Exact Evaluation of 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 with m initial batches (of size Q), and places an order to an outside source immediately after the retailer's inventory position reaches R + s. The lead time of the retailer is determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the supplier. In a recent paper the expected value of this random delay is used for evaluating the approximate cost of this inventory system, while in this paper using the idea of the one-for-one policy we implicitly incorporate the distribution function of the random delay to obtain the exact value of the expected system costs