Square Root Law (SRL) of Inventory

As regards inventory, many a time companies believe that centralization will cost them more as compared to decentralization. However, as per the business expert D.H. Maiser, maintaining the inventory in a variety of warehouses instead of just one would result in saving money. This he proved mathematically in 1976. His law is known as the square root law of inventory. This law is the basis of the concepts of risk pooling and inventory centralization. According to SRL:

“Total safety stock inventories in a future number of facilities can be approximated by multiplying the total amount of inventory at existing facilities by the square root of the number of future facilities divided by the number of existing facilities.”

In other words, the increase in number of warehouses of a company will cause a specific increase in certain costs. Thus, with lesser number of warehouses, the company will enhance its savings of certain costs. This increase, either in a positive or negative direction, can be mathematically com­puted using the square root law indicated below:

where

n₁ = number of existing facilities

n₂ = number of future facilities

X₁ = total inventory in existing facilities

X₂ = total inventory in future facilities.

For example, if a business firm has a network of 15 field warehouses for stocking their inven­tory, their costs would likely be almost 75 per cent greater than if they used a single warehouse. Also, if Company B originally had five warehouses and decided to centralize their inventory, they would see a saving ofjust over 50 per cent.

The following data from an actual company demonstrate how average inventory level increases as the number of stocking locations increase. Though the number is given as average inventory, this level is directly related with safety inventory (see Table 7.3).

The assumptions to square root law are as follows:

• Inter-location inventory transfer is not at the same common level
• Lead times do not vary
• No change in customer service level
• Normal distribution of demand at each location

The most important limitation attached to the effectiveness of SRL (Zinn, Levi and Bowersox 1989) is the demands across the markets served by the various stocking points. This means that SRL will be most effective when markets have demands that are negatively correlated, and there is little or no benefit from consolidation when demands faced by the various stocking points are positively correlated. Hence, more the uncertainty of demand at each location, measured by the coefficient of variation, the better the SRL of inventory works.

According to this formula, with the multiplicity of warehouses the fixed costs increase in the same proportions. In addition, multiple warehouses are more difficult to manage because keeping track of the inventory at several locations, watching stock amounts, handling orders, and planning distribution are all the more complicated when a company has to deal with more than one or two warehouses. Switching to a more centralized warehouse system may not seem possible to many busi­nesses, but the change is possible. Manufacturing companies can collaborate with logistics vendors in reducing their own stocking points. SRL cannot be used in isolation. The decision on the num­ber of warehouses considering SRL should be weighed in light of other factors like transportation costs, lead time, inventory availability and warehouse proximity.

Source: Sople V.V (2013), Logistics Management, Pearson Education India; Third edition.