Dual-channel supply chain competition with channel preference and sales effort under uncertain environment

In this paper, we investigate a dual-channel supply chain under uncertain environment. Channel preference and sales effort are taken into account to explore their effects on supply chain members' profits with uncertain information. Then we analyze the dual-channel supply chain in centralized and decentralized cases, and give closed-form expressions for equilibriums in the two cases. A series of numerical experiments are implemented to examine the impacts of uncertainty distributions of parameters on supply chain profits. We conclude that the total profit of the supply chain in the centralized case is invariably higher than that in the decentralized case under different uncertainty degrees of these parameters. It is shown that the supplier's profit first decreases then increases as the expected value of customers' preference to the direct channel increases, and the retailer's profit decreases with the increase of the expected value of customers' preference to the direct channel. In addition, the results indicate that the total profits in the centralized and decentralized cases, the supplier's profit and the retailer's profit all increase when the expected value of the retailer's sales effort elasticity increases.