Risk Pooling: Safety Stock & the Square Root Law

Network Layout

Mode: Decentralized (N warehouses)

Warehouses N 4

Demand std. dev. σ (units/period) 8

Target service level 95% (z=1.65)

Live Readouts

Total safety stock

0 units

Periods elapsed

Achieved service level

—

Stockout events

Pooling would cut safety stock by

How it works

Each warehouse faces independent, identically-distributed random demand per period, D ~ Normal(μ, σ). To hedge against a stockout, a site orders up to a target level that includes a safety stock buffer set by the target service level's z-score:

SS_i = z · σ            (one decentralized site)
SS_decentralized = N · z · σ

Pooled center serves the sum of N independent demand streams.
Var(ΣD_i) = N·σ²  →  σ_pooled = √N · σ
SS_pooled = z · σ_pooled = z · σ · √N

Reduction = 1 − SS_pooled / SS_decentralized = 1 − 1/√N

Because independent random fluctuations partly cancel when summed, the *combined* demand is relatively less variable than any one site's own demand — the coefficient of variation shrinks by √N. This is the risk-pooling principle behind centralized distribution centers, and it is why consolidating N=4 warehouses into one pooled buffer needs only half (1 − 1/√4 = 50%) the total safety stock for the same service level.

Switch to Pooled — replaces the N separate silos with one central buffer serving the summed demand of all N sites, using the pooled formula above.
N / σ / service level — change the network size, demand noise and target reliability; the required safety stock and the 3D silos update live.
Stockout events — counted whenever a silo's stock would go negative before replenishment; the achieved service level is 1 − (stockout periods / total periods), which should track your chosen target.

Current stock Safety-stock line Order-up-to target

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