Resource-robust valid inequalities for vehicle routing and related problems

Branch-price-and-cut algorithms play an important role in solving many vehicle routing problems (VRPs). Adding valid inequalities in this framework can impact the pricing subproblem, for which the literature distinguishes between ‘robust’ and ‘non-robust’ cuts. We define the ‘robust application’ of a cut in a specific context, making this distinction more precise. Next, we define broader ‘resource-robust applications’ that can be handled efficiently in the subproblem. We then introduce new resource-robust valid inequalities and show computational benefits for the capacitated VRP.