中文摘要：

为了研究顾客退货条件下的供应链最优价格和服务水平决策，构建了零售商提供服务下的顾客退货模型，分别在垂直集成博弈和制造商为斯坦伯格主导者博弈下得出了最优决策结果和最优利润．通过与不提供服务情形下的最优利润进行对比，得出了零售商应该提供服务的边界条件．结果表明：制造商为斯坦伯格主导者博弈下，提供服务的零售商和制造商比无服务提供的总是获得更高的利润；而垂直集成博弈下的供应链应该在某一特定条件下提供服务．最后，通过数值举例，分析了提供服务的成本和退货概率的变化对最优决策的影响．

英文摘要：

To investigate the optimal retail price and service level in a supply chain under consumer returns, a consumer returns model under the retailer＇s service provision is built. The optimal decision results and optimal profits are obtained in the vertical integration game and the manufacturer Stackelberg game, respectively. Through comparing the optimal profits with service provision with those of no service provision, the boundary conditions that the retailer＇s service should be provided are derived. The results show that in the manufacturer Stackelberg game, the optimal profit of the retailer and the manufacturer with service is always superior to that of a no service provision. However, in the vertical integration game, the supply chain can only benefit from the service under certain conditions. Finally, through numerical examples, the impacts of the cost for providing services and the consumer return rate on the optimal decisions are analyzed.