# Newsvendor Single-Period Order Quantity Calculator

> Source: https://netray.co/tools/newsvendor-single-period-order-quantity-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find the best one-time order quantity for seasonal, short-life or last-time buys using the critical ratio.

## Category

supply-chain

## Audience

- Materials planner
- Buyer
- Demand planner

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Selling price per unit

**Key:** price

**Type:** number

**Default:** 25

**Min:** 0

**Step:** 0.5

**Unit:** $

#### Purchase cost per unit

**Key:** cost

**Type:** number

**Default:** 10

**Min:** 0

**Step:** 0.5

**Unit:** $

#### Salvage value of leftovers

**Key:** salvage

**Type:** slider

**Default:** 4

**Min:** 0

**Max:** 9

**Step:** 0.5

**Unit:** $

**Help:** What you recover per unsold unit, after disposal costs.

#### Mean demand for the period

**Key:** mu

**Type:** number

**Default:** 2000

**Min:** 0

**Step:** 50

**Unit:** units

#### Std deviation of demand

**Key:** sd

**Type:** number

**Default:** 500

**Min:** 0

**Step:** 25

**Unit:** units

**Outputs:**

#### Underage cost per unit

**Key:** cu

**Expr:** price - cost

**Format:** currency

**Description:** Margin lost for each unit of demand you cannot serve.

#### Overage cost per unit

**Key:** co

**Expr:** cost - salvage

**Format:** currency

**Description:** Loss on each unsold unit.

#### Critical ratio

**Key:** cr

**Expr:** clamp(cu / (cu + co), 0.001, 0.999)

**Format:** decimal

#### Z score

**Key:** z

**Expr:** normsinv(cr)

**Format:** decimal

#### Optimal order quantity

**Key:** q

**Expr:** max(0, mu + z * sd)

**Format:** integer

**Primary:** true

#### Unit normal loss L(z)

**Key:** lz

**Expr:** exp(0 - z * z / 2) / sqrt(2 * pi) - z * (1 - normsdist(z))

**Format:** decimal

#### Expected lost sales

**Key:** lost

**Expr:** sd * lz

**Format:** integer

#### Expected profit

**Key:** profit

**Expr:** cu * (mu - lost) - co * (q - mu + lost)

**Format:** currency

**Primary:** true

**Chart:**

#### Optimal order quantity vs salvage value

**Type:** line

**X:** salvage

**From:** 0

**To:** 9

**Steps:** 19

**Series:**

- q

**Disclaimer:** Assumes normally distributed demand and a single purchase with no reorder. Use for seasonal, perishable or last-time-buy decisions.

## Content

**Intro:** 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.

**Sections:**

#### How to use it

**Body:** 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.

**Bullets:**

- 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

**Body:** 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

**Body:** 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

**Body:** 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.

**Cta:** If you want last-time buys and seasonal quantities pulled from item history in your ERP, Netray can build that workflow.

**Faq:**

#### When should I use the newsvendor model?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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?

**Answer:** 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.

## Search terms

newsvendor model calculator, single period inventory model, critical ratio calculator, seasonal order quantity calculator, last time buy quantity, optimal order quantity one time, newsvendor problem solver, overage underage cost calculator

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