Bullwhip Entropy Analysis and Chaos Control in the Supply Chain with Sales Game and Consumer Returns

In this paper, we study a supply chain system which consists of one manufacturer and two retailers including a traditional retailer and an online retailer. In order to gain a larger market share, the retailers often take the sales as a decision-making variable in the competition game. We devote ourselves to analyze the bullwhip effect in the supply chain with sales game and consumer returns via the theory of entropy and complexity and take the delayed feedback control method to control the system’s chaotic state. The impact of a statutory 7-day no reason for return policy for online retailers is also investigated. The bounded rational expectation is adopt to forecast the future demand in the sales game system with weak noise. Our results show that high return rates will hurt the profits of both the retailers and the adjustment speed of the bounded rational sales expectation has an important impact on the bullwhip effect. There is a stable area for retailers where the bullwhip effect doesn’t appear. The supply chain system suffers a great bullwhip effect in the quasi-periodic state and the quasi-chaotic state. The purpose of chaos control on the sales game can be achieved and the bullwhip effect would be effectively mitigated by using the delayed feedback control method.