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

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