Newsvendor · critical fractile

DON'T MAKE THE FORECAST. MAKE A QUANTILE OF IT.

Q* = F−1 ( CuCu + Co )

Make too much and you eat the product. Make too little and you eat the order. The optimal quantity is not the average demand — it is the point where the chance of running out equals the cost ratio between those two mistakes. Only the ratio matters: double both costs and nothing moves. When a stockout hurts nine times more than waste, you deliberately plan to throw some away.