Optimal ordering policy in a distribution system

In conventional inventory management, the retailers monitor their own inventory levels and place orders at the distributor when they think it is the appropriate time to reorder. The distributor receives these orders from the retailers, prepares the product for delivery. Similarly, the distributor will place an order at the manufacturer at the appropriate time. Generally, the order that the distributor places at the manufacturer is larger than that the retailer places at the distributor. In order to afford this large order, there should exist a long-term supply contract between the manufacturer and distributor that can guarantee a stationary supply to the distributor. This paper discusses this case, and derives the optimal stationary supply, that is, the optimal ordering policy of the distributor. Also computational results are presented.