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.”


2 Replies to “Square Root Law – inventory in multiple locations”

  1. 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).

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