In this research note, we show that a simple application of Breiman’s work on optimal stopping in 1964 leads to an elementary proof that $(s,S)$ policies minimize the long-run average cost for periodic-review inventory control problems. The method of proof is appealing as it only depends on the fundamental concepts of renewal-reward processes, optimal stopping, dynamic programming, and root-finding. Moreover, it leads to an efficient algorithm to compute the optimal policy parameters. If Breiman’s paper would have received the attention it deserved, computational methods dealing with $(s,S)$-policies would have been found about three decades earlier than the famous algorithm of Zheng and Federgruen (1991).

在本研究报告中，我们展示了 Breiman 在 1964 年关于最佳停止的工作的简单应用，得出了一个基本证明： $（s,S）$政策最大限度地降低了定期审查库存控制问题的长期平均成本。证明方法很有吸引力，因为它只依赖于更新奖励过程、最优停止、动态规划和寻根等基本概念。此外，它还产生了计算最优策略参数的有效算法。如果 Breiman 的论文得到了应有的关注，那么处理以下问题的计算方法$（s,S）$-政策的发现比著名的郑和费德格鲁恩算法（1991）早大约三十年。