We address a fundamental two-echelon distribution system in which the sales volumes of the retailers are endogenously determined on the basis of known demand functions. Specifically, this paper studies a distribution channel where a supplier distributes a single product to retailers, who in turn sell the product to consumers. The demand in each retail market arrives continuously at a constant rate that is a general decreasing function of the retail price in the market. We have characterized an optimal strategy, maximizing total systemwide profits in a centralized system. We have also shown that the same optimum level of channelwide profits can be achieved in a decentralized system, but only if coordination is achieved via periodically changed, fixed fees, and a nontraditional discount pricing scheme under which the discount given to a retailer is the sum of the three discount components based on the retailer's (i) annual sales volume, (ii) order quantity, and (iii) order frequency, respectively. Moreover, we show that no (traditional) discount scheme, based on order quantities only, suffices to optimize channelwide profits when there are multiple nonidentical retailers. The paper also considers a scenario where the channel members fail to coordinate their decisions and provides numerical examples that illustrate the value of coordination. We extend our results to settings in which the retailers' holding cost rates depend on the wholesale price.
Chen, Fangruo, Awi Federgruen, and Yu-Sheng Zheng. "Coordination mechanisms for a distribution system with one supplier and multiple retailers." Management Science 47, no. 5 (May 2001): 693-708.
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