# Bullwhip Effect Calculator

> Source: https://netray.co/tools/bullwhip-effect-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

See how much order variability a supplier sees compared with end customer demand, based on replenishment lead time and the number of periods used in the moving average forecast.

## Category

supply-chain

## Audience

- Demand planner
- Supply chain manager
- S&OP lead

## Tool

**Kind:** calculator

**Inputs:**

#### Standard deviation of end customer demand

**Key:** sigma_d

**Type:** number

**Default:** 100

**Min:** 0

**Step:** 5

**Unit:** units per period

#### Replenishment lead time

**Key:** lead

**Type:** number

**Default:** 4

**Min:** 0

**Step:** 1

**Unit:** periods

**Help:** Order to receipt, in forecast periods.

#### Moving average periods in forecast

**Key:** p

**Type:** slider

**Default:** 6

**Min:** 1

**Max:** 26

**Step:** 1

**Unit:** periods

#### Number of stages in chain

**Key:** stages

**Type:** slider

**Default:** 3

**Min:** 1

**Max:** 6

**Step:** 1

**Help:** Each stage is assumed to use the same policy, so the effect compounds.

**Outputs:**

#### Variance ratio at one stage

**Key:** ratio1

**Expr:** 1 + 2 * lead / p + 2 * lead * lead / (p * p)

**Format:** decimal

**Primary:** true

**Description:** Lower bound of order variance divided by demand variance.

#### Standard deviation amplification

**Key:** sd_ratio

**Expr:** sqrt(ratio1)

**Format:** decimal

#### Std deviation of orders placed

**Key:** sd_order

**Expr:** sigma_d * sd_ratio

**Format:** decimal

**Description:** What your supplier sees for one stage.

#### Variance ratio across all stages

**Key:** ratio_chain

**Expr:** pow(ratio1, stages)

**Format:** decimal

**Primary:** true

#### Std deviation at top of chain

**Key:** sd_chain

**Expr:** sigma_d * sqrt(ratio_chain)

**Format:** integer

**Chart:**

#### Variance amplification vs lead time (one stage)

**Type:** line

**X:** lead

**From:** 0

**To:** 20

**Steps:** 20

**Series:**

- ratio1

**Disclaimer:** Based on the order-up-to policy with moving average forecasting and no price fluctuation or batching. Real chains add batching, promotions and rationing, so treat the value as a lower bound.

## Content

**Intro:** The bullwhip effect is the growth of order variability as you move upstream from the customer. A stable end demand can turn into wild swings at the raw material supplier. This calculator uses the well known Lee, Padmanabhan and Whang lower bound to show how lead time and forecast smoothing drive it.

**Sections:**

#### How to use it

**Body:** Enter the standard deviation of end customer demand per period, the replenishment lead time in the same periods, and the number of periods in the moving average that your replenishment forecast uses. Set the number of stages that follow the same logic, for example retailer, distributor and plant. The tool shows the variance ratio at one stage and compounded over the chain.

**Bullets:**

- Use consistent period lengths
- Lead time includes review period
- Try a longer moving average to see the damping
- Chart shows the cost of long lead times

#### The formula

**Body:** For an order-up-to policy with a p-period moving average and lead time L, the variance of orders divided by the variance of demand is at least one plus 2L over p plus 2L squared over p squared. The ratio rises with lead time and falls when p grows. Compounding across stages multiplies the ratios, which is why a few stages can produce a many-fold amplification.

#### Reading the result

**Body:** With L of 4 and p of 6 the single stage ratio is 2.78, so order standard deviation is about 1.7 times demand. Over three stages the variance ratio is about 21 and standard deviation is 4.6 times. Doubling p to 12 brings the single stage ratio to 1.89. Shorter lead times, shared point of sale data and smaller order batches all pull the number down.

#### Practical countermeasures

**Body:** Share end demand with suppliers instead of passing on your orders, shorten lead times, stabilise pricing so forward buying disappears, cut order batch sizes, and avoid rationing games during shortages. Inside one company, a stable production plan with a frozen horizon also damps the whip between sales, planning and the shop floor. Do not smooth so heavily that you cannot react to a real change in demand.

**Cta:** Netray can compare actual order variance against demand variance across your ERP's customers, plants and suppliers and show where the whip is largest.

**Faq:**

#### What is the bullwhip effect?

**Answer:** It is the increase in demand variability moving up a supply chain from retailer to manufacturer to supplier, caused by forecast updating, order batching, price fluctuation and shortage gaming.

#### How do you measure the bullwhip ratio in practice?

**Answer:** Divide the variance of orders placed by the variance of demand received over the same periods, per item or family. A ratio above 1 means amplification.

#### Why does a longer lead time increase it?

**Answer:** Longer lead times require covering more periods of demand with the order-up-to level, so a small change in the forecast produces a larger change in the order. The formula grows with L and L squared.

#### Is the calculated value exact?

**Answer:** No. It is a lower bound under simple assumptions. Batching, promotions and rationing push real ratios higher.

## Search terms

bullwhip effect calculator, bullwhip effect formula, demand amplification supply chain, order variance ratio, lee padmanabhan whang bullwhip, reduce bullwhip effect, supply chain variability calculator, order up to policy variance

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