中文摘要：

文章研究了制造商/回收中心将新旧产品分开来销售,满足不同消费者需求,其中新产品经一级零售商售予一级需求市场,旧产品经二级零售商售予需求随机的二级需求市场的网络均衡问题.将闭环供应链网络均衡模型的求解问题转换为等价的变分不等式求解问题,并利用Nash均衡理论得到了整个闭环供应链达到均衡时的均衡条件,设计了求解该模型的投影收缩算法.结合算例对模型的合理性进行了验证,结果表明：适当提高废旧品的转化率、可再制造品占有率、可修复品占有率对网络整体及资源的循环利用都具有促进意义.

英文摘要：

A closed-loop supply chain equilibrium model is proposed in this paper, both for level-one market and level-two market. The manufacturer/recovery points sell the new products to level one market, and sell reprocessing products to level-two market where the demand is random. With the help of variational inequality theory, the network structure of the closed-loop supply chain is identified. Then the equilibrium conditions of the closed-loop supply chain are obtained by the Nash equilibrium theory. Finally, numerical examples are given to illustrate the beneficial impacts of conversion rate of waste products, remanufacturing part of recycling products, repair part of recycling products on the chain network and cyclic utilization.