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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.

What is Square Root Law of Inventory Management?

The Square Root Law of Inventory Management is a concept used in inventory management to optimise inventory levels based on the trade-off between holding costs and ordering costs. It’s also known as the “Square Root Formula” or “Square Root Model”.

The basic idea behind the Square Root Law is that as the quantity of inventory increases, the costs associated with holding that inventory (such as storage, insurance, obsolescence, etc.) increase, but the costs associated with ordering (such as setup costs, transportation, etc.) decrease.

Here’s how it works:

  • Holding Costs: These are the costs associated with storing and holding inventory. Holding costs typically include expenses such as warehousing, insurance, taxes, and the opportunity cost of tying up capital in inventory.
  • Ordering Costs: These are the costs associated with placing and receiving orders for inventory. Ordering costs include expenses like setup costs, transportation costs, and other costs related to the procurement process.

The Square Root Law states that the total cost of inventory is minimised when the sum of holding costs and ordering costs is minimized. This occurs at a certain inventory level, which can be approximated using the square root of the product of the demand rate and the ordering cost divided by the holding cost per unit.

As the demand rate increases, the optimal order quantity also increases, but at a decreasing rate. This is because the cost of holding inventory increases with higher demand, but the cost of ordering decreases due to the spread of fixed costs over a larger quantity.

It is important to note that while the Square Root Law provides a useful approximation for determining optimal inventory levels, it may not always accurately reflect the complexities of real-world inventory management situations. Factors such as lead times, variability in demand, and supplier constraints also need to be considered in practical inventory management decisions.

Square Root Law on How Warehouse Location Affects the Size of your Inventory

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. Referring to, 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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In summary, the Square Root Law explains why the number of warehouse locations can affect the size of your inventory. It is crucial for businesses to balance the need to have multiple warehouse locations versus one single location for the business to run efficiently at the lowest cost.

As businesses navigate the complexities of inventory and warehousing, embracing a Warehouse Management System (WMS) is pivotal to streamline operations, mitigate risks, and improve profitability. Unlock new levels of efficiency in your warehouse with a WMS – schedule acall for a no-obligation chat on how we can assist you.


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