Outsourcing through competition: What is the best competition parameter?

In this paper we consider a single buyer who wants to outsource the manufacturing of a product to N potential suppliers. The buyer's objective is to maximize the service level she receives from the suppliers. The suppliers compete for the buyer's demand based on a competition parameter which the buyer announces along with an allocation rule. We model each supplier as a make-to-stock queueing system. Using a simple proportional allocation function, we compare two competition parameters: service level and inventory level. We show that inventory competition creates a higher overall service level for the buyer. We also show an optimal form of competition parameter which can induce the maximum feasible service level. Our base model shows the results for the competition between identical suppliers. We then extend the results to a case where the suppliers are heterogeneous.