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Optimization Models for the Vehicle Routing Problem under Disruptions

Author

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  • Kai Huang

    (DeGroote School of Business, McMaster University, Hamilton, ON L8S 4M4, Canada)

  • Michael Xu

    (School of Computational Science and Engineering, McMaster University, Hamilton, ON L8S 4M4, Canada)

Abstract

In this paper, we study the role of disruptions in the multi-period vehicle routing problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that at any time during the delivery phase, each vehicle could have chance to be disrupted. When a disruption happens, vehicles will be unable to continue their journeys and supplies will be unable to be delivered. We model the occurrence of disruption as a given probability and consider the multi-period expected delivery. Our objective is to either minimize the total travel cost or maximize the demand fulfillment, depending on the supply quantity. This problem is denoted as the multi-period vehicle routing problem with disruption (VRPMD). VRPMD does not deal with disruptions in real-time and is more focused on the long-term performance of a single routing plan. We first prove that the proposed VRPMD problems are NP-hard. We then present some analytical properties related to the optimal solutions to these problems. We show that Dror and Trudeau’s property does not apply in our problem setting. Nevertheless, a generalization of Dror and Trudeau’s property holds. Finally, we present efficient heuristic algorithms to solve these problems and show the effectiveness of the proposed models and algorithms through numerical studies.

Suggested Citation

  • Kai Huang & Michael Xu, 2023. "Optimization Models for the Vehicle Routing Problem under Disruptions," Mathematics, MDPI, vol. 11(16), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3521-:d:1217535
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    References listed on IDEAS

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    1. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    2. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1994. "A Tabu Search Heuristic for the Vehicle Routing Problem," Management Science, INFORMS, vol. 40(10), pages 1276-1290, October.
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    4. Stewart, William R. & Golden, Bruce L., 1983. "Stochastic vehicle routing: A comprehensive approach," European Journal of Operational Research, Elsevier, vol. 14(4), pages 371-385, December.
    5. Moshe Dror & Pierre Trudeau, 1990. "Split delivery routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 383-402, June.
    6. Sebastián Muñoz-Herrera & Karol Suchan, 2022. "Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    7. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
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    Cited by:

    1. Nur Insani & Sona Taheri & Mali Abdollahian, 2024. "A Mathematical Model for Integrated Disaster Relief Operations in Early-Stage Flood Scenarios," Mathematics, MDPI, vol. 12(13), pages 1-22, June.

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