Abstract: To explore the price decision problem in the dual-channel closed-loop supply chain,the single period static game model and the dynamic game model with two delays were built on the recovery rate and the remanufacturing cost difference.The optimal strategy analytic formula was given by using the method of operational research and optimization under the centralized decision and decentralized decision of the static model.The influence of the remanufacturing cost difference on the optimal strategy was analyzed.Moreover,the local asymptotic stability conditions of the system and the analytical formula of the bifurcation point were given by dynamic model using the nonlinear dynamics theory and the system complexity theory.The influence of delay parameter,recovery rate,remanufacturing cost difference and price adjustment speed on the stability and complexity of the system was revealed through simulation.The variable feedback control method was used to control the unstable system effectively.The study showed that the increase of remanufacturing cost could reduce the retail price and increase the recovery rate as well as profit.And the delay parameter and price adjustment speed should be moderate to prevent the system from losing stability.

Key words: closed-loop supply chain, recovery rate, remanufacturing cost difference, bifurcation, stability, game analysis

摘要： 为探究制造商回收的双渠道闭环供应链中的价格决策问题,在考虑回收率和再制造成本差异的情形下,建立了单周期静态博弈模型和时滞动态博弈模型。静态模型采用运筹和优化的方法,给出集中决策和分散决策下的最优策略解析式,分析了再制造成本差异对最优策略的影响;动态模型借助非线性动力学理论和系统复杂性理论,给出系统局部渐近稳定的条件和分岔点的解析式;通过仿真揭示了时滞参数、回收率、再制造成本差异和价格调整速度对系统稳定性和复杂性的影响。利用变量反馈控制法对失稳系统实现了有效控制。研究表明,增加再制造成本差异会降低销售价格,但能提高回收率和利润;同时,时滞参数和价格调整速度应适中,从而防止系统失稳。

关键词: 闭环供应链, 回收率, 再制造成本差异, 分岔, 稳定性, 博弈分析