Optimization Models for the Vehicle Routing Problem under Disruptions

Kai Huang () and Michael Xu
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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

Mathematics, 2023, vol. 11, issue 16, 1-21

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.

Keywords: vehicle routing problem; disruption; expected delivery; multi-period; split delivery; mixed-integer programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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