A Location-inventory Model with Echelon Stock Policy for Four-echelon Supply Chain Network Design

An integrated supply chain network design needs to simultaneously optimize the decisions of facility location and inventory control. However, most of the integrated location-inventory models developed did not include the selection of suppliers and location decisions of plants, so these models can´t meet the need of some integrated supply chain network design. In this paper, we consider a network design problem for a four-echelon supply chain consisting of suppliers, plants, distribution centers (DC´s) and customers, where the echelon stock policy for two-level inventory systems is considered. The problem is formulated as a nonlinear mixed integer programming model. The objective is to determine the number and locations of suppliers, plants and DC´s, the assignment of each located plant to a selected supplier, each located DC to an open plant and that of each customer to a DC, the transportation quantity between suppliers, plants and distribution centers, and the optimal inventory control parameters in the open plants and DC´s, which minimizes the system-wide location, production, purchase, transportation, and inventory costs. In a numerical application, we found that the potential cost reduction reached by proposed model, compared to the other approaches, increases when the inventory holding costs are higher or the unit transportation costs are lower.