The truck scheduling problem at cross-docking terminals

Cross docking is a warehouse management concept in which items delivered to a warehouse by inbound trucks are immediately sorted out, reorganized based on customer demands and loaded into outbound trucks for delivery to customers, without requiring excessive inventory at the warehouse. Compared to traditional warehousing, the storage as well as the length of the stay of a product in the warehouse is limited, which requires an appropriate coordination of inbound and outbound trucks. The truck scheduling problem, which decides on the succession of truck processing at the dock doors, is especially important to ensure a rapid turnover and on-time deliveries. The problem studied in this paper concerns the operational level: trucks are allocated to the different docks so as to minimize the storage usage during the product transfer. The internal organization of the warehouse is not explicitly taken into consideration. We also do not model the resources that may be needed to load or unload the trucks, which implies the assumption that these resources are available in sufficient quantities to ensure the correct execution of an arbitrary docking schedule. The concept of cross docking has received a lot of attention in recent literature: cases with one receiving and one shipping door are most frequently studied. A comprehensive overview of different variations and the existing literature can be found in Boysen and Fliedner (2010). Carlo and Bozer (2011) state that in a typical cross-dock application, each dock serves exclusively either as an outbound dock or as an inbound dock throughout the schedule’s execution; this is called the exclusive mode. Their experiments show that clustering the inbound docks together and the outbound docks together is generally not a good configuration when minimizing the travel distance of the forklifts inside the warehouse. For this reason, we study the more general case in which each dock can be used both for loading and unloading; this is referred to as the mixed mode. In the following section, a detailed problem statement is given. A time-indexed (linear programming) formulation is presented in Section 3. Section 4 describes a branch-andbound algorithm, and Section 5 summarizes our contributions.