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）

摘要： 在考虑新产品和再制造品碳排放差异的情况下，建立了制造商回收模式下的多周期混合制造/再制造系统的最优运作及补贴策略模型。假设回收品质量水平服从指数分布，回收成本、回收率和再制造成本是回收品质量水平的负指数函数，建立包含碳税的平均总成本函数，并采用遗传算法（GA）和粒子群算法（PSO）验证模型的信度和效度。结果表明：无补贴情况下，企业可对回收品质量水平为0.28~0.84的产品进行再制造；考虑补贴情况下，政府可对回收品质量水平为0.28~0.42的产品采取补贴机制，达到引导企业回收再制造的目的。该研究为政府制定合理的补贴政策及企业权衡碳排放因素降低总成本提供理论依据。

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）