The uncapacitated fixed-charge facility location problem with a multi-echelon inventory system

In this paper, we simultaneously study the uncapacitated fixed-charge location problem (UFLP) and a multi-echelon inventory problem. We initially develop an approximate integer programming formulation for the inventory problem. The later problem is combined with the UFLP and the integrated model is presented as a 0-1 integer program that we refer to as the joint facility location inventory problem (JFLIP). The novel model deals with the storage and movement of a single product from a single plant to a set of retailers though a set of candidate distribution centers (DCs). We assume single sourcing in which the entire demand of each retailer is served by a single distribution center. The objective of the model is to determine (1) the number of distribution centers to establish, (2) their locations, (3) the sets of retailers that are assigned to each distribution center, and (4) the size and timing of orders for each facility so as to minimize the sum of inventory, shipping, ordering, and location costs while satisfying a predetermined Type 1 service level of end-customer demand.