Optimality of (s, S) policies in EOQ models with general cost structures

The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories. We study an extension of the original EOQ model that permits a minimal set of assumptions on the ordering/procurement and holding/backorder costs and establish necessary and sufficient conditions for the existence of an optimal policy of the (s, S) type. Our work lends theoretical credibility to the practice of using (s, S) policies for virtually any cost structure of practical interest. Our proof is constructive and elementary, in the sense that it is based on first principles that do not rely on advanced mathematical machinery. We also prove that an optimal policy, not necessarily of the (s, S) type, always exists within our general EOQ framework.