Manufacturer Competition Using Supply Functions in a Retail Supply Chain
41 Pages Posted: 8 Jul 2019
Date Written: July 4, 2019
This paper studies contract design between a retailer and two or more competing manufacturers who supply substitutable products to the retailer for sales in a consumer market. We consider a setting in which the same contracts are used in each period of a planning horizon. We first show that it is optimal for each manufacturer to offer a cost-plus contract. In the case of just two manufacturers this result allows us to characterize an equilibrium in which the retailer's choice maximizes the supply chain profit, each manufacturer makes a profit equal to its marginal contribution to the supply chain, and the retailer takes the remaining profit. In addition, the optimal ordering policy of the retailer can be characterized by separate regions that exhibit monotone properties. We extend our baseline model to cases with more than two manufacturers, and show that in the case of linear demand functions the optimal supply chain profit as a set function of manufacturer indices is submodular. Using this submodularity property, we demonstrate that the equilibrium results for the two-manufacturer case continue to hold.
Keywords: supply contracts, supply function competition, general cost functions, retail supply chains, submodularity
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