Operations Research & Inventory Optimization Lab

Newsvendor Model Calculator

Calculate optimal stocking quantity, critical fractile service level, expected profit, stockout risk, and waste using the single-period Newsvendor model.

Newsvendor Engine Quantity Sweep Analysis Mathematical Theory FAQ

Industry Archetypes

Load benchmark single-period models.

Step 1: Set Unit Economics, Salvage & Demand Distribution

Economic & Stochastic Demand Parameters

Full retail selling price.
Direct acquisition or production cost.
Markdown or clearance price for leftovers.
Net destruction or holding cost.
Forecasted average customer demand.
Demand uncertainty volatility measure.
Optimal Stocking Q*
1,173 units
+173 vs mean demand (z = 0.69)
Critical Fractile Service Level
75.6%
Cu: $170.00 | Co: $55.00
Expected Net Profit
$151,842
Exp Sales: 954 | Leftover: 219
Value of Perfect Info (EVPI)
$18,158
Perfect Info Max Profit: $170,000

Order Quantity Decision Sweep & Profit Curve

Comparison of expected sales, leftover waste, stockout risk, and net profit across stocking quantities from μ - 2σ to μ + 2σ.

Order Quantity (Q) In-Stock Probability Stockout Risk Expected Sales Expected Leftover Expected Lost Sales Expected Profit

Operations Research & Supply Chain

Principles of Single-Period Inventory Optimization

Core operational takeaways from the Newsvendor model:

  • Asymmetric Loss: When the profit per sale ($C_u$) is greater than the loss per unsold unit ($C_o$), stocking above the average demand is mathematically optimal.
  • The Critical Fractile ($SL^*$): Balances marginal benefit and marginal cost: $P(D le Q^*) = rac{C_u}{C_u + C_o}$.
  • The Cost of Uncertainty: The Value of Perfect Information (EVPI) measures the exact maximum budget an executive should allocate to predictive AI demand forecasting.
  • Salvage Value Leverage: Increasing secondary channel salvage recovery ($S$) directly lowers overage penalty ($C_o$), allowing higher initial orders.

Test multi-echelon demand distortion in the Bullwhip Effect Lab.

Mathematical Formulation

Newsvendor equations

Cost_of_Underage: C_u = Price - Cost

Cost_of_Overage: C_o = Cost - Salvage + Penalty

Critical_Fractile: SL* = C_u ÷ ( C_u + C_o )

Optimal_Order: Q* = μ + Φ^-1( SL* ) × σ

Expected_Profit: E[Π] = P × E[Sales] + S × E[Leftover] - C × Q*

Model reorder cycles in the Safety Stock & Reorder Point Lab.

FAQ

Newsvendor model questions

What is the Newsvendor model in inventory management?

The Newsvendor (or Newsboy) model is a mathematical optimization framework used in supply chain management to determine the profit-maximizing inventory order quantity for perishable or single-period goods with stochastic (uncertain) demand.

How is the Critical Fractile calculated?

The critical fractile (optimal in-stock probability) is calculated as Cu / (Cu + Co), where Cu is the cost of underage (Price - Cost) and Co is the cost of overage (Cost - Salvage + Penalty).

Why shouldn't a business just stock the average demand?

Stocking average demand yields a 50% in-stock rate. When profit margin per unit (Cu) is significantly higher than salvage loss (Co), stocking above the mean captures high-margin sales and dramatically increases total expected profit.

What is the Expected Value of Perfect Information (EVPI)?

EVPI represents the maximum financial gain a business could achieve if demand uncertainty were completely eliminated through perfect predictive forecasting.

Can I export the Newsvendor optimization model to CSV?

Yes. You can export complete economic parameters, optimal order quantity Q*, critical fractiles, expected sales, leftovers, and quantity sweep matrices as a UTF-8 CSV spreadsheet with formula defense.

Continue Exploring Inventory & Operations Tools

Explore our Retail & Inventory Hub, analyze multi-echelon distortion in the Bullwhip Effect Lab, calculate buffer stock in the Safety Stock & Lead Time Lab, model batch ordering in the EOQ Lab, or optimize clearance discounts in the Markdown Optimization Lab.