A column generation approach for a cross-docking network design problem

Cost reduction in logistics has been an important issue in supply chain management. Cross-docking is known as one of distribution strategies to cope with cost reduction. A cross-docking center is a warehouse in which incoming commodities from venders are transshipped and from which stores are supplied, without holding any stock in it. In this paper, we consider a cross-docking network design problem and propose a mathematical programming model for it. In this problem, decision variables are whether each cross-docking center is established or not, transportation quantity among venders, cross-docking points and stores in the established network. Transportation is performed by vehicles and we consider two types of vehicles. The difference between them is their capacity. This problem can be formulated into a mixed integer programming problem. We reformulate it into a set-partitioning-type problem and apply the column generation method. In the formulation, each column includes information corresponding to a "transportation pattern" giving the type and the number of vehicles used as well as their origin and destination. We also propose an acceleration strategy of column generation for finding, with a simple detection method, "effective" sub-problems which tend to yield columns with negative reduced cost. Finally, we demonstrate numerical results from computational experiments. The results suggest that our approach works well and provides good solutions within acceptable time.