Flexible and Risk-Sharing Supply Contracts Under Price Uncertainty

Abstract

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.supply contracts, global operations, flexibility, binomial lattice

Competitive Options, Supply Contracting, and Electronic Markets

“…Compared with Araman et al (2002) and Li and Kouvelis (1999), efficiency is achieved here without the use of any penalty for unused contract capacity. Competition, together with proper design of the options contracts, is the underlying efficiency driver.…”

Optimal spot market inventory strategies in the presence of cost and price risk

“…Optimal contract selection and utilization policies were characterized. In [21], deterministic demand must be met after a deterministic time period, but the firm has a contract to procure supply on the spot market at some point before demand is realized, where spot market price is a continuous random process. The optimal purchase time was derived numerically.…”

“…We assume that the price of each unit of inventory is stochastic and is a Brownian motion process as in [17] and [21]. We also assume that the time until the (single) demand arrives, as well as the amount of that demand, is random.…”

Implications of Renegotiation for Optimal Contract Flexibility and Investment

“…The payment p i q is in addition to any up-front transfer payment, so that under a quantity flexibility contract, when the buyer comes to choosing his order quantity, he has already paid for the first Q i − i units and hence has no incentive to take less than this. Quantity flexibility contracts are widely used and studied (Bassok and Anupindi 1997, Li and Kouvelis 1999, Tsay 1999, Tsay and Lovejoy 1999, Cachon and Lariviere 2001, BarnesSchuster et al 2002, Lariviere 2002.…”