Study On Stochastic Differential Game In The Closed-Loop Supply Chain With Third-Party Collecting And Fairness Concerns

With the rapid development of economy,the shortage of earth resources and the destruction of ecological environment have become the problems that all countries in the world have to deal with.Remanufacturing closed-loop supply chain is a new mode of sustainable production,which can not only reduce waste emissions,but also improve the efficiency of resource utilization.Because of its huge advantages in social benefits,economic benefits and environmental benefits,it has attracted much attention from the industry and academia.How to realize effective recycling is always a key problem in closed-loop supply chain.This paper investigates the optimal return control problem in a closed-loop supply chain consisted of one leading manufacturer,one retailer,and one third-party collector,in the presence of stochastic return disturbance and fairness concern of followers.By formulating the stochastic differential game-theoretic models and resolving the feedback Stackelberg equilibriums without and with fairness concern,the study also derives the evolutionary paths of the stochastic return rate and the value functions of the supply chain members under the optimal control strategies.The results show that the feedback equilibrium exists only under a specific condition,and the expectation and variance of the return rate both approach the stable state for a specific closed-loop supply chain system.The study further discussed the impact of fairness concerns on the supply chain system.The results state that the higher the level of concern of the retailer and the third-party collector,the lower the wholesale price of dynamic equilibrium and the higher the retail price of dynamic equilibrium.At the same time,the third party would lower its collecting effort,and the expected return rate will decrease with the extent of fairness concerns.The manufacturer can shift profit to the retailer by lowering the wholesale price,while he cannot shift profit to the third party.The stable expected return rate will be lower in the supply chain with fairness concerns,as the third party will have less incentive to collect used products,considering unfairness.As a result,the manufacturer should set a higher transfer subsidy to incentivize the third party to collect when the third party is concerned with fairness.