中文摘要：

立足于闭环供应链,以循环视点在随机需求条件下,对基于两层的闭环供应链网络均衡问题进行研究,得到了制造商、消费者市场以及整个闭环供应链的均衡条件。针对所建模型,利用拟牛顿算法进行了算例分析,结果表明：废旧产品的回收再制在供应链均衡管理中是双赢的。

英文摘要：

Based on the closed-loop supply chain and from the perspective of cycle under random demands conditions, this peper studies the problem of closed-loop supply chain network equilibrium consisting of manufacturers and consumer markets, the mathimatic models have been built and the equilibrium conditions of the manufacturers, the consumer markets and the closed-loop supply chain have been obtained. In the end, the results obtained through a numerical exemplification by Qusi-Newton algorthem indicate that the recycling of waste products in a closed-loop system of balanced supply chain management is a win-win solution.