Supply chain system design integrated with risk pooling

This paper considers the location, production–distribution and inventory system design model for supply chain for determining facility locations and their capacity. Risk pooling effect, for both safety stock and running inventory (RI), have been incorporated in the system to minimize the supply chain cost along with determining facility location and capacity. In order to study the benefit of risk pooling for safety stock and RI two cases have been considered, first when retailers act independently and second when DCs‐retailers work jointly. The model is formulated as mixed integer nonlinear problem and divided into two stages. The first stage determines the optimal locations for plants and flow relation between plants‐DCs and DCs‐retailers. At this stage the problem has been linearized using piece‐wise linear function. Second stage enumerates the required capacity of opened plants and DCs. The first stage problem is further divided in two sub‐problems using Lagrangean relaxation. First sub‐problem determines the flow relation between plants and DCs whereas; second sub‐problem determines the DCs‐ retailers flow. Solution of the sub‐problems provides the lower bound for the main problem. Computational results reveal that main problem is within the 8.25% of the lower bound and significant amount of cost reduction can be achieved for safety stock and RI costs when DC‐Retailer acts jointly.