The mathematical model for optimal inventory ordering under uncertain demand is the newsvendor model.
It addresses a single-period stocking decision: how many units should be ordered before demand is known? The classic example is a newspaper vendor choosing a morning quantity. Too few copies mean lost sales, while too many leave unsold papers with little or no value. The same logic applies to seasonal goods, fashion items, fresh food, spare capacity, and other products whose demand or usefulness is limited in time.
The model balances underage cost—the consequence of ordering too little—against overage cost—the cost of ordering too much. In the standard formulation, the optimal quantity is determined by a critical fractile, which selects a percentile of the demand distribution rather than simply using average demand.
The model is also called the newsboy, single-period, or salvageable model. It is not the same as EOQ, which is designed for repeated replenishment with relatively stable assumptions. Wagner–Whitin concerns dynamic lot sizing over multiple periods, while EPQ models production lot sizing. Real-world extensions can include salvage value, fixed costs, lead times, capacity limits, and multiple ordering opportunities.