Robust cross-dock scheduling with time windows

• We propose robust methods for the crossdock truck scheduling problem with time windows.
• Methods from the field ofrobust project scheduling are succesfully applied to the cross-docking case.
• The methods based on the redundancy of doors give the best results.

Cross-docking is a logistic technique that helps to accelerate the goods flow and to reduce inventory costs; but it requires a perfect coordination of the inbound and outbound trucks. The truck scheduling problem has been studied by many authors, but mainly in a deterministic case. And yet, many uncertainties can arise in the process: if a truck is delayed, or the process times change, does the truck schedule remain feasible and stable? This article proposes robust models for the truck scheduling model with time windows. The reformulations of the original model are based on classical techniques in robust optimization (minimax and minimization of the expected regret) but also on techniques from robust project scheduling (resource redundancy and time redundancy). The numerical study carried out to compare the nine different models shows that the methods based on resource redundancy give good results in the cross-docking case. Minimizing the average number of trucks docked at a given door is a good way to ensure robustness in the schedule, but it also increases storage.