Abstract: Considering a dynamic closed-loop supply chain system consisting of a manufacturer and a retailer, Stackelberg differential game models under three kinds of behavior mode—the altruism of manufacturer, the altruism of retailer, and the altruism of both parties were built. By using the Bellman’s continuous dynamic planning theory, the recycling effort input, the wholesale price strategies of manufacture, the sales price strategy of retailer and recovery rate of waste product, as well as the value function of both parties in the three kinds of altruism modes were obtained and analyzed. A numerical example was given to verify the previous conclusion, and further analyze the effects of altruism coefficient of the manufacturer and that of the retailer on the steady-state index. Besides, the time-evolution of supply chain performance in the three altruistic models is compared and analyzed while using the self-supporting situation as the benchmark model. The result shows that altruism is a positive social preference. The altruistic behavior of the manufacturer can effectively reduce the double marginal effect of the supply chain and improve the consumer surplus, while that of the retailer may increase profit of the manufacturer at the expense of himself and can make consumer demand more sensitive to price changing. In contrast, the altruistic behavior of both parties is the optimal behavior pattern of the supply chain, which can improve the triple-bottom-line performance of economy, environmental protection, and society.

Key words: closed-loop supply chain, differential game, altruism, triple-bottom-line

摘要： 针对一制造商和一零售商组成的动态闭环供应链系统，分别构建了制造商利他、零售商利他以及双方利他3种行为模式下的Stackelberg微分博弈模型，借助贝尔曼连续型动态规划理论得到了3种利他模式下，制造商的回收努力投入和批发价格策略、零售商的产品销售价格策略、废旧产品回收率以及成员的值函数并进行了对比分析。算例验证了先前结论，进一步分析了制造商利他系数和零售商利他系数对稳态指标的影响，并以自立情形为基准模型，对比分析了3种利他模式下的供应链绩效时间演进规律。研究表明：利他行为是一种正向的社会偏好；制造商的利他行为能够有效地减缓供应链的双重边际效应，提高消费者剩余；零售商的利他行为虽会提高制造商利润，但却以牺牲自身利润为代价，也会使消费者需求量对价格的变动更为敏感；相比之下，双方利他行为是供应链的最优行为模式，可以带来经济、环保、社会三位一体总绩效的提升。

关键词: 闭环供应链, 微分博弈, 利他, 三位一体