Truck scheduling problem in a cross-docking system with release time constraint

In a supply chain, cross-docking is one of the most innovative systems for ameliorating the operational performance at distribution centers. Cross-docking is a logistics strategy in which freight is unloaded from inbound trucks and (almost) directly loaded into outbound trucks, with little or no storage in between, thus no inventory remains at the distribution center. In this study, we consider the scheduling problem of inbound and outbound trucks with multiple dock doors, aiming at the minimization of the makespan. The considered scheduling problem determines where and when the trucks must be processed; also due to the interchangeability specification of products, product assignment is done simultaneously as well. Inbound trucks enter the system according to their release times, however, there is no mandatory time constraint for outbound truck presence at a designated stack door; they should just observe their relative docking sequences. Moreover, a loading sequence is determined for each of the outbound trucks. In this research, a mathematical model is derived to find the optimal solution. Since the problem under study is NP-hard, a simulated annealing algorithm is adapted to find the (near-) optimal solution, as the mathematical model will not be applicable to solve large-scale real-world cases. Numerical examples have been done in order to specify the efficiency of the metaheuristic algorithm in comparison with the results obtained from solving the mathematical model.