Integrating dock-door assignment and vehicle routing with cross-docking

This paper presents an integrated cross-dock door assignment and vehicle routing problem arising in the operation of cross-dock terminals. It consists of assigning origins to inbound doors, transferring commodities between doors, and routing vehicles from outbound doors to destinations. The objective is to jointly minimize the total material handling and transportation costs. Two formulations of the problem are presented and computationally compared. In addition, we develop a column generation algorithm based on the most promising formulation and a heuristic to obtain lower and upper bounds for the optimal solution of the problem, respectively. Numerical results on a set of benchmark instances with up to 20 origins and 50 destinations confirm the efficiency of the proposed solution algorithms.