Operations & Logistics
Maister’s Square-Root Law of Warehouse Centralization & Correlated Safety Stock
Project safety-stock savings when consolidating N_old regional depots into N_new hubs using David Maister’s (1976) SQRT(N_new / N_old) law plus inter-regional demand correlation rho.
Why naive SQRT(N_new / N_old) overstates inventory savings when regional demand is correlated
David Maister (1976) showed that under independent, identically distributed regional demand, consolidating N_old = 16 decentralized warehouses into N_new = 4 central distribution hubs shrinks network safety stock by SQRT(4 / 16) = 0.50—cutting 20,000 safety-stock units down to 10,000 units! Yet real retail and spare-parts networks experience macroeconomic, promotional, and weather shocks shared across regions (correlation rho > 0).
Incorporating pairwise inter-regional demand correlation rho (Zinn, Levy & Bowersox, 1989) generalizes the pooling multiplier to SQRT((N_new / N_old) * (1 - rho) + rho). Test the sensitivity directly: at rho = 0.00, centralized safety stock is 10,000 units (50% savings); at rho = 0.52, it rises to 20,000 * SQRT(0.25 * 0.48 + 0.52) = 20,000 * SQRT(0.64) = 16,000 units (only 20% savings); and at perfect correlation rho = 1.00, safety stock stays at 20,000 units (0% pooling benefit).
| Demand Correlation rho (16 Depots -> 4 Hubs) | Generalized Multiplier | Centralized Safety Stock (from 20,000) |
|---|---|---|
| rho = 0.00 (Independent — Classic Maister) | SQRT(4 / 16) = 0.5000 | 10,000 units (10,000 saved) |
| rho = 0.52 (Seasonal / Promo Co-Movement) | SQRT(0.25*0.48 + 0.52) = 0.8000 | 16,000 units (4,000 saved) |
| rho = 1.00 (Perfectly Synchronized Shocks) | SQRT(1.0000) = 1.0000 | 20,000 units (0 saved) |
Correlation-Adjusted Square-Root Law Safety Stock Formula
Multiply current network safety stock B4 by SQRT((N_new / N_old) * (1 - rho) + rho), which reduces identically to Maister’s SQRT(N_new / N_old) when rho = 0.
=ROUND(B4 * SQRT((B3 / B2) * (1 - B5) + B5), 2)Net Inventory Reduction & Naive Overstatement Check
Compare correlation-adjusted savings B4 - E3 against classic uncorrelated Maister savings B4 - E2 so network redesign business cases never overpromise working-capital release.
=ROUND(B4 - E3, 2)Try the example
Use the original values or change them to test your understanding.