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

2026-01-05

arXiv.org

AI Summary

This study addresses the Multi-Depot Split Delivery Vehicle Routing Problem (MD-SDVRP), which seeks to minimize total routing costs under multiple depots, vehicle capacity constraints, and splittable customer demands. For the case of a constant number of depots, the paper presents the first improvement over the long-standing 6-approximation algorithm, achieving a (6 − 2×10⁻³⁶)-approximation and thereby breaking the previous approximation barrier. Furthermore, it introduces novel constant-factor, parameterized (with respect to the number of depots and vehicle capacity), and bi-criteria approximation algorithms that apply even when the number of depots is non-constant. By integrating techniques from combinatorial optimization and approximation algorithm design, the work establishes a more general and efficient framework for approximating solutions to this challenging logistics problem.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Multiple-Depot
• Split Delivery
• Vehicle Routing Problem
• Approximation Algorithms
• Logistics

Innovation

• approximation algorithms
• vehicle routing
• split delivery
• multiple depots
• combinatorial optimization