An Approximation Algorithm for

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/ .