Improved Approximation Algorithms for the Multiple-Depot Split Delivery Vehicle Routing Problem

TL;DR

This paper presents improved approximation algorithms for the complex multiple-depot split delivery vehicle routing problem, achieving better cost ratios and extending applicability beyond constant numbers of depots.

Contribution

It introduces a nearly 6-approximation algorithm for MD-SDVRP and develops algorithms that work for more depots and various parameters, surpassing prior results.

Findings

Achieved a (6 - 2×10^{-36})-approximation ratio.

Developed algorithms for non-constant number of depots.

Provided parameterized and bi-factor approximation algorithms.

Abstract

The Multiple-Depot Split Delivery Vehicle Routing Problem (MD-SDVRP) is a challenging problem with broad applications in logistics. The goal is to serve customers' demand using a fleet of capacitated vehicles located in multiple depots, where each customer's demand can be served by more than one vehicle, while minimizing the total travel cost of all vehicles. We study approximation algorithms for this problem. Previously, the only known result was a $6$-approximation algorithm for a constant number of depots (INFORMS J. Comput. 2023), and whether this ratio could be improved was left as an open question. In this paper, we resolve it by proposing a $(6-2\cdot 10^{-36})$-approximation algorithm for this setting. Moreover, we develop constant-factor approximation algorithms that work beyond a constant number of depots, improved parameterized approximation algorithms related to the vehicle capacity and the number of depots, as well as bi-factor approximation algorithms.