Deriving the Exact Cost Function for a Two-Level Inventory System with Information Sharing

In this paper we consider a two-level inventory system with one warehouse and one retailer with information exchange. transportation times are constant and retailer faces independent poisson demand. the retailer applies continuous review (r.q)-policy. the supplier starts withm initial batches (of size q), and places an order to an outside source immediately after the retailer's inventory position reaches r+s. in this system the lead time of the retailer is determined not only by the constant transportation time but also by the random delay incurreddue to the availability of stock at the supplier. a recent paper has obtained the approximate value of the expected cost for this system by using the expected value of the retailer's lead time and hence has pointed out that the optimal supplier policy is an open question. in this paper we tackle this open question and obtain the exact value of the expected system cost by using the idea of the one-for-one ordering policy and implicitly incorporating the distribution function ofthe random delay.