Complex Dynamics in a Closed-Loop Supply Chain with Risk Aversion and Fairness Concerns Under Supply Disruption

In this paper, we consider a closed-loop supply chain (CLSC) consisting of two suppliers, one manufacturer, one risk-averse retailer and one fair-caring third-party in the presence of supply disruption. We focus on establishing a dynamic Stackelberg game model with bounded rational expectation and analyzing the game evolution process. The effects of key parameters on the Nash equilibrium solutions and their stability are investigated, as well as the complex dynamical behaviors of the CLSC system are explored by using the stability region, bifurcation graph, the largest Lyapunov exponent (LLE), strange attractors, etc. Moreover, the performance of channel members under different values of parameters is researched by utilizing the (average) expected profits or utilities index. The analysis results reveal that the excessive fast adjustment speed of the manufacturer will lead to the system losing stability and falling into chaos. Also, the retailer's risk aversion and the third party's fairness concerns have a destabilization effect on the Nash equilibrium point, while the possibility of supply disruption has different effects on the scope of the adjustment speed of decision variables of the manufacturer. Furthermore, in most cases, an over the top adjustment speed of the manufacturer is disadvantageous to all the channel members for more expected profits, but the third-party can achieve a better performance when the system is in periodic state. Finally, the time-delay feedback control method is proposed to eliminate the system chaos.

Automated summary

This study investigates a closed-loop supply chain system with two suppliers, one manufacturer, one retailer, and one third-party under supply disruption, by analyzing the dynamic Stackelberg game model with key parameter effects and channel member performances. Findings suggest that excessive adjustment speed of the manufacturer leads to system instability and chaos, while the risk aversion of the retailer and fairness concerns of the third party impact the stability of the system. Furthermore, fast adjustment speed of the manufacturer may not be beneficial for all channel members, but the third party can perform better in periodic state.