New formulations for the robust vehicle routing problem with time windows under demand and travel time uncertainty

We present new formulations for the robust vehicle routing problem with time windows (RVRPTW) under cardinality- and knapsack-constrained demand and travel time uncertainty. They are the first compact models to address the RVRPTW under travel time uncertainty while considering the knapsack uncertainty set. Moreover, our models employ different types of constraints to control time propagation based on Miller–Tucker–Zemlin and single commodity flow constraints, which are derived from the linearization of recursive equations. We develop branch-and-cut methods based on the proposed formulations, leveraging a dynamic programming algorithm to verify the robust feasibility of solutions concerning both demand and travel time uncertainty, in addition to specific and standard separation procedures from the literature. We present detailed computational results on RVRPTW benchmark instances to compare the performance of our models and algorithms. Furthermore, we evaluate the impact and advantages of implementing each studied uncertainty set.