Approximation Algorithms for Vehicle Routing Problems with Stochastic Demands on Trees

TL;DR

This paper develops approximation algorithms for the vehicle routing problem with stochastic demands on trees, providing guarantees for split and un-split delivery scenarios, optimizing expected route length.

Contribution

It introduces the first approximation algorithms with provable guarantees for VRPSD on trees, addressing both split and un-split delivery cases.

Findings

Achieves a 2-approximation for split-delivery VRPSD

Achieves a 3-approximation for un-split delivery VRPSD

Provides theoretical bounds for stochastic vehicle routing on trees

Abstract

We consider the vehicle routing problem with stochastic demands (VRPSD) on tree structured networks with a single depot. The problem we are concerned with in this paper is to find a set of tours for the vehicle with minimum expected length. Every tour begins at the depot, visits a subset of customers and returns to the depot without violating the capacity constraint. Randomized approximation algorithm achieving approximation guarantees of 2 for split-delivery VRPSD, and 3 for un-split delivery VRPSD are obtained.