Strategic Allocation of Time Windows in Vehicle Routing Problems under Uncertainty

We consider the problem of allocating long-term delivery time windows to customers in the context of vehicle routing operations. Once the time windows have been assigned, the distributor must attempt to meet them on a daily basis as well as possible. Given that operational parameters, such as customer demands or travel times, vary from day to day, assigning time windows in a way that minimizes the expected routing costs is non-trivial. This problem can be modeled as a two-stage stochastic program where the time window assignments constitute first-stage decisions and the optimal vehicle routes constitute secondstage decisions that depend on the realizations of the uncertain parameters. We show that a sampled deterministic equivalent of this stochastic model can be reduced to a variant of a large class of problems known as Consistent Vehicle Routing Problems in the literature. We adapt an algorithmic framework we had previously developed for the latter class of problems and solve to guaranteed optimality instances of the former. Our approach is highly competitive when compared to the previous state-of-the-art as it achieves the fastest computation time on all literature benchmark instances. Moreover, and in contrast to existing approaches, we can readily incorporate uncertainty in customer presence and travel times.