Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty

We examine the robust counterpart of the classical capacitated vehicle routing problem (CVRP). We consider two types of uncertainty sets for the customer demands: the classical budget polytope and a partitioned budget polytope. We show that using the set-partitioning formulation it is possible to reformulate our problem as a deterministic heterogeneous vehicle routing problem. Thus, many state-of-the-art techniques for exactly solving deterministic VRPs can be applied to the robust counterpart, and a modern branch-cut-and-price algorithm can be adapted to our setting by keeping the number of pricing subproblems strictly polynomial. More importantly, we introduce new techniques to significantly improve the efficiency of the algorithm. We present analytical conditions under which a pricing subproblem is infeasible. This result is general and can be applied to other combinatorial optimization problems with knapsack uncertainty. We also introduce robust capacity cuts that are provably stronger than the ones known in the literature. Finally, a fast-iterated local search algorithm is proposed to obtain heuristic solutions for the problem. Using our branch-cut-and-price algorithm incorporating existing and new techniques, we solve to optimality all but one of the open instances from the literature.