Newsvendor Model
The Newsvendor Model helps determine the optimal order quantity for perishable goods when demand is uncertain. It balances the costs of overordering (excess inventory) and underordering (lost sales).
Critical Ratio = Cu / (Cu + Co)
Where:
- Cu = Cost of underordering (profit per unit)
- Co = Cost of overordering (loss per unsold unit)
- Optimal Quantity = Smallest quantity where cumulative probability ≥ Critical Ratio
Results
Optimal Order Quantity: units
Cost of Underordering (Cu)
Profit per unit
Cost of Overordering (Co)
Loss per unsold unit
Critical Ratio
Target service level
Calculation Details
| Demand | Probability | Cumulative Probability | Optimal? |
|---|
Practical Examples
Example 1: Newspaper Sales
Cost: $0.50 | Price: $2.00 | Salvage: $0.10
Discrete Demand: 100(0.2), 150(0.5), 200(0.3)
Cu: $1.50 | Co: $0.40 | Critical Ratio: 0.789
Optimal Quantity: 200 units
Example 2: Bakery Goods
Cost: $1.00 | Price: $3.00 | Salvage: $0.50
Normal Demand: μ=200, σ=30
Cu: $2.00 | Co: $0.50 | Critical Ratio: 0.8
Optimal Quantity: ~215 units
Example 3: Seasonal Fashion
Cost: $20 | Price: $50 | Salvage: $5
Uniform Demand: 100-300 units
Cu: $30 | Co: $15 | Critical Ratio: 0.667
Optimal Quantity: ~233 units
Newsvendor Model Interpretation
| Critical Ratio Range | Interpretation | Business Implication |
|---|---|---|
| Below 0.5 | High cost of overordering | Conservative ordering strategy |
| 0.5 | Equal costs | Median demand is optimal |
| Above 0.5 | High cost of underordering | Aggressive ordering strategy |
| Approaching 1.0 | Very high cost of underordering | Order to meet nearly all possible demand |