Newsvendor Single-Period Order Quantity Calculator
When you can order only once, too little loses margin and too much leaves stock you must scrap or discount. The newsvendor model balances those two costs and gives the order quantity with the best expected profit.
Your numbers
What you recover per unsold unit, after disposal costs.
Your results
Assumes normally distributed demand and a single purchase with no reorder. Use for seasonal, perishable or last-time-buy decisions.
Optimal order quantity vs salvage value
Sweeps Salvage value of leftovers from 0 to 9, holding your other inputs fixed.
Last-time-buy review
Optional: we can review end-of-life parts and quantities against your ERP history.
Optional. The tool and every export work without this. No spam.
How to use it
Enter the selling price, purchase cost and what an unsold unit is worth, then the mean and standard deviation of demand for the selling window. The tool computes underage and overage costs, the critical ratio and the quantity to buy. It also shows expected lost sales and expected profit at that quantity.
- Net salvage value of disposal or restocking fees
- Use demand for the whole window, not per week
- Good fit for last-time buys on end-of-life parts
The method
Underage cost Cu is price minus cost. Overage cost Co is cost minus salvage. The optimal service probability is the critical ratio Cu / (Cu + Co). The order quantity is the demand mean plus z times the standard deviation, where z is the normal inverse of that ratio. Expected lost sales use the unit normal loss function.
Reading the result
A high margin product with low salvage still gets a quantity above the mean, because stockouts hurt more than leftovers. When salvage rises, Co falls and the optimal quantity rises. The chart shows exactly that. Compare the optimal quantity with supplier minimum order quantities, which may force you away from the optimum.
Common mistakes
Using revenue instead of margin for the underage cost, ignoring disposal fees, and using monthly sigma for a seasonal total are the usual errors. For repeat replenishment, use a reorder point or periodic review policy instead. This model is for one purchase decision with no second chance.
Frequently Asked Questions
When should I use the newsvendor model?
Use it when you place one order for a selling window and cannot replenish, such as seasonal goods, event stock, short shelf-life items or a last-time buy before a part goes obsolete.
What is the critical ratio?
It is underage cost divided by the sum of underage and overage cost. It is the probability that demand will not exceed your order quantity at the optimum, so it also acts as the target service level.
What if salvage is higher than cost?
Then overage cost is negative, which means leftovers have value greater than what you paid. The model no longer applies in the usual sense. Check the inputs or treat the item as a normal stocked part.
How do I estimate demand sigma?
Use the spread of demand across comparable past windows, or the forecast error from your planning system for the same horizon. Do not scale a weekly sigma by guesswork. Ask your demand planner for the window level.
If you want last-time buys and seasonal quantities pulled from item history in your ERP, Netray can build that workflow.
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