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.
@article{arxiv.1202.5797,
title = {Stochastic Vehicle Routing with Recourse},
author = {Inge Li Goertz and Viswanath Nagarajan and Rishi Saket},
journal= {arXiv preprint arXiv:1202.5797},
year = {2012}
}
Comments
20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.2