Stochastic Vehicle Routing with Recourse

TL;DR

This paper introduces an approximation algorithm for the stochastic vehicle routing problem with recourse, achieving a logarithmic approximation ratio and establishing hardness results under the Unique Games Conjecture.

Contribution

It presents the first logarithmic approximation algorithm for StochVRP with arbitrary distributions and relates it to submodular orienteering, also improving approximation ratios for related problems.

Findings

O(log^2 n log(n λ))-approximation algorithm for StochVRP

Relation of StochVRP to knapsack rank-function orienteering

Hardness of approximation results based on the Unique Games Conjecture

Abstract

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.