The Impacts of Fairness Concern and Different Business Objectives on the Complexity of Dual-Channel Value Chains

This paper considers a Stackelberg game model in a dual-channel supply chain, which is composed of a manufacturer and a retailer. The manufacturer and retailer consider fairness concern in the market competition, and the manufacturer takes market share and profit as his/her business objectives. The entropy complexity and dynamic characteristic of the dual-channel system are analyzed through mathematical analysis and numerical simulation, such as local stability, bifurcation, entropy, and chaos. The results show that, with the increase of price adjustment speed, the dual-channel supply chain is more complex and falls into a chaotic state in which system entropy increases; the stability of the dual-channel supply chain will be robust with the increase of weight of market share and weaken with the increase of the fairness concern level of the manufacturer and retailer. The high level of fairness concern of the manufacturer and retailer is always disadvantageous to the leading manufacturer but not always bad for the follower retailer. The performance of the dual-channel supply chain is improved with a high level of the manufacturer’s fairness concern and reduced with a high level of the retailer’s fairness concern. We also find the retailer will gain more profits in the chaotic state than the stable state in the Stackelberg game model. The variable feedback control method is applied to control the chaos of the dual-channel supply chain, and choosing appropriate control parameters can make the dual-channel supply chain system return to the stable state from the chaotic state, or delay the system to enter the bifurcation state. The research results can provide a guideline for enterprise decision-making.