Inventory
How much to order: newsvendor.
For stock you can only order once before demand arrives and that loses value afterwards. Enter price, cost, salvage value and your demand estimate to get the profit-maximising order.
Order up to the point where the chance that demand is at or below your order equals the underage cost divided by (underage plus overage cost). At a $5.00 price, $2.00 cost and $0.50 salvage, with demand averaging 80 and a spread of 15, order 86 units.
Your numbers
Result
Worked example
A cafe bakes a batch of pastries each morning. Each sells for $5.00 and costs $2.00 to make, and leftovers are sold at day-end for $0.50. Demand averages 80 with a standard deviation of 15. Selling one more pastry earns $3.00 (the underage cost); a leftover loses $1.50 (the overage cost). The critical ratio is $3.00 / ($3.00 + $1.50) = 66.7%, so the order should cover demand 66.7% of the time. The matching z-score is 0.431, giving 80 + 0.431 x 15 = 86.46, so 86 units. Expected sales are 76.5 units, expected leftovers 9.5, and expected profit $215.45. With no salvage value at all the ratio is (5 - 2) / 5 = 60% and the order drops to 84.
How it works
The newsvendor model applies to a single period, with random demand and stock delivered before demand is known. Wikipedia lists the assumptions as separable products, planning for a single period, random demand, deliveries made in advance of demand, and linear costs of overage and underage. With a zero salvage value the optimal quantity is q = F-1((p - c) / p), the critical fractile, where F is the demand distribution, p the price and c the unit cost.
This page extends that to a salvage value s by using underage cost p - c and overage cost c - s, so the critical ratio is (p - c) / (p - s). With s = 0 it reduces to the formula above. That extension is our own derivation of the same balance between the cost of running out and the cost of a leftover, not a formula quoted from the source. Demand is modelled as a normal curve with the mean and standard deviation you enter: q = mean + z x sd, where z is the inverse normal of the critical ratio. Because the normal curve is only a rough fit, treat the result as a starting point and check it against how much demand has actually varied. The whole-number order is the one of the two nearest integers with the higher expected profit.
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Sources
- Newsvendor model - Wikipedia (opened 2026-10-08): the model assumptions and the critical fractile formula q = F^-1((p - c) / p) for the zero-salvage case.
The salvage-value extension and the normal-demand arithmetic (z-score, expected sales and leftovers) are standard mathematics applied here by us and are not quoted from the source.
FAQ
What is the newsvendor model?
A single-period inventory model for products with uncertain demand where leftovers lose value, such as newspapers, fresh food or event merchandise. It finds the order quantity that maximises expected profit.
What is the critical ratio?
The underage cost divided by the sum of the underage and overage cost. It is the probability that demand is at or below your order quantity at the optimum. A higher margin and a lower loss on leftovers push it up, which means ordering more.
What do I enter for the standard deviation?
A measure of how much demand varies from period to period. Take the standard deviation of your past sales for the same kind of day or event. If demand is very steady, a small number gives an order close to the average.
Why does a high margin mean ordering more than average?
When the profit on a sale is larger than the loss on a leftover, running out costs more than overstocking, so the best order is above expected demand. When leftovers are costly relative to margin, the best order is below it.
When should I not use this?
When you can reorder during the period, when unsold stock keeps its full value, or when demand is nowhere near a bell curve. For regular restocking use the reorder point and EOQ calculators instead.