In Capacitated Vehicle Routing with Multiple Depots (CVRP-MD) we are given a set of client locations C and a set of depots R located in a metric space with costs c(i,j) between u,v∈C∪R. Additionally, we are given a capacity bound k. The goal is to find a collection of tours of minimum total cost such that each tour starts and ends at some depot r∈R and includes at most k clients and such that each client lies on at least one tour. Our main result is a 3.9365-approximation based on rounding a new LP relaxation for CVRP-MD.
Cite
@article{arxiv.2510.05321,
title = {Approximating Multiple-Depot Capacitated Vehicle Routing via LP Rounding},
author = {Zachary Friggstad and Tobias Mömke},
journal= {arXiv preprint arXiv:2510.05321},
year = {2025}
}