Optimization and coordination of supply chains under the retailer's profit margin constraint

Using the context of a single-supplier single-retailer supply chain, this paper investigates the supplier's optimal decision under the retailer's profit margin constraint and the effect of that constraint on supply chain coordination. We focus on the wholesale-price contracts and the revenue-sharing contracts under this supply chain structure. We first prove that under wholesale-price contracts, the function of the supplier's expected profit is pseudo-concave with respect to wholesale price, and we thereby derive the supplier's optimal wholesale price under the retailer's profit margin constraint. We also reveal that although the action of a retailer pursuing a desired profit margin can alleviate channel profit loss with wholesale-price contracts, it also results in the supplier receiving lower profits. Furthermore, to improve the channel profit, we introduce revenue-sharing contracts under the retailer's profit margin constraint and derive the optimal wholesale price and the optimal revenue sharing coefficient, which not only meets the retailer's profit margin constraint but also achieves supply chain coordination. Especially, according to the retailer's profit margin constraint, the revenue-sharing contracts can allocate the optimal channel profit between the retailer and the supplier.