Price and Service Competition in an Outsourced Supply Chain

We study the problem faced by a buyer who outsources the manufacturing of a given product to multiple symmetric make-to-stock suppliers who compete on both price and service (as measured by fill rate). The buyer allocates demand to the suppliers using a two-dimensional score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his own costs, while the suppliers choose their prices and fill rates to maximize their own profits. For the case of dual-sourcing, we characterize the optimal parameter of the exponential score function, considering the impact of the buyer's decisions on the suppliers and considering how the suppliers compete against each other to earn a larger portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then extend the model to consider a general number of suppliers and show that the equilibrium prices and fill rates, as well as the buyer's equilibrium cost, are increasing in the number of suppliers from which the buyer sources. We then compare these results to a model of single-sourcing, in which the buyer is the Stackelberg leader and thus is able to extract all profits from the single supplier. We find that the buyer always prefers single-sourcing to multi-sourcing. We conclude by studying the optimal behavior of a centralized system and use the results to develop a coordinating contract for the decentralized system, which encourages the suppliers to choose the system-optimal service level.