A Robust Optimization Approach for the Capacitated Vehicle Routing Problem with Demand Uncertainty∗

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. We present computational results that investigate the trade-offs of a robust solution for the Augerat et al. suite of capacitated VRP problems and for families of clustered instances. Our computational results show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most profound for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We observe that the robust solution amounts to a clever management of the remaining vehicle capacity. ∗Research supported by NSF under grant CMS-0409887 †Corresponding author