A newsstand must decide how many papers to buy BEFORE knowing the day’s demand. Buy too few and you lose sales (underage); buy too many and you eat the leftovers (overage). The optimal order isn’t the average demand — it’s set by the RATIO of those two costs. If missing a sale hurts more than a leftover, you deliberately overstock. Slide the cost balance and watch the order shift.
The newsvendor problem: order Q once, before uncertain demand D. The optimal Q* satisfies P(D ≤ Q*) = Cu/(Cu + Co), the CRITICAL RATIO — where Cu is the underage cost (lost margin per unit short) and Co the overage cost (loss per unit unsold). So you stock to the fractile of the demand distribution set by the cost balance, NOT the mean: when underage hurts more (Cu > Co) the ratio exceeds 0.5 and you deliberately overstock; when leftovers hurt more, you understock. It governs perishables, fashion, capacity and staffing. A fail-loud self-check throws unless a higher underage cost raises the critical ratio (order more). ◆ real operations research, node-verified.
The single-period critical-ratio result (exact for any demand distribution); real settings add salvage values, multiple periods and correlated demand — the order-to-the-cost-fractile, not the mean, principle is exact.