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Square Root Law of Inventory Management

Square Root Law of Inventory Management: Why Less Is More.

There is a good reason why warehouses tend to be significantly large: they are cost-effective. Carrying inventory under a single roof is cheaper than spreading the same inventory among multiple warehouses. There is less duplication of warehouse labour, management, and equipment. The utility expenses and rent of a single large warehouse are also less costly than the sum across several warehouses.

square root law ofinventory management

Acquisition of goods from suppliers for a single large warehouse would likely be less expensive than for multiple smaller warehouses because the purchases and shipments of these items are consolidated. Larger purchases for a single large warehouse means you get better bulk deals. The shipping costs of purchased goods would also cost less for a single large warehouse. It would occur in fewer but larger shipments than the case with multiple smaller warehouses in different locations.

There is still another reason why having a single warehouse or having fewer warehouses is better than having more: you will need less inventory to service the same market. This seems counter-intuitive since the overall market demand will not merely decrease because you consolidated your warehouse locations. The reason for needing less inventory is that fewer warehouse locations will require less safety stock.

To understand this, imagine having several warehouses that service different localities, and no cross shipping between warehouses is allowed. This means that each warehouse must carry enough safety stock to handle the demand variability of its own district. Assuming the regions’ demands are not in sync with each other, then when some areas experience periods of higher than regular demand, others will experience lower than regular demand. This means that there will always be warehouses that are overstocked because of the lower than average demand for their localities.

On the other hand, consolidating the warehouses into a single centrally located warehouse means that the peak and valley demands of the separate regions cancel when servicing all areas. Inventory management’s square root law gives you an estimate of how the number of warehouse locations affects the size of your inventory. From leanmath.com, the formula is:

X2 = (X1) * v(n2/n1) where v is the square root.

n1 = number of existing facilities

n2 = number of future facilities

X1 = existing inventory

X2 = future inventory

If you had four existing facilities (n1 = 4) and plan to consolidate them into a single facility (n2 = 1), then the square root law gives you:

X2 = (X1) * v (1/4) = (X1) * (1/2)

Therefore, a single warehouse reduces the inventory by one half. Provided your shipping times and costs to the combined four regions are reasonable, the square root law makes a strong case for consolidating the four warehouses into one.

For more information about inventory management and how our software can help your business, please contact us.

The original article appeared in MicroChannel Australia’s blog


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