We consider a buyer who outsources the manufacturing of a product to multiple symmetric make-to-stock suppliers who compete on price and service (fill rate). The buyer allocates demand to the suppliers using a score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his costs, while the suppliers choose their prices and fill rates to maximize their 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 portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then consider a general number of suppliers and show that the equilibrium prices and fill rates, and the buyer's cost, are increasing in the number of suppliers. We compare these results to a model of single-sourcing, in which the buyer is the Stackelberg leader and extracts all profits from the supplier. We find that the buyer always prefers single-sourcing to multisourcing. Finally, we study a centralized system and use the results to develop a coordinating contract for the decentralized system.