Determination of the economical policy of a three-echelon inventory system with (R, Q) ordering policy and information sharing

In this work, we consider a three-echelon serial inventory system with two warehouses (suppliers) and one retailer with information exchange. The retailer applies continuous review (R, Q) policy. The warehouses have online information on the inventory position and demand activities of the retailer. We present a new ordering policy to share information among inventory echelons. The warehouse I and II start with m ₁ and m ₂ initial batches of the same order size of the retailer, respectively. The warehouse I places an order to an outside source immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₁, and the warehouse II places an order to the warehouse I immediately after the retailer’s inventory position reaches an amount equal to the retailer’s order point plus a fixed value s ₂. Transportation times are constant and the retailer faces independent Poisson demand. The lead times of the retailer and the warehouse II are determined not only by the constant transportation time but also by the random delay incurred due to the availability of stock at the warehouses. 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 inventory system cost. Resorting some numerical examples in three different scenarios, we show how information sharing reduces the inventory costs.