A long-term capacity reservation contract

By committing to a long-term replenishment contract, buyers can purchase a product at a lower price from a supplier who is less pressured to find new customers due to the long-term contract and can charge a discounted price. We develop an analytical model from the buyer's perspective to investigate a capacity reservation contract. We are considering the system with a single supplier and a buyer. The buyer can purchase any desired amount from a spot markeat at a higher price in addition to the contracted amount. For such a system, we propose an algorithm to derive the optimal contract terms. The result of computational experiments shows that the algorithm finds the global optimum solution in a reasonable amount of time.