HesapHanem

Newsvendor Optimal Order Calculator

Enter price, cost, salvage value and demand statistics to find the optimal order quantity.

How it is calculated

The tool assumes demand is normally distributed for one selling period. First the critical ratio CR = (price − cost) ÷ (price − salvage), which is the probability of not running out that maximizes expected profit. Then z = Φ⁻¹(CR), the inverse standard normal value (a numerical approximation), and the order quantity is Q = μ + z × σ with μ the mean demand and σ its standard deviation, both in units. Salvage is optional and defaults to 0. The tool needs price > cost > salvage and σ > 0, otherwise there is no result. Q is rounded to whole units. It does not cap Q at zero, so a very wide σ with a low CR can give a small or negative figure, and it ignores shortage penalties and order minimums.

Worked example

Price 25, cost 10, salvage 4, mean demand 100 and standard deviation 20. Critical ratio: (25 − 10) ÷ (25 − 4) = 15 ÷ 21 = 0.7143, or 71.43%. The z value for 0.7143 is 0.566. Order quantity: 100 + 0.566 × 20 = 111.3, shown as 111 units. Without a salvage value the ratio would be 60.00% and the order only 105 units.

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Common mistakes

  • Entering profit per unit in place of price. Price and cost are the full selling price and full purchase cost, because the formula subtracts them itself.
  • Entering a salvage value higher than cost. The model then has no result, since unsold units would be worth more than they cost.
  • Using the standard deviation of a single day's demand for a week-long selling period. μ and σ must describe demand over the same period you order for.
  • Expecting the order to equal mean demand. A critical ratio above 50 percent pushes Q above μ, and a ratio below 50 percent pulls it below.
  • Applying the formula to demand that is clearly not bell-shaped, for example very skewed or lumpy sales. The normal assumption then makes the quantity unreliable.

About this calculator

The newsvendor model (also called the newsboy problem) is a classic operations-research answer to a single-period inventory question: how much of a perishable or seasonal good should you order when leftover units are salvaged for less than they cost, and stockouts mean lost sales? The optimum balances the cost of over-ordering against under-ordering through the critical ratio CR = (p − c)/(p − s), where p is selling price, c is unit cost, and s is salvage value.

Assuming demand is normally distributed with mean μ and standard deviation σ, the profit-maximizing order quantity is Q* = μ + σ·Φ⁻¹(CR), where Φ⁻¹ is the inverse standard normal CDF — so a higher critical ratio (high margin relative to loss) pushes the order quantity above the mean demand, while a low critical ratio pulls it below. Retail buyers use this model for newspapers, fashion apparel, and other single-selling-season goods, and supply chain planners apply the same logic to spare parts and seasonal produce where unsold stock loses most of its value.

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Comments (1)

  • Editorial team

    Spread matters as much as the average. With price 25, cost 10 and salvage 4, a mean demand of 100 gives an order of 111 when sigma is 20 and 123 when sigma is 40, because the critical ratio stays at 71.43%. Uncertain demand therefore pushes the order further from the mean. If the ratio is low, the formula can return a negative quantity, which really means order nothing. How do you estimate sigma for your own product?

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