Search

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. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 71971177, 71725001, U1811462], Research Grants Council of Hong Kong SAR, China [Grant 15221619], and Guangdong Basic and Applied Basic Research Foundation [Grant 2023A1515030260]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2021.0193. The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0193) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0193). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]