A constant approximation for the one-warehouse multi-retailer problem with backorder

Abstract

Abstract We consider two deterministic inventory models : the One-Warehouse Multi-Retailer problem and its special case the Joint Replenishment Problem. Both models have been studied extensively in their classical version, where demand has to be satisfied on time, but there are very few results in the case where backlog is allowed. This work aims to develop a simple and fast method to provide an approximate solution for both models. More precisely, our algorithm has a worst case guarantee of three for the One-Warehouse Multi-Retailer problem with backlog. To the best of our knowledge, it is the first constant approximation for such a general and complex model. We also introduce a new lower bound based on a decomposition into single-echelon systems of these problems and improve the approximation guarantee to two in the special case of the Joint Replenishment model.