关键词: 碳排放差异化, 回收品质量水平, 碳税, 补贴, 多周期闭环混合系统, 遗传算法（GA）, 粒子群算法（PSO）

Abstract: The optimal operation and subsidy strategies model is built under manufacturer-collection channel considering the differences of carbon emissions for manufacturing/remanufacturing products in a multi-period closed-loop hybrid manufacturing/remanufacturing system. A function is developed to formulate the problem to minimize the total cost of the system considering carbon tax. It is assumed that the quality of returned products is set to be exponential distribution. Buyback cost, remanufacturing cost and return rate are negative exponential function of quality level of returned items. A numerical example is used to verify the effectiveness and credibility of the model by adopting Genetic Algorithm（GA） and Particle Swarm Optimization（PSO） algorithm. The results show that the enterprises can remanufacture products without subsidy mechanism of government when the quality level of returned items is between 0.28 and 0.84； the government can adopt an appropriate subsidy policy to promote the recovery when the quality level of returned items is between 0.28 and 0.42. The theoretical foundation could be provided for initiating a reasonable subsidy policy as well as minimizing the total cost considering the carbon emission for enterprises.

Key words: differences of carbon emissions, quality level of returned items, carbon tax, subsidy, multi-period closed-loop hybrid system, Genetic Algorithm（GA）, Particle Swarm Optimization（PSO）