Experiments & Data
Newsvendor Order Quantity Calculator
How much to order when you get exactly one shot and demand is uncertain — the Christmas tree, the printed programme, the perishable batch, the launch run. The instinct is to order the average, and the average is almost always the wrong answer. What decides it is the ratio between what a stockout costs you and what a leftover costs you; when they are not equal, the right order quantity is not the mean.
Inputs
- Unit cost
- Selling price
- Salvage value of a leftover — What an unsold unit is worth at the end — markdown price, scrap, or zero.
- Mean demand
- Demand standard deviation — Roughly two thirds of seasons land within one of these of the mean.
How to use this calculator
- Use this when you order once and live with it: a seasonal run, an event print, a perishable batch, a launch quantity. If you can reorder mid-season, this is the wrong model.
- Enter what one unit costs you, what it sells for, and what an unsold one is genuinely worth at the end: the markdown price, the scrap value, or zero. Salvage is where people flatter themselves, and it moves the answer more than they expect.
- Enter mean demand and its standard deviation. If you have no history, take your realistic best and worst cases, and use about a quarter of the gap between them as the standard deviation.
- Read the critical ratio first. It is the whole lesson. It is the share of the total mistake cost that a stockout represents, and it is also exactly the chance of not running out that the optimal order buys you. Above 50% you should order above your forecast; below 50%, under it.
- Compare the expected profit at Q* with the profit from simply ordering the mean. That gap is what the calculation is worth, and it is why 'order what we think we'll sell' is a habit rather than a decision.
What each term means
- Underage cost (Cu)
- What one unit of unmet demand costs you: the margin you did not earn. Price minus cost.
- Overage cost (Co)
- What one unsold unit costs you: the money you spent that you only partly get back. Cost minus salvage.
- Critical ratio
- Cu ÷ (Cu + Co). The single number that decides the order, and the service level it buys: a 69% critical ratio means the optimal plan runs out in about three seasons in ten.
- Safety stock
- The units ordered above the mean forecast to cover demand landing high. Negative when leftovers cost more than stockouts, and the maths then tells you to deliberately under-order.
- Expected units short
- Average unmet demand at that order quantity. It is never zero unless you order absurdly deep, and pretending otherwise is what produces warehouses full of last year's stock.
- Cost of uncertainty
- The gap between expected profit and what you would earn if you knew demand in advance. It is the price of the forecast being a forecast, and it is what better demand data is worth.
Educational disclaimer: Outputs are simplified educational estimates built from the numbers you enter — they are not financial, legal, tax, or investment advice, and real decisions deserve verified figures and qualified professionals.