Analysis of supply contracts with minimum total order quantity commitments and non-stationary demands

In this paper we address a buyer–supplier arrangement of particular importance: total order quantity commitment (TOQC). Under the TOQC contract that has been negotiated between the buyer and the supplier, the former agrees to an obligation to procure a certain quantity of an item from the latter over the predetermined period of time (additional quantity can be obtained maybe at a different price). The optimal inventory replenishment policy is shown to be dual order-up-to levels under a given TOQC, and the optimal TOQC is also demonstrated to be mathematically straightforward to obtain.