🎱 Risk Pooling

Ten warehouses each need their own safety cushion. Merge them into one and the total cushion shrinks β€” because when one region runs hot, another runs cold, and they cancel out. This is why consolidation is one of the most reliable ways to cut inventory. The magic number is √N.

The network

Std. dev. of one location's demand
How alike the locations move. 0 = independent (full pooling benefit); 100% = identical (no benefit).

Buffer policy

Periods; safety stock scales with √(lead time)
Individual locations Pooled total (Γ· N to compare) Average
The pooled line (total demand divided by N so it shares the scale) is visibly steadier than any single location β€” that relative smoothness is the whole benefit.

Safety stock: separate vs. pooled

Kept separate

–
N buffers, one per location

Pooled in one

–
a single shared buffer

Pooling cuts safety stock by –

Pooling factor = βˆš( (1 + (Nβˆ’1)ρ) β„ N ) =  – At ρ = 0 this is simply 1β„βˆšN. Pooled safety stock = separate total Γ— this factor.
Separate total = N Γ— z Γ— Οƒ Γ— √L Β· Pooled = z Γ— Οƒβˆš(N(1+(Nβˆ’1)ρ)) Γ— √L –

Try this: drag locations up β€” the savings climb, but with diminishing returns (that's the √, not a straight line: going 1β†’4 halves the buffer; 4β†’16 only halves it again). Then raise correlation toward 100%: if every region spikes together, there's nothing to pool and the benefit vanishes. This is why pooling works for independent demand but not for market-wide swings. It's the flip side of demand variability and sizes the safety stock you actually need.