A comparison of formulations and relaxations for cross-dock door assignment problems

•Two new MIP mathematical formulations for Cross-dock Door Assignment Problems (CDAPs).•A column generation algorithm.•Theoretical comparisons of different lower bounds.•Comparative computational experiments involving different formulations and algorithms.•Sensitivity analysis with respect to several CDAP parameters. This paper deals with cross-dock door assignment problems in which the assignments of incoming trucks to strip doors, and outgoing trucks to stack doors are determined, with the objective of minimizing the total handling cost. We present two new mixed integer programming formulations which are theoretically and computationally compared with existing ones. One of such requires a column generation algorithm to solve its associated linear relaxation. We present the results of a series of computational experiments to evaluate the performance of the formulations on a set of benchmark instances. We also perform sensitivity analysis with respect to several input parameters of the Cross-dock Door Assignment Problems.