中文摘要：

假设在再制造闭环供应链中,集中决策者、第三方和制造商分别从最终客户那里回收废旧品,其回收数量受回收价格和随机因素影响,制造商对获得的旧部件进行再制造,如果旧部件不能满足生产需求,制造商将从新部件供应商那里以高价格采购新部件来补充短缺。本文按照废旧品回收的供应链成员不同,建立了3个定价决策模型,证明了每个模型最优解的存在性和唯一性,然后在特殊情形下进一步求得各模型最优解的解析式,最后用具体算例对模型进行了验证。

英文摘要：

This paper assumes that the centralized decision maker, third party and manufacturer recover the waste products from end users respectively in the remanufacturing closed-loop supply chain. The recovery quantity is affected by price and random factors. The manufacturer remanufactures the recovered old parts, and will purchase new parts with a higher price from suppliers if the demand can＇t be met. This article establishes three pricing models according to different supply chain members responsible for recovering waste products, proves the existence and uniqueness of the optimal solutions for each model, then obtains analytical formulae for the optimal pricing strategies in special cases, and validates the model by conducting numerical examples in the end.