Optimal decisions in a retailer Stackelberg supply chain

In the context of a retailer Stackelberg supply chain, we examine how a direct channel added by a manufacturer can influence the decisions of the retailer and the manufacturer, and the impact it will have on their profits. We obtain equilibrium prices for a retailer Stackelberg dual-channel supply chain. We find that, as compared to a single retail channel supply chain, a dual-channel supply chain can enhance the profits of the manufacturer and the supply chain. The retailer, however, will benefit from the direct channel when the maximum sales in the retail channel are high. We further propose a retailer's margin contract that can coordinate the dual-channel supply chain and ensure that both the retailer and the manufacturer will be more profitable. The implications of the coordination are also discussed. Numerical examples are included to illustrate the major results of the paper.