Square Root Law – inventory in multiple locations

Got asked what would happen to inventory when the number of stocking locations change.  I thought for a minute and remembered a quick rule of thumb … The Inventory Square Root Law states that …

Average inventory increases proportionally  to the square root of the number of locations in which inventory is held.

X2 = (X1) * √ (n2/n1)

n1 = number of existing facilities
n2 = number of future facilities
X1 = existing inventory
X2 = future inventory

Here’s an example:

Current inventory is 4000 units, 2 facilities grow to 8.  Using the square root law the future inventory = (4000) * √ (8/2) = 8000 units.


* The Square Root Law was mathematically proven by D.H. Maister in his 1975, International Journal of Physical Distribution article entitled “Centralization of Inventories and The Square Root Law.”



  1. KEK says:

    Square Root Law was shown in 1976 by David Maister (then at Harvard Business School) to apply to a set of inventory facilities facing identical demand rates. SQRL is a single product rule when EOQ order batching with identical batch sizes wll be used across a set of invenrory facilities. While SQRL applies to cycle stocks, it does not necessarily apply to safety stocks. See Das, Evers, Evers & Maier, Ballou, Ballou & Burnetas, Levy & al, Zinn, Mahmoud etc etc for further details (most of these have published their work in the Journal of Business Logstics).

  2. BTW: the original article by D. Maister has been publicly available on the net for some while (the erticle is in PDF format).