Flexible and risk-sharing supply contracts under price uncertainty

We study supply contracts for deterministic demand but in an environment of uncertain prices. We develop valuation methodologies for different types of supply contracts. A "time-inflexible contract" requires the firm to specify not only how many units it will purchase, but also the timing of the purchase. A "time-flexible contract" allows the firm to specify the purchase amount over a given period of time without specifying the exact time of purchase. Other than time flexibility, the suppliers may offer "quantity flexibility" to the firm as well, i.e., purchase quantities could be within a prespecified quantity window. Finally, "risk-sharing" features can be incorporated in the contract in terms of the purchase price that the firm eventually pays to a supplier. Within a prespecified price window the firm pays the realized price, but outside of it the firm shares, in an agreed way, added costs or benefits. Given the structure of a supply contract, we study the firm's decision when to purchase and how many units in each purchase such that the expected net present value of the purchase cost plus inventory holding cost is minimized. We discuss optimal purchasing strategies for both time-flexible and time-inflexible contracts with risk-sharing features. Other interesting results include the analysis of two-supplier sourcing environments and the exploitation of quantity flexibility in such contracts. Our discussion illustrates how time flexibility, quantity flexibility, supplier selection, and risk sharing, when carefully exercised can effectively reduce the sourcing cost in environments of price uncertainty.