The Square Root Law's Impact on Inventories - And you thought you would never use real math after college!

The Square Root Law states that The Total Inventory in a System is proportional to the Square Root of the Number of Locations at which a product is stocked. 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." Whoa! I'm surprised I was even able to type that...

The significance of The Square Root Law is that a company operating five warehouses, which then centralizes into one warehouse, can theoretically reduce inventory carried in stock by 55 percent. This will reduce inventory carrying costs, which may be slightly offset by more costly transport options to meet a customer's service requirements.

Since I am someone who just knows enough to be dangerous on these type of issues, especially when working directly with mathematical minutiae, I am not equipped to review the detailed method of calculation. You simply have to trust the facts as stated.

There are large potential benefits to reducing the number of locations and on the flip side, also significant inventory increase penalties to adding to the number of stocking locations. However, it is important when looking at such opportunities, not to do so in isolation, but to take into account all aspects including DC Cost, Transport Cost, as well as Customer Lead Times and Replenishment before any final decisions are made.

Lets review two of these strategies. Specifically, Slow Moving Goods (SMG) and Network Centralization, just to give you some ideas where you may begin with direct application to your own organization (or client).

A Slow Moving Goods strategy consists of the seg&sort of a product range by velocity. Typically, Pareto's Law ( the 80/20 rule, which by the way, we need to discuss if it really is relevant in this day and age) can assist in this regard with the slower moving 80% of products which might represent 20% of sales volume being pulled from the current DC network. These SKUs would then be serviced from 1 or 2 more centralized Slow Moving Distribution Centers with the appropriate Square Root Law of Inventory applying depending on how many existing locations these products were held at. An example would be that these have been pulled back from four locations to one resulting in roughly a 50% inventory reduction, which is significant.

In addition, the picking productivity benefits can also accrue assuming all products were in a consolidated pick line in the previous four full line facilities. By pulling these SMG products out, and creating new pick lines, one SMG and four FMG (Fast Moving Goods) in each of the current facilities, both picking operations will be immediately improved. The FMG by reduced travel times due to not having to pass all of the previous SMG slots and the SMG by focusing on one pick slot within a more compact picking layout.

Slow Moving Goods network strategies can also be useful in addressing networks which are over capacity and require expansion with the SMG facility reducing the overall stock holding and space requirement in the existing full line facilities.

Network Centralization analysis may often result in significant benefits as well where multiple regional facilities are consolidated to only one or two locations. A determination of the appropriate centralized network strategy for a firm can also be completed by modeling the optimal intersection of number of locations, transportation costs and inventory carrying costs. This calculation must of course be governed by business defined customer service levels and can vary based on the product density and the relative value of different product lines.

It seems we are returning to the location issue (as referenced in last week's RFID missive), which again plays an important role in this decision process. How are you dealing with these types of challenges in your organization? How about with your clients? It would very educational to get some feedback.