Newsvendor

The Newsvendor problem gives the optimal order quantity for a single-period inventory decision when the demand distribution is known. The name comes from a newspaper vendor who orders the morning print run; whatever sells is profit, whatever doesn't is scrapped. The same structure appears in fresh food, seasonal apparel, event tickets, blood inventory, and airline overbooking. The solution rests on the 'critical fractile': optimum service level = margin / (margin + spoilage cost). This ratio tells you what percentile of the demand distribution to order to. Formalized in 1951 by Arrow, Harris, and Marschak, it is one of the most fundamental and still-active models in inventory theory; current work extends it with machine-learning demand forecasts and multi-product substitution models.