Robust vehicle routing under uncertainty via branch-price-and-cut

This paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate "partially robust" vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.