Making Sense of the Square Root Law of Inventory Management

The square root law of inventory management is often presented as a formula, but little explanation is ever given about why your inventory costs go up when you increase the number of warehouse locations. Even if you subtract the obvious suspects that would make your costs rise – extra rent, extra staffing, upkeep of multiple locations, etc. – your inventory costs still increase.

Why? Because the total amount of inventory you must hold is now higher; in order to properly utilize multiple warehouse locations and to maintain customer satisfaction, you will be storing more inventory than you would with only one inventory location.

Many companies choose to go with multiple warehouses because they have expanded and their one warehouse is having trouble getting product to all of their clients. Multiple warehouses mean that you are closer to your customers and can offer better customer service, but they also mean that each warehouse much have its own safety stock to cover the demand variability of its local customers.

As you know, if you’ve been reading our blogs, safety stock a necessary evil – important for customer service but also tied up capital. You’ll see that when you look at all of the warehouses as a whole, only a fraction of the combined safety stock is ever used. You can’t reduce the amount of safety stock, however, because each warehouse is an independent location with its own customer base and its own inventory needs. While you can look at your sales numbers and get a basic idea of the minimum safety stock you probably need, you can’t determine which location will need it from month to month.

One way to reduce the combined safety stock is to allow cross shipments from warehouses experiencing low demand to warehouses experiencing peak demand. However, this shuffling of inventory wastes a lot of money in transport costs. You could also ship directly from any warehouse to any customer, but then the purpose of having multiple locations is lost.

Another way to reduce the amount of safety stock you must maintain is using one central location to keep all the safety stock. Your multiple warehouses can keep up with their own customer base for the most part, and when they can’t, they can call upon the central safety stock location. This eliminates the duplicated safety stock that occurs when using multiple warehouses. You still won’t know which of your different regions will see the next demand spike, but it won’t technically matter any more since you have all your safety stock in a single location – although longer shipping times may decrease your customer satisfaction rates.

All of this is nicely summed up in the square root law, which gives you a good estimate of how the number of warehouse locations affects your overall inventory requirements:

The equation looks like this: X2 = (X1) * v (n2/n1)

  • With n1 = number of existing facilities
  • and n2 = number of future facilities
  • and X1 = existing inventory
  • and X2 = future inventory

As an example, if you have four warehouses and find that you need a total of 20,000 widgets to service your customers without running out of stock, and you decide to consolidate the entire inventory into one central warehouse, then the minimum amount of inventory you would need is: X2 = (20,000) * v (1/4) = (20,000) * (1/2) = 10,000 widgets

This reduces your inventory by 50%.

The square root law is also a form of risk pooling

If this is something you’d like to learn more about, or if you have other inventory concerns, please contact Acumen Information Systems today – we’re here to help you build your business acumen!


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