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/ )