绿色闭环供应链网络解的存在性研究

利用变分不等式相关知识对绿色闭环供应链网络均衡条件进行研究。构建各个决策者的可行策略的集值映射，将绿色闭环供应链网络均衡问题转化为广义 Nash 均衡问题，结合集值映射的连续性、凸性与紧性，利用不动点定理研究绿色闭环供应链网络解的存在性与均衡条件。基于研究结论，提出绿色闭环供应链网络各层决策者对应的变分不等式以及多准则网络均衡条件和绿色闭环供应链网络解的存在性定理。

Existence of Green Closed-loop Supply Chain Network Solutions from a Generalized Nash Equilibrium Perspective

To study the examines the existence and equilibrium conditions for green closed-loop supply chain network solutions, the equilibrium conditions of the green closed-loop supply chain network are investigated by using the knowledge related to variational inequalities. Then the set-value mapping of the feasible strategies of each decision maker is constructed, and the green closed-loop supply chain network equilibrium problem is transformed into a generalized Nash equilibrium problem, which is investigated by using immovable point theorem in combination with the continuity, convexity, and tightness of the set-value mapping. Based on the conclusions, the variational inequalities corresponding to the decision makers at each level of the green closed-loop supply chain network, as well as the multicriteria network equilibrium conditions, and the existence theorem for the solutions of the green closed-loop supply chain network are given.