Cross-docking is a logistic strategy in which products arrive at terminals, are handled and then shipped to the corresponding destinations. Cross-docking consists of unloading products from inbound trucks and loading these products directly into outbound trucks with little or no storage in-between. Cross-docking aims to reduce or eliminate inventory by achieving an efficient synchronization of unloading trucks, material handling and loading trucks. This thesis introduces an integrated dock-door assignment and vehicle routing problem that consists of assigning a set of origin points to inbound doors at the cross-dock, consolidating commodities in-between inbound and outbound doors, and routing vehicles from outbound doors to destination points. The objective is to minimize the sum of the material handling cost at the cross-dock and the transportation cost for routing the commodities to their destinations. Five mixed integer programming formulations are presented and computationally compared. A column generation algorithm based on a set partitioning formulation is developed to obtain lower bounds on the optimal solution value. In addition, a heuristic algorithm is used to obtain upper bounds. Computational experiments are performed to assess the performance of the proposed MIP formulations and solution algorithms on a set of randomly generated instances
