以一个制造商和一个供应商所构成的两级供应链为研究对象，运用微分博弈理论与方法研究了考虑消费者低碳偏好和参考低碳水平效应的供应链联合减排动态优化与协调问题。先后考察并比较了分散决策和集中决策下制造商和供应商的最优减排策略、利润现值和供应链系统总利润现值。结果表明，与斯坦伯格主从博弈相比，合作博弈的均衡结果具有Pareto优势。在此基础上，提出了双边补助契约，并指出在一定条件下，该契约可以实现制造商和供应商的Pareto改善。最后通过数值仿真，进一步验证本文的主要结论，并对重要参数进行了敏感性分析。研究发现：在双边补助契约可以协调供应链的情况下，随着消费者低碳偏好程度的增加，制造商和供应商的最优减排努力水平以及利润现值会同时增加；初始参考低碳水平的差异会影响分散决策和双边补助契约下制造商和供应商的利润现值随着参考低碳水平参数的变化趋势；尽管初始参考低碳水平的差异会影响参考低碳水平随时间的变化趋势，但针对同一渠道结构，参考低碳水平最终会趋于同一稳定值。
As a result of global warming, low-carbon economic development is widely accepted, thereby the low-carbon supply chain management has come up as an important research paradigm in operations management. Due to the environmental pressures and the guidance of the government, the low-carbon consciousness of consumers is increasing and low-carbon consumption is becoming more and more popular in the whole society. Through literature review, it is found that the consumer preference to low carbon and reference effect have strong impacts on the supply chain management. Therefore, it is important to study low-carbon supply chain management considering these two types of consumers' behavior. In this paper, for one manufacture-one supplier supply chain, a dynamic optimization and coordination about joint emission reduction is discussed. The reference low-carbon level for a product is assumed to be a weighted average of the historical low-carbon level. In addition, the low-carbon level is assumed to have a positive effect on the market demand, and the reference low-carbon level is assumed to have a negative effect on the market demand. Based on the differential game theory and method, the manufacturer and the supplier's optimal emission reduction strategy, revenue and the total revenue of the supply chain in decentralized and centralized decision making mode are investigated and compared. The results show that cooperative game equilibrium has more Pareto advantage. According to the comparison, a two-way subsidy contract is proposed. With this contract, both the manufacturer and the supplier achieve the Pareto improvement in a certain condition. Finally, based on the parameter values chosen from the previous literature (e.g. Liu et al., 2015[7]), a numerical example verifies the main conclusions of this paper and the sensitivity analysis of key parameters is also presented. The research shows that the manufacturer and supplier's revenue increases as the increase of the level of consumers' preference to low carbon under the condition that the two-way subsidy contract can coordinate the supply chain. The initial reference low-carbon level can affect the tendency of the manufacturer and supplier's revenue with the reference low-carbon level parameter in decentralized and decision making and two-way subsidy contract mode. Although the initial reference low-carbon level can affect the tendency of the reference low-carbon level with time, the reference low-carbon level tends to the same stable value for the same channel structure. In this study, the scope and content of the low-carbon supply chain management problem under the consideration of the consumers' behavior are enriched, and the guidance for the related study on the behavioral operation problem is provided.
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