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Procurement Auctions with Capacity Reservation It frequently happens that a supplier needs to invest in building capacity prior to supplying a product. Then the buyer will need to reserve capacity from suppliers and pay for this in advance of knowing the final demand. "Capacity Games with Supply Function Competition" by Edward Anderson, Bo Chen, and Lusheng Shao studies a very general version of this problem, in which both capacity and production costs are volume dependent. They explore how an auction will operate in this setting and allow supply function bids from suppliers. They apply this framework to a newsvendor problem with unreliable suppliers, a portfolio procurement setting with supply options and a spot market, and a bundling problem with nonsubstitutable products. This helps to understand when we may expect the buyer to make a reservation choice that maximizes the overall supply chain profit. The key to these results is to show that the supply chain optimal profit is submodular in the set of suppliers. We introduce a general model for suppliers competing for a buyer's procurement business. The buyer faces uncertain demand, and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two-dimensional, with some capacity costs incurred prior to production and some production costs incurred at the time of delivery. These costs are general functions of quantity, and this naturally leads us to a supply function competition framework in which each supplier offers a schedule of prices and quantities. We show that there is an equilibrium of a particular form: the buyer makes a reservation choice that maximizes the overall supply chain profit, each supplier makes a profit equal to their marginal contribution to the supply chain, and the buyer takes the remaining profit. This is a natural equilibrium for the suppliers to coordinate on, since no supplier can do better in any other equilibrium. These results make use of a submodularity property for the supply chain optimal profits as a function of the suppliers available and build on the assumption that the buyer breaks a tie in favor of the solutions that give the largest supply chain profit. We demonstrate the applications of our model in three operations management problems: a newsvendor problem with unreliable suppliers, a portfolio procurement problem with supply options and a spot market, and a bundling problem with nonsubstitutable products. [ABSTRACT FROM AUTHOR]

We model a modular assembly system in which a final assembler outsources some of the assembly task to first-tier suppliers (subassemblers), who produce modules made up of multiple components. The assembler sets module prices it will pay to the subassemblers, the subassemblers set component prices they will pay to suppliers, and then all players choose how much capacity to install, with the minimum capacity choice determining system capacity. Finally, stochastic end-product demand is observed and all players produce (and are paid for) the same number of units—the minimum of demand and system capacity. We characterize equilibrium price and capacity choices, and then use that characterization to derive results regarding higher-level structural choices by the assembler—such as how to group components into modules and which suppliers to choose as subassemblers. We also compare performance of the system to a traditional assembly system with an assembler and suppliers but without subassemblers. [ABSTRACT FROM AUTHOR]