Abstract

In a cross-dock, goods coming from numerous origins get unloaded from incoming trucks, consolidated according to their destinations, and then loaded into outgoing trucks with little or no storage in between. We study a class of cross-dock door assignment problems where the assignments of origins (or incoming trucks) to inbound doors, and destinations (or outgoing trucks) to outbound doors are determined with the objective of minimizing the handling cost. Cross-dock door assignment problems are a fundamental class of optimization problems in cross-docking as they arise in more complex operational problems incorporating other decisions such as scheduling, routing, and workforce allocation. We first introduce several linear mixed integer programming formulations with Lagrangean relaxation and column generation algorithms based on some of these formulations. We then theoretically and computationally compare these formulations in terms of their linear, Lagrangean and combinatorial relaxations. Finally, we integrate the assignments with sequencing and selection decisions, based on our observations on a large cross-dock company in the USA, and introduce two new integer programming formulations. Where possible, our work is compared with existing ones, and new sets of instances are generated to either vary or enlarge the current data sets in the literature.