The Pickup and Delivery Problem with Cross-Docking

Usual models that deal with the integration of vehicle routing and cross-docking operations impose that every vehicle must stop at the dock even if the vehicle collects and delivers the same set of goods. In order to allow vehicles to avoid the stop at the dock and thus, reduce transportation costs, we introduce the Pickup and Delivery Problem with Cross-Docking (PDPCD). An Integer Programming formulation and a Branch-and-price algorithm for the problem are discussed. Our computational results indicate that optimal or near optimal solutions for PDPCD indeed allow total costs to be significantly reduced. Due to improvements in the resolution of the pricing problems, the Branch-and-price algorithm for PDPCD works better than similar algorithms for other models in the literature.