关键词: 闭环供应链, 微分博弈, 利他, 三位一体

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