Dynamic analysis of a dual-channel closed-loop supply chain with fairness concerns under carbon tax regulation

In this work, we study a dual-channel closed-loop supply chain (CLSC) where the manufacturer sells the new products via one fair caring retailer in the traditional channel and distributes the remanufactured products through her own direct channel in the presence of the carbon tax regulation. After solving the single-period Stackelberg game model by backward induction and analyzing the impacts of key parameters on the optimal pricing strategies and the performance of channel members, a multi-period dynamic Stackelberg game model with heterogeneous players is further established. The local stability of the Nash equilibrium point and complexity properties of the model are investigated by numerical simulation. The results reveal that (1) the retailer's fairness concern degree is negatively related to the optimal wholesale price as well as positively related to the optimal retail price of the new product. A high level of consumer discount perception for the remanufactured product is conducive to the manufacturer obtaining more profits while it is detrimental to the retailer. (2) The excessive value of the price adjustment speed, carbon tax rate or retailer's fairness concern degree has a strong destabilization effect on the system's stability. (3) The manufacturer suffers profit loss while the retailer's utility levels are elevated when the system falls into periodic cycles and chaotic motions. (4) The delay feedback control method can eliminate the chaos effectively in the dual-channel CLSC system.