Approximating the chance-constrained capacitated vehicle routing problem with robust optimization

The Capacitated Vehicle Routing Problem (CVRP) is a classical combinatorial optimization problem that aims to serve a set of customers, using a set of identical vehicles, satisfying the vehicle capacities, and minimizing the total traveling distance. Among the possible approaches to extend the CVRP for handling uncertain demands, we highlight the robust optimization with budgeted uncertainty, and chance-constrained optimization. Another simpler and often omitted option is to apply the deterministic CVRP model over augmented demands in such a way to reduce the capacity violation probability. In this paper, we propose a suitable way to adjust the input data of both the deterministic CVRP and the robust CVRP with budgeted uncertainty so that the corresponding output approximates the chance-constrained CVRP for the case of independently normally distributed demands. In order to test our approach, we present quite extensive experiments showing that it leads to very small deviations with respect to the optimal chance-constrained solutions, and that the robust model brings significant benefits with respect to the deterministic one. In order to optimally solve the proposed chance-constrained benchmark instances, we also introduce a new technique to tighten a family of known inequalities for this problem.