How to use the newsvendor order quantity calculator
- Enter the cost per unit and the selling price per unit.
- Enter the value of a leftover unit, such as a clearance price, or 0 if leftovers are wasted.
- Enter the average demand and its standard deviation, the usual spread around the average.
- Read the best order quantity, the expected profit and the expected leftovers and unmet demand.
Formula
underage cost = price - cost, overage cost = cost - leftover value
critical ratio = underage / (underage + overage)
best order = average demand + z x standard deviation, where z has cumulative probability equal to the critical ratio
expected leftover = sd x (z x Phi(z) + phi(z))
Phi is the standard normal cumulative distribution and phi its density, with z = (order - average) / sd. Expected sales are the order less the expected leftover, and expected profit is price x sales + leftover value x leftovers - cost x order.
A seasonal item with uncertain demand
A unit costs $6 and sells for $15. Leftovers fetch $2. Demand averages 400 units with a standard deviation of 80. Selling one more unit earns $9, while a unit left over loses $4 ($6 cost less $2 recovered), so the critical ratio is 9 / (9 + 4) = 0.6923. The exact best order is 440.19 units, and 440 whole units has the higher expected profit.
At 440 units the expected profit is $3,234.29, with 384.2 units sold on average, 55.8 left over and 15.8 of demand unmet. Ordering the average demand of 400 instead gives an expected profit of $3,185.10, so the shift to 440 earns about $49 more. Ordering less loses sales and ordering more loses on leftovers.
The idea behind the critical ratio
Every extra unit ordered either sells, earning the margin, or does not, losing the part of its cost you cannot recover. The best order is the point where the chance that the last unit sells balances those two outcomes. That chance is the critical ratio, and it is higher when the margin is large and the loss on leftovers is small. The best order is then the demand level that is not exceeded that share of the time.
A high ratio calls for ordering above the average demand, and a low ratio for ordering below it. When the margin equals the loss on leftovers, the ratio is one half and the answer is the average.
When this model applies
It fits one selling period, one order and demand you can describe by an average and a spread: fashion, a seasonal food item, event stock or a daily bake. If you reorder through the year with steady demand, use the EOQ Calculator and the Reorder Point Calculator instead. For ordering with price breaks, use the EOQ with Quantity Discounts Calculator. The Expected Value Calculator helps weigh uncertain outcomes more generally.
Assumptions and limits
- Demand follows a normal curve with the average and spread you enter. Real demand can be skewed, and the curve allows a little negative demand.
- There is one selling period and one order. Lost sales carry no extra goodwill cost.
- The cost, price and demand in the fields are examples. Use your own numbers.
- The price must be above the cost and a leftover must be worth less than it cost.
Frequently asked questions
What does the critical ratio tell me?
It is the chance, at the best order, that demand will not be higher than what you ordered. A ratio of 0.69 means you plan to cover demand about 69% of the time.
Why does the page refuse a leftover value equal to the cost?
If a leftover is worth what it cost, there is no loss from ordering too much, so the best order would have no upper limit. The model needs a leftover value below the cost.
How do I find the standard deviation of demand?
Use the standard deviation of past demand for the same period, such as the units sold each week. It measures how much demand usually varies around its average.
Why is the answer a whole number when the exact value is not?
You can only order whole units, so the page compares the whole numbers on either side of the exact value and shows the one with the higher expected profit.