Newsvendor Optimal Order Calculator

About this calculator

The newsvendor model (also called the newsboy problem) is a classic operations-research answer to a single-period inventory question: how much of a perishable or seasonal good should you order when leftover units are salvaged for less than they cost, and stockouts mean lost sales? The optimum balances the cost of over-ordering against under-ordering through the critical ratio CR = (p − c)/(p − s), where p is selling price, c is unit cost, and s is salvage value.

Assuming demand is normally distributed with mean μ and standard deviation σ, the profit-maximizing order quantity is Q* = μ + σ·Φ⁻¹(CR), where Φ⁻¹ is the inverse standard normal CDF — so a higher critical ratio (high margin relative to loss) pushes the order quantity above the mean demand, while a low critical ratio pulls it below. Retail buyers use this model for newspapers, fashion apparel, and other single-selling-season goods, and supply chain planners apply the same logic to spare parts and seasonal produce where unsold stock loses most of its value.