In this paper, we study an outsourced supply chain consisting of one buyer and two suppliers in which the buyer outsources manufacturing of a physical product to two competing suppliers. The suppliers compete for the buyers' demands share, and the buyer allocates the demands to the competing suppliers based on three-dimensional allocation functions. We consider two certain types of allocation function which depend on price, service level and product quality level. They include the exponential allocation function and the Cobb-Douglas allocation function. A three-stage game-theoretic framework is presented to derive the equilibrium values. Since the problem lacks a closed-form solution, numerical studies are conducted over a wide range of some key parameters.
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