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

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

square root law of inventory management

There is a good reason why warehouses tend to be 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 is also less costly than the sum across several warehouses.

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. Bigger 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 because 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 at least 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 decrease simply 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 locality. Assuming the demands in the regions are not in synch with each other, then when some regions experience periods of higher than normal demand, others will experience lower than normal demand. This means that there will always be warehouses that are overstocked because of the lower than normal demand for their localities.

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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 of the regions as a whole. The square root law of inventory management gives you an estimate of how the number of warehouse locations affect the size of your inventory. From, 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 you 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.

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