Multi-door cross-dock scheduling under flexible doors mode and material handling resource restrictions

Abstract

Cross-docks are used in distribution networks to improve efficiency by minimizing the need for warehouse space and optimizing the supply chain. Cross-docks are primarily implemented for consolidating less-than-truckload shipments to realize gains from economies of scale in transportation. This is accomplished by scheduling inbound truck arrivals to the strip doors where their freight is either moved directly to outbound trucks parked at the stack doors or held for a very short time waiting for the assigned outbound truck to arrive. This research focuses on two important operating dimensions of cross-docks. The first is the decision to preassign each door in the cross-dock to either be used for strip or stack operations exclusively (separate door operations) or dynamically assign doors for strip or stack operations as needed (mixed door operations). The second examines assigning material handling devices (e.g., forklifts) to various tasks to make the cross-dock operate efficiently and achieve the required high throughput. A mathematical programming model of mixed door operation is developed and compared with a separate doors model that exists in the literature. A second mathematical programming model is presented that has finite material handling capacity and explicitly models the unloading and loading tasks. To improve computation times, a convex hull formulation of the separate-door model is developed and compared with the widely used Big-M method. Simulated annealing based algorithms are developed to solve cross-dock problems for medium to largescale instances. An integrated simulated annealing algorithm decodes a genotypic representation for the restricted material handling model’s solution to assign doors and forklifts to trucks simultaneously via a series of operating rules. Simulated annealing is used to improve the resultant forklift assignments from the integrated method to produce an upper bound for the limited material handling problem. Numerical results provide important insights into improved delivery times associated with using a mixed door strategy in certain situations. Additionally, results indicate transition points exist that allow decision makers to determine the minimum number of forklifts required for various cross-dock sizes to avoid bottleneck delays.