Newsvendor Model Optimizer
Balance the cost of ordering too little against the cost of ordering too much for a single selling period with uncertain demand.
Browser-based calculation
Five demand models
CSV processed locally
Why use this tool?
Decision Supported
Use this tool for one-time or perishable inventory decisions where demand is uncertain and unsold units lose value after the selling period.
What It Tells You
It estimates the profit-balanced order quantity, implied service level, stockout probability, expected sales, leftovers, lost sales, and expected profit.
Example Input
Load the sample to review weekly demand, selling and purchase prices, salvage value, shortage cost, disposal cost, pack size, and a current order quantity.
Sample Output Interpretation
The result explains whether additional availability is worth the extra overstock exposure and compares the optimized policy with the current quantity.
1. Demand Model
Choose a demand distribution and enter the uncertainty expected during one selling or replenishment period.
Demand history and calculations remain in your browser and are not uploaded to a server.
Normal demand is symmetric around the mean. Negative demand is excluded by using a zero lower bound in the numerical evaluation.
Optional expert-adjusted demand
Blend the baseline demand estimate with a documented expert estimate. This is a scenario adjustment, not evidence that the expert estimate is more accurate.
2. Economics and Order Constraints
Use values for the same item, currency, and decision period as the demand model.
Operational constraints
Optional limits are applied after the theoretical Newsvendor quantity. Leave a field blank when it does not apply.
Salvage Value
Cash recovered from an unsold unit through markdown, return, reuse, or disposal proceeds. Enter zero when there is no recovery.
Shortage Cost
An additional penalty beyond the lost unit margin, such as expediting, contractual penalties, or measurable loss of goodwill.
Holding / Disposal Cost
Additional end-of-period cost for an unsold unit, such as storage, destruction, return handling, or write-off processing.
Is Newsvendor the Right Method?
Choose the method that matches the timing and structure of the inventory decision.
NewsvendorOne order for one uncertain selling period.
Economic Order QuantityRepeated ordering with reasonably stable demand.
Safety Stock & Reorder PointOngoing replenishment under demand or lead-time uncertainty.
Exponential SmoothingEstimate future demand before setting an inventory policy.
Monte Carlo SimulationExplore uncertain outcomes from a selected or custom formula.
About the Newsvendor Model
The Newsvendor model supports a single-period inventory decision when demand is uncertain and there is one meaningful opportunity to order before demand is known. Typical applications include seasonal products, event stock, fresh food, fashion, spare parts for a planned shutdown, and other short-life or one-time purchasing decisions.
It is not a continuous-replenishment model. Use EOQ for repeated stable-demand ordering and Safety Stock & Reorder Point when inventory can be replenished during an ongoing operating cycle.
Guidance
- Define demand for one decision period and select a distribution supported by evidence.
- Enter economic inputs without double-counting lost margin, salvage recovery, or disposal costs.
- Review the underage cost, overage cost, and critical ratio before accepting the quantity.
- Apply pack-size constraints and compare the optimized quantity with the current policy.
- Use scenario planning to understand how much expected profit changes around the recommendation.
- Compare demand models and the bootstrap range before relying on a precise quantity from limited history.
Methodology, Assumptions, and Limitations
Formula Logic
Underage cost
Cu = selling price - unit cost + additional shortage cost
Overage cost
Co = unit cost - salvage value + holding/disposal cost
Critical ratio
CR = Cu / (Cu + Co)
Unrounded optimum
Q* = F-1(CR), where F is the demand cumulative distribution
Sales, leftovers, and lost sales
Sales = min(D, Q); leftovers = max(Q - D, 0); lost sales = max(D - Q, 0)
Expected profit
E[π(Q)] = pE[sales] + vE[leftovers] - cQ - hE[leftovers] - kE[lost sales]
Service level
Pr(D ≤ Q) = F(Q); stockout probability = 1 - F(Q)
Expert-adjusted moments
μ = wμh + (1 - w)μe; variance includes within-estimate variance and the difference between each estimate and the blended mean
Near-optimal range
Feasible pack quantities where expected profit is at least 99% of the maximum feasible expected profit
Bootstrap stability
Repeated resamples of empirical history produce a distribution of recommended pack quantities; the displayed range uses its 10th and 90th percentiles
Assumptions
There is one order opportunity, demand belongs to one decision period, unit economics are constant, and unsold units have a known end-of-period value or cost.
Distribution Treatment
Normal, Uniform, and symmetric Triangular models use mean and standard deviation. Poisson uses its mean rate. Empirical analysis uses the uploaded observations directly.
Limitations
The model does not include multiple replenishments, capacity interactions, substitution, demand learning during the period, price optimization, or risk preferences beyond expected profit.
FAQ
When should I use the Newsvendor model?
Use it when one order must cover one uncertain selling period and leftover inventory has reduced value or creates a disposal cost.
Why is the optimal service level not automatically 95%?
The model balances shortage and overage economics. A higher shortage cost raises the critical ratio; a higher overage cost lowers it.
Does salvage value mean the normal selling price?
No. It is the amount recovered from each unsold unit after the regular selling opportunity, such as markdown revenue, return credit, or reuse value.
Which distribution should I choose?
Use Normal for roughly symmetric continuous demand, Uniform when only a credible range is known, Triangular for a symmetric peaked range derived from mean and variability, Poisson for integer event counts, and empirical demand when sufficient relevant history is available.
How does expert adjustment work?
The tool blends baseline and expert means and variances using the selected weight. The adjustment should be documented and tested as a scenario rather than treated as objective evidence.
How is this different from Monte Carlo simulation?
The Newsvendor model solves one defined decision: how much to order for a single uncertain period. It uses demand and inventory economics to calculate a profit-balanced quantity. Monte Carlo simulation is broader: it samples uncertain inputs in a selected or custom formula to estimate an outcome distribution and target probability, but it does not inherently optimize an order quantity.
Are uploaded demand values sent anywhere?
No. The current tool parses the CSV and performs all calculations locally in your browser.