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Integrated facility location and supplier selection decisions in a distribution network design

This paper deals with the integration of facility location and supplier selection decisions for the distribution network design problem. More specifically, the distribution network under consideration is composed of a set of suppliers serving a set of retailers through a set of Distribution Centers (DCs). To manage its inventory, the EOQ policy is used by each DC, and a safety stock level is maintained to ensure a given retailer service level. In this study, we assume that each retailer faces a random demand of a single product type, the supply lead-time from each supplier to each DC is constant, and no supply lead-time between DCs and retailers. The problem concerns the selection of suppliers, the location of DCs, the allocation of suppliers to DCs, and the allocation of retailers to DCs, where the goal is to minimize inventory and safety stock costs at the DCs, ordering costs and transportation costs across the network, and fixed DCs location costs. The introduction of inventory and safety stock costs leads to an NP-hard non-linear optimization problem. A Lagrangian relaxation approach is proposed to generate efficient solutions. Some numerical experiments are presented and analyzed showing the effectiveness of the proposed approach