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An Approximation Algorithm for k -Depot Split Delivery Vehicle Routing Problem

Author

Listed:
  • Xiaofan Lai

    (Institute of Big Data Intelligent Management and Decision, College of Management, Shenzhen University, Shenzhen 518055, China)

  • Liang Xu

    (School of Business Administration, The Southwestern University of Finance and Economics, Chengdu 611130, China)

  • Zhou Xu

    (Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong, China)

  • Yang Du

    (School of Business Administration, The Southwestern University of Finance and Economics, Chengdu 611130, China)

Abstract

A multidepot capacitated vehicle routing problem aims to serve customers’ demands using a fleet of capacitated vehicles located in multiple depots, such that the total travel cost of the vehicles is minimized. We study a variant of this problem, the k -depot split delivery vehicle routing problem (or k -DSDVRP in short), for the situation where each customer’s demand can be served by more than one vehicle, and the total number of depots, denoted by k ≥ 2 , is a fixed constant. This is a challenging problem with broad applications in the logistics industry, for which no constant ratio approximation algorithm is known. We develop a new approximation algorithm for the k -DSDVRP, ensuring an approximation ratio of ( 6 − 4 / k ) and a polynomial running time for any fixed constant k ≥ 2 . To achieve this, we propose a novel solution framework based on a new relaxation of the problem, a cycle splitting procedure, and a vehicle assignment procedure. To further enhance its efficiency for practical usage, we adapt the newly developed approximation algorithm to a heuristic, which runs in polynomial time even when k is arbitrarily large. Experimental results show that this heuristic outperforms a commercial optimization solver and a standard vehicle routing heuristic. Moreover, our newly proposed solution framework can be applied to developing new constant ratio approximation algorithms for several other variants of the k -DSDVRP with k ≥ 2 being a fixed constant.

Suggested Citation

  • Xiaofan Lai & Liang Xu & Zhou Xu & Yang Du, 2023. "An Approximation Algorithm for k -Depot Split Delivery Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1179-1194, September.
  • Handle: RePEc:inm:orijoc:v:35:y:2023:i:5:p:1179-1194
    DOI: 10.1287/ijoc.2021.0193
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    References listed on IDEAS

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