Newsvendor Model (Single-Period Inventory)
Decide how much to stock for a single selling period when demand is uncertain and leftovers are wasted. The newsvendor model balances the cost of ordering too much against the cost of ordering too little to find the profit-maximizing order quantity.
Solve Newsvendor Model →What is the Newsvendor Model?
The newsvendor model determines the optimal order quantity for a single selling period when demand is uncertain and unsold units have little or no value afterward. Its name comes from the classic problem of a newspaper seller who must decide how many papers to buy each morning, knowing that unsold papers are worthless by evening.
The decision balances two costs of being wrong. The overage cost is incurred for each unit ordered but not sold (the loss on excess stock). The underage cost is incurred for each unit of demand that could not be met (the lost profit, and sometimes goodwill). Ordering more reduces underage risk but increases overage risk, and vice versa.
The optimal order quantity is found using the critical ratio, the underage cost divided by the sum of underage and overage costs. This ratio is the target probability that demand will be at or below the order quantity, so the optimal order is the demand level at that percentile of the demand distribution. It elegantly converts the cost trade-off into a single service-level target.
In plain terms: Some things you order once for a single period, and leftovers are worthless, fresh produce, holiday goods, newspapers. Order too many and you eat the loss on unsold units; too few and you miss sales. The newsvendor model weighs those two mistakes and tells you the order quantity that maximizes expected profit.
The Cost Trade-off
Overage Cost
The loss per unit ordered but not sold. Higher overage cost pushes the optimal order down.
Underage Cost
The lost profit per unit of unmet demand. Higher underage cost pushes the optimal order up.
Critical Ratio
Underage / (underage + overage). The target probability that demand is at or below the order, giving the optimal percentile.
Key Formulas
Using the Critical Ratio
The critical ratio is the heart of the model. If unmet demand is far costlier than leftover stock (high underage), the ratio is high and you order generously; if leftovers are costly and lost sales cheap, the ratio is low and you order conservatively. The optimal order is the demand level at that percentile.
This means the optimal order is rarely the average demand. It is shifted above or below the mean depending on which error is more expensive, which is a key insight: matching supply to average demand is generally not profit-optimal under uncertainty.
Assumptions & Validation
Single Period
There is one order and one selling period; leftovers are not carried forward at full value.
If violated: For repeated ordering, use EOQ with a reorder point instead.
Known Demand Distribution
The demand distribution (or its mean and spread) is estimated.
If violated: Estimate the distribution from history or judgment.
Defined Over/Underage Costs
The costs of overstock and understock are quantified.
If violated: Quantify salvage value and lost margin to set the costs.
⚠️ Check assumptions first
The newsvendor model applies to single-period decisions where leftover stock loses most of its value, and it depends on quantifying the overage and underage costs and the demand distribution. A common error is ordering to average demand; the model shows the optimum is usually above or below the mean depending on which error costs more. For repeated replenishment of durable goods, the EOQ and reorder-point framework applies instead.
When NOT to Use Newsvendor Model
Repeated Replenishment
For items ordered repeatedly with carry-over stock, use EOQ and a reorder point.
Steady Known Demand
When demand is constant and known, deterministic order sizing suffices.
Multi-Period Perishables
For perishables managed over several periods, more general stochastic models apply.
Industry Applications
Perishable Goods
Set order quantities for fresh food, flowers or newspapers with no salvage value.
Seasonal & Fashion
Decide production or purchase quantities for one-season items.
Event Inventory
Stock for a one-time event where leftovers cannot be reused.
Capacity Booking
Set booking or overbooking levels where unused capacity expires.
Frequently Asked Questions
What is the newsvendor model?
The newsvendor model determines the optimal order quantity for a single selling period when demand is uncertain and unsold units have little or no residual value. It balances the overage cost of ordering too much against the underage cost of ordering too little, finding the quantity that maximizes expected profit. It is named after the classic problem of a newspaper seller deciding how many papers to buy each day.
What is the critical ratio?
The critical ratio is the underage cost divided by the sum of the underage and overage costs. It represents the target probability that demand will be at or below the order quantity, so the optimal order is the demand level at that percentile of the demand distribution. The critical ratio elegantly converts the cost trade-off between overstocking and understocking into a single service-level target.
Why isn't the optimal order just the average demand?
Because the costs of the two possible errors are usually not equal. If unmet demand is much more costly than leftover stock, it pays to order above average to reduce the chance of a shortage; if leftovers are costly and lost sales cheap, it pays to order below average. The optimal order is shifted from the mean toward whichever error is less expensive, which is a central insight of the model.
When should I use the newsvendor model?
Use it for single-period decisions where you order once, demand is uncertain, and leftover stock loses most of its value, such as perishable food, seasonal fashion, newspapers, or event inventory. It does not apply to items replenished repeatedly with carry-over stock, which are handled by the Economic Order Quantity and reorder-point framework. The defining feature is the single, non-repeating selling period.
What are overage and underage costs?
The overage cost is the loss incurred for each unit ordered but not sold, essentially the purchase cost minus any salvage value. The underage cost is the profit lost for each unit of demand that could not be met, and may include goodwill effects. These two costs drive the critical ratio and therefore the optimal order quantity; quantifying them accurately is essential to applying the model.
How does demand uncertainty affect the newsvendor solution?
Greater demand uncertainty, a wider demand distribution, generally moves the optimal order further from the mean and increases the expected cost of the mismatch between supply and demand. The model handles uncertainty directly by ordering at the critical-ratio percentile of the demand distribution rather than at its average, so the spread of the distribution, not just its mean, shapes the optimal quantity.
Order Optimally for a Single Uncertain Period
Balance overage and underage costs to maximize expected profit. Free during Beta.
Solve Newsvendor Model →