A monolithic approach to vehicle routing and operations scheduling of a cross-dock system with multiple dock doors

• We present a monolithic formulation for the whole planning of cross-dock systems.
• The model chooses the best vehicle pickup and delivery routes.
• It also decides on the dock door allocation and the truck scheduling at the dock.
• The model includes constraints mimicking the sweep-based algorithm.
• A significant number of examples have been successfully solved.

Cross-docking is a logistic strategy for moving goods from suppliers to customers via a cross-dock terminal with no permanent storage. The operational planning of a cross-dock facility involves different issues such as vehicle routing, dock door assignment and truck scheduling. The vehicle routing problem seeks the optimal routes for a homogeneous fleet of vehicles that sequentially collects goods at pickup points and delivers them to their destinations. The truck scheduling problem deals with the timing of unloading and reloading operations at the cross-dock. This work introduces a mixed-integer linear programming formulation for the scheduling of single cross-dock systems that, in addition to selecting the pickup/delivery routes, simultaneously decides on the dock door assignment and the truck scheduling at the cross-dock. The proposed monolithic formulation is able to provide near-optimal solutions to medium-size problems involving up to 70 transportation orders, 16 vehicles and 7 strip/stack dock doors at acceptable CPU times.