A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem

In a cross-dock, goods are unloaded from incoming trucks, consolidated according to their destinations, and then, loaded into outgoing trucks with little or no storage in between. In this paper, we study the cross-dock door assignment problem in which the assignment of incoming trucks to strip doors, and outgoing trucks to stack doors is determined, with the objective of minimising the total material handling cost. We present a new mixed integer programming formulation which is embedded into a Lagrangean relaxation that exploits the special structure of the problem to obtain bounds on the optimal solution value. A primal heuristic is used at every iteration of the Lagrangean relaxation to obtain high quality feasible solutions. Computational results obtained on benchmark instances (with up to 20 origins and destinations, and 10 strip and stack doors) and on a new and more difficult set of instances (with up to 50 origins and destinations, and 30 strip and stack doors) confirm the efficiency of the algorithm.