📝 SummarXiv

Abstract

We study a broad class of vehicle routing problems in which the cost of a route is allowed to be any nonnegative rational value computable in polynomial time in the input size. To address this class, we introduce a unifying framework that generalizes existing integer L-shaped (ILS) formulations developed for vehicle routing problems with stochastic demands (VRPSDs). This framework and subsequent analysis allow us to generalize previous ILS cuts and pinpoint which assumptions are needed to apply those generalizations to other problems. Using these tools, we develop the first algorithm for the VRPSD in the case where the demands are given by an empirical probability distribution of scenarios - a data-driven variant that tackles a significant challenge identified in the literature: dealing with correlations. Indeed, all previous ILS-based exact algorithms for the VRPSD assume either independence of customer demands or correlations through a single external factor. This shows the potential of this generic unifying framework to be applied to a multitude of different variants of the problem.