# Risk Pooling Safety Stock Centralization Calculator

> Source: https://netray.co/tools/risk-pooling-safety-stock-centralization-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

See how much safety stock you save by pooling several locations into one, given how correlated their demand is.

## Category

supply-chain

## Audience

- Supply chain manager
- Materials planner
- Distribution planner

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Number of locations

**Key:** n

**Type:** slider

**Default:** 4

**Min:** 1

**Max:** 20

**Step:** 1

**Unit:** sites

#### Daily demand std deviation per site

**Key:** sigma

**Type:** number

**Default:** 25

**Min:** 0

**Step:** 1

**Unit:** units

#### Demand correlation between sites

**Key:** rho

**Type:** slider

**Default:** 0.2

**Min:** 0

**Max:** 1

**Step:** 0.05

**Help:** 0 means independent, 1 means sites move together.

#### Replenishment lead time

**Key:** lt

**Type:** number

**Default:** 14

**Min:** 1

**Step:** 1

**Unit:** days

#### Cycle service level

**Key:** service

**Type:** select

**Default:** 0.95

**Options:**

##### 90%

**Value:** 0.9

##### 95%

**Value:** 0.95

##### 99%

**Value:** 0.99

#### Unit cost

**Key:** ucost

**Type:** number

**Default:** 32

**Min:** 0

**Step:** 1

**Unit:** $

#### Annual carrying rate

**Key:** carry

**Type:** number

**Default:** 20

**Min:** 0

**Step:** 1

**Unit:** %

**Outputs:**

#### Z score

**Key:** z

**Expr:** normsinv(service)

**Format:** decimal

#### Safety stock, separate sites

**Key:** ss_dec

**Expr:** n * z * sigma * sqrt(lt)

**Format:** integer

#### Pooled daily std deviation

**Key:** sigma_c

**Expr:** sigma * sqrt(n + n * (n - 1) * rho)

**Format:** decimal

#### Safety stock, pooled

**Key:** ss_cen

**Expr:** z * sigma_c * sqrt(lt)

**Format:** integer

#### Units of safety stock saved

**Key:** saved

**Expr:** ss_dec - ss_cen

**Format:** integer

**Primary:** true

#### Reduction

**Key:** pct

**Expr:** if(gt(ss_dec, 0), saved / ss_dec * 100, 0)

**Format:** percent

#### Working capital released

**Key:** cash

**Expr:** saved * ucost

**Format:** currency

#### Annual carrying cost saved

**Key:** annual

**Expr:** cash * carry / 100

**Format:** currency

**Primary:** true

**Chart:**

#### Safety stock vs number of locations pooled

**Type:** line

**X:** n

**From:** 1

**To:** 20

**Steps:** 20

**Series:**

- ss_dec
- ss_cen

**Disclaimer:** Pooling saves stock but adds transport time and cost to customers. Compare the saving with the service and freight impact before consolidating.

## Content

**Intro:** Holding safety stock at each warehouse duplicates protection that one central pool could provide. This calculator quantifies the saving from pooling, based on how many sites you have and how correlated their demand is.

**Sections:**

#### How to use it

**Body:** Enter the number of sites, the daily demand standard deviation at a typical site, the correlation between sites, lead time, service level, unit cost and carrying rate. The tool compares the sum of site-level safety stocks with the safety stock of one pooled location and values the difference.

**Bullets:**

- Estimate correlation from weekly demand across sites
- Use the same service level in both cases
- Run it per item family, not once for the whole range

#### The method

**Body:** Separate sites need n times z times sigma times the square root of lead time. Pooled demand has a standard deviation of sigma times the square root of (n + n(n - 1) times rho). With rho at zero this is the classic square root law: safety stock falls to about one over the square root of n of the separate total. At rho of one, pooling saves nothing.

#### Reading the result

**Body:** The chart shows separate safety stock growing linearly with the number of sites, while pooled safety stock grows slowly. Gains are largest for many sites with uncorrelated demand and expensive items. Move the correlation slider to see how regional demand patterns erode the benefit.

#### Common mistakes

**Body:** Ignoring the downside is the big one: central stock means longer delivery to customers and higher freight. Another error is assuming zero correlation when sites serve the same customers. Consider keeping a small forward stock for fast movers and pooling slow movers, which is a common hybrid in ERP distribution setups.

**Cta:** If you want to test consolidation scenarios against real site-level demand in your ERP, Netray can build that model with you.

**Faq:**

#### What is risk pooling?

**Answer:** Combining demand from several locations into one stock lowers relative variability, because high demand at one site tends to offset low demand at another. That lets you hold less safety stock for the same service level.

#### Why does correlation matter?

**Answer:** If sites move together, their highs and lows coincide and cancel less. Positive correlation reduces pooling benefit, and perfect correlation eliminates it. Independent or negatively correlated demand pools best.

#### What is the square root law?

**Answer:** With independent, identical sites, pooled safety stock is the separate total divided by the square root of the number of sites. Four sites merged into one cut safety stock by about half.

#### What should I weigh against the saving?

**Answer:** Delivery time to customers, outbound freight, emergency transfer costs, customs for cross-border pooling and contractual service commitments. A saving in stock can be erased by higher freight on every order.

## Search terms

risk pooling calculator, centralize inventory safety stock, square root law inventory, warehouse consolidation safety stock, multi location safety stock, inventory pooling savings, demand correlation safety stock, central vs decentralized inventory

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