6.3 A Single Warehouse Multi-Retailer Model
6.3.1 Introduction
Many distribution systems involve replenishing t,he inventories Of geographically dispersed retailers. Consider a distribution system in which a single warehouse supplies a set, of retailers with a single product. Each ret,ailer faces a constant retailer-specific demand that must, be met without shortage or backlogging. The warehouse faces orders for the product from the different, retailers and in turn places orders to an outside supplier. A fixed, facility-dependent, set-up cost, is charged each time the warehouse or the retailers receive an order and inventory carrying cost is accrued at each facility at a constant facility-dependent rate. The objective is to determine simultaneously the t,iming and sizes of retailer deliveries to the warehouse as well as replenishment strategies at the warehouse so as minimize long-run average inventory purchasing and carrying costs.
In the absence Of a fixed set-up cost, charged when the warehouse places an order, the problem can be decomposed into an EÅtonornic Lot Size mode! for each retailer. That, is, the existence of this cost ties together the different retailers requiring the warehouse to coordinate its orders and deliveries to the different retailers. It, is well known that, optimal policies can be very complex and thus the problem has attracted a considerable amount of attention in recent years (gee Graves and Schwarz, 1977; Roundy, 1985). The latter paper presents the best approach currently available for this model; it suggests a set of power of two reorder intervals for each facility and show that the cost of this solution is within 6% of a lower bound on the optimal cost. In this section, we present this method along with the worst-case bound.