在随机库存管理研究中, 当发生缺货时, 管理者可通过延期交付的方式满足愿意等待的顾客需求, 但现有研究较少考虑退货行为对订货策略的影响。事实上, 大量的退货能够显著影响库存水平。本文针对有退货情形的库存系统, 综合考虑顾客的退货行为以及缺货时顾客耐心的随机性, 证明了在零交货期条件下, 基本库存策略为最优策略, 并给出其解析解。有趣的是, 最优库存水平可能为负值。 

In stochastic inventory management studies, managers can fulfill the demand of customers willing to wait through replenishment and delayed fulfillment when stockouts occur. However, the impact of product returns on ordering policies has received limited attention. In fact, a large volume of product returns can significantly affect inventory levels. This paper investigates an inventory system with product returns, comprehensively considering customer return behavior. and the randomness of customer patience during stockouts. It is proved that the base-stock policy is optimal under the condition of zero lead time, and the analytical solution is derived. Interestingly, the optimal inventory level may be negative.