A Mathematical Model for Two Dimensional Loading Problem in Cross-Docking Network Design

In this paper, the transportation problem of cross-docking network is taken into account. Cross-docking centers differ from distribution centers or warehouses in that the loads are transported from origins to destinations through cross-docking centers without storing them for a long time. Goods are unloaded from incoming trucks and reloaded immediately onto outgoing trucks in these cross-docking centers. This problem is formulated using a mixed integer programming with two-dimensional loading constraints. The two-dimensional shapes are applied for both trucks and loads in order to find exact capacity of each truck in basis of each product. The illustrative problems are solved and results show that the proposed model finds practical solutions with two- dimensional loading constraints.