ANALYSIS OF SUPPLY CONTRACTS WITH TOTAL MINIMUM COMMITMENT

In this paper we analyze a supply contract for a single product that s pecifies that the cumulative orders placed by a buyer, over a finite h orizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer pl aces orders periodically. We derive the optimal purchase policy for th e buyer for a given total minimum quantity commitment and a discounted price. We show that the policy is characterized by the order-up-to le vels of the corresponding finite horizon and a single-period standard newsboy problem with no commitment but with discounted price. We show that this policy can be computed easily. We can use this to evaluate a ny discount schedule characterized by a set of (price discount, minimu m commitment) pairs.