Technical Note—Optimal Inventory Policy in the Presence of a Long-Term Supplier and a Spot Market

We consider a stochastic inventory control problem in which a buyer makes procurement decisions while facing periodic random demand and two supply sources, namely, a long-term contract supplier and a spot market. The contract between the buyer and the supplier partially shields the latter from the vicissitudes of the spot market, in that the price paid by the buyer to the supplier is only partially linked to the spot price at the moment. After fulfilling the minimum-order commitment with the supplier, the buyer has the full freedom to source from both the supplier and the market. Procurement from the spot market also incurs a fixed setup cost. We show that an optimal policy consists of three different policy forms, with the realization of each depending on the buyer's inventory level and the prevalent spot price. Certain conditions are identified under which monotone trends exist between policy parameters and the current spot price.