Truck scheduling in cross-docking terminals with fixed outbound departures

At a cross-docking terminal, inbound shipments are directly transshipped across the terminal to designated outbound trucks, so that delays and inventories are kept as low as possible. We consider an operational truck scheduling problem, where a dock door and a start time have to be assigned to each inbound truck. A set of outbound trucks is scheduled beforehand and, therefore, departure times are fixed. If a shipment is not unloaded, transshipped to the outbound gate and loaded onto the designated outbound truck before its departure, we consider the shipments's value as lost profit. The objective is to minimize total lost profit. This paper at hand formalizes the resulting truck scheduling problem. We settle its computational complexity and develop heuristics (namely, decomposition procedures and simulated annealing) in order to tackle the problem. We show the efficiency of these heuristics by means of a computational study. Last but not least, a case study is presented.