NewsvendorModell

The NewsvendorModell, often referred to in English as the Newsvendor model, is a classic one-period inventory problem in operations research. It is used to determine the optimal order quantity for perishable or single-period products when demand is uncertain. The objective is to maximize expected profit or minimize expected cost, given selling price, purchase cost, and any salvage value for leftover stock.

The model considers a single decision variable Q (the order Quantity) and a random demand D during the period. Parameters typically include the selling price p, purchase cost c, and salvage value s for unsold units. A common setup assumes no backlogging: if demand exceeds supply, unmet demand is a lost sale; if supply exceeds demand, excess units can be salvaged at value s. The realized profit is p·min(D,Q) + s·max(0,Q−D) − c·Q.

A key result is the critical fractile solution. Define Cu = p − c as the underage (lost sales) cost and Co = c − s as the overage (excess stock) cost. The optimal quantity Q* satisfies the condition F(Q*) = Cu/(Cu + Co) = (p − c)/(p − s), where F is the cumulative distribution function of D. In a continuous-demand setting, Q* is the q-quantile of D with q = (p − c)/(p − s).

Extensions include multi-product or multi-period settings, service-level constraints, and dynamic or robust approaches. Limitations involve the assumption of a known demand distribution, fixed prices, no backorders, and a single period. The model remains widely used for fashion, perishables, and seasonal goods.