problem with resource constraints on a modified version of the original customer-depot network. The second one exploits the relationship between the sets of routes and rotations but results in a model with many columns. We discuss some issues related to solving this second pricing subproblem by column generation and we introduce an alternate approach to alleviate these difficulties. We show through computational experiments that the second pricing mechanism performs better than the first to compute the linear programming relaxation lower bound. We then embed it within a branch-and-bound algorithm to compute optimal integer solutions. Moreover, we assess the benefits of allowing interdepot routes in multidepot vehicle routing.

Suggested Citation

  • Ibrahim Muter & Jean-François Cordeau & Gilbert Laporte, 2014. "A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes," Transportation Science, INFORMS, vol. 48(3), pages 425-441, August.
    • Handle: RePEc:inm:ortrsc:v:48:y:2014:i:3:p:425-441
    DOI: 10.1287/trsc.2013.0489
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    References listed on IDEAS

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    10. Markov, Iliya & Varone, Sacha & Bierlaire, Michel, 2016. "Integrating a heterogeneous fixed fleet and a flexible assignment of destination depots in the waste collection VRP with intermediate facilities," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 256-273.
    11. Tânia Rodrigues Pereira Ramos & Maria Isabel Gomes & Ana Paula Barbosa-Póvoa, 2020. "A new matheuristic approach for the multi-depot vehicle routing problem with inter-depot routes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 75-110, March.
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    14. Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    15. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
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    18. Meng, Qiang & Wang, Shuaian & Lee, Chung-Yee, 2015. "A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 1-19.

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