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A common inventory management problem occurs when the product in question has limited shelf life (e.g., newspapers, produce, computer hardware). There is a cost of over ordering, because the product will shortly become obsolete and worthless. There is also an opportunity cost of under ordering associated with forgone sales. Under such a situation, the question of how much product to order to maximize expected profit is classically referred to as the newsboy problem. In this example, we assume demand has a normal distribution. However, this is not mandatory. Refer to any operations research textbook for a derivation of the formulas involved.
This model also has a fixed ordering charge to deal with. Assuming you decide to order, the fixed charge is a sunk cost and you should therefore order up to the same quantity, S, as when there is no fixed ordering charge. However, there may be cases where preexisting inventory is of a level close enough to S that the expected gains of a minimal increase in inventory are not outweighed by the fixed order charge. The problem now is to not only determine S (or "big S"), but also to determine the additional parameter, s (or "little s"), where when inventory exceeds s the optimal decision is to not incur a fixed charge by foregoing an order for additional stock. Inventory strategies such as this are referred to as "littles-big S", or (s,S), policies.