Coordination Mechanisms for a Distribution System with One Supplier and Multiple Retailers

TLDR

The paper studies a two‑level distribution system where retailer sales volumes are endogenously set by known demand functions. The authors analyze a centralized and decentralized supplier–retailer channel with a single product, continuous demand that decreases with price, and extensions where retailer holding costs depend on wholesale price. They show that an optimal profit‑maximizing strategy exists, and that the same channelwide profits can be achieved in a decentralized setting only with coordinated fixed fees and a three‑component discount scheme, whereas traditional quantity‑based discounts are insufficient, with numerical examples confirming the coordination benefit.

Abstract

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 charged, fixed fees, and a nontraditional discount pricing scheme under which the discount given to a retailer is the sum of 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.