政府奖惩下考虑回收率动态随机的闭环供应链微分博弈

Differential Game of Closed-Loop Supply Chain with Dynamic Stochastic Recovery Rate under Reward-penalty Mechanism of Government

本文研究了政府奖惩机制下零售商主导、制造商回收的闭环供应链中成员的动态均衡策略。利用伊藤过程刻画了废弃电器电子产品回收率的随机演化过程,在回收动力学模型的基础上构建了三个Stackelberg随机微分博弈模型:政府不实施奖惩机制、政府只对制造商实施奖惩机制和政府同时对制造商和零售商实施奖惩机制。利用随机微分博弈理论,构造了不同模式下制造商和零售商最优利润函数应满足的偏微分方程组,进一步求解得到供应链成员的最优利润函数和均衡策略值并对其进行了比较分析。为了进一步研究政府奖惩力度对供应链均衡策略的影响,揭示回收率的随机演化规律,结合算例,对供应链系统是否达到稳定状态进行了稳态分析和非稳态分析。研究结果表明:政府实施奖惩机制有利于激励制造商付出更多的回收努力进而提高回收率,但不利于减缓双重边际效应;相比于零售商分担回收责任,政府只对制造商实施奖惩机制更有利于提高供应链整体获利水平,同时带来经济和环保效益的提高。

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 unsteadystate 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.