Differential Game of Closed-Loop Supply Chain with Dynamic Stochastic Recovery Rate under Reward-penalty Mechanism of Government
The dynamic equilibrium strategy of the members in a closed-loop supply chain(CLSC)dominated by retailers and recycled by manufacturers is studied under reward-penalty mechanism(RPM).The random evolution process of the recovery rate is described by using the ITO process.Based on the dynamics model of recycling,three Stackelberg stochastic differential game models of CLSC are established:the government does not impose RPM,the government imposes RPM on the manufacturer as well as the government imposes RPM on both the manufacturer and the retailer.By using stochastic differential game theory,the partial differential equations which the optimal profit function should be satisfied are given.Furthermore,the optimal profit func-tion and equilibrium strategy value of members of CLSC are obtained and compared.In order to further study the effect of RPM on equilibrium strategy and to reveal the stochastic evolution nature of recovery of Waste Electrical and Electronic Equipment(WEEE).By numerical example,the steady-state analysis and unsteady-state analysis of closed-loop supply chain system are carried out.The results show that the RPMcan encourage manufacturers to make more recycling efforts and thus increase the recycling rate,but it can not mitigate the double marginal effects.Compared with the retailers sharing the responsibility of recycling,the RPM imposed on the manufacturer is more beneficial to the CLSC,which can bring about both economic and environmental benefits.
closed-loop supply chaindynamic recovery ratereward-penalty mechanismdifferential gameIto process
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