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Technical Note - Monotone Optimal Issuing Policies in a Deterministic Inventory Model

We consider the problem of optimal issuing policies in deterministic inventory theory. We show that monotone policies are optimal for any number of items if they are optimal for two items. We do this by extending the models in the literature to allow the possibility of replacing items before the end of their lifetime. This option simplifies proofs. Moreover, as we demonstrate under certain conditions there are optimal policies in the extended model in which no replacement occurs until the end of an item's lifetime. Connections to existing literature are provided.