Achieving Efficiency in Capacity Procurement

This chapter studies a capacity procurement problem in which a buyer meets an uncertain demand using a combination of spot purchases and supply options that are offered by a number of competing suppliers. The specific setting we consider involves the suppliers each owning a block of capacity and the buyer restricted to reserving the entire block or none. For this setting, we are interested in understanding the buyer's optimal procurement strategy and the suppliers' competitive bidding behavior in the supply option market. To this end, we first examine the buyer's optimal decision given a set of supply options, and then study the suppliers' optimal bidding strategies in equilibrium. We find that it is optimal for suppliers to set execution price at cost and hence make a profit only through the reservation payment. We also prove that when all the blocks have the same size the buyer's optimal profit as a function of supplier set is submodular. This property allows us to characterize an equilibrium in which the supply chain optimum is achieved, each supplier makes a profit equal to their marginal contribution to the supply chain and the buyer takes the remaining profit. When the blocks have different sizes, we develop a recursive procedure to characterize a class of equilibria in which the supply chain efficiency is achieved.