An intuitive approach to inventory control with optimal stopping

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 con-cepts 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). (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

In this research note, it is shown that applying Breiman's work from 1964 on optimal stopping can lead to an elementary proof of the fact that (s, S) policies minimize the long-run average cost for periodic-review inventory control problems. The proof method is appealing as it only relies on basic concepts of renewal-reward processes, optimal stopping, dynamic programming, and root-finding. Furthermore, it provides an efficient algorithm for computing the optimal policy parameters. If Breiman's paper had received the attention it deserved, computational methods for (s, S)-policies could have been discovered about three decades earlier than the famous algorithm by Zheng and Federgruen (1991).