Truck synchronization at single door cross-docking terminals

We address the problem of synchronizing the loading and discharging operations of trucks at a particular cross-docking center, with one door at both the inbound and outbound sides, aiming at minimizing the makespan of the whole process. We propose a mixed integer linear model and a Lagrangian decomposition scheme. We derive conditions for optimally solving both the Lagrangian relaxation and the dual problems. Based on the theoretical results, we propose a Lagrangian heuristic for computing many feasible solutions and gathering the best one among them. An extensive computational experience validates our Lagrangian heuristic, also in comparison with a state-of-the-art benchmark solver and a heuristic algorithm from the literature.