A robust optimization approach for the vehicle routing problem with cross-docking under demand uncertainty

This research addresses the Vehicle Routing Problem with Cross-docking under Demand Uncertainty (VRPCD-DU) where a set of homogeneous vehicles is used to transport orders from the suppliers to the corresponding customers via a cross-dock. VRPCD-DU considers customer demand volumes as random variables and determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. A robust optimization counterpart of a deterministic VRPCD formulation is derived where support for the demand is a polyhedral set. The robust formulation can only be used to solve small VRPCD-DU instances, and an effective adaptive large neighborhood search (ALNS) algorithm is proposed for solving large instances. Extensive numerical experiments are conducted on benchmark sets for both VRPCD and VRPCD-DU. The results show that the ALNS algorithm computes new best-known solutions of the VRPCD benchmark instances. Moreover, demand uncertainty is extensively analyzed by investigating managerial insights. The price of robustness (PoR) is compared by considering various budget sets and alternative partitioning methods for the customers (i.e., "random" and "clustered"). The findings imply that a higher probability of capacity constraints' violation is generally observed for the suppliers and that customer partitioning methods share similar PoR.