•The square root law states that “The total inventory in a system is proportional to the Square Root of the Number of Locations at which a product is stocked.”
•The significance of The square Root Law is that a firm currently operating out of five warehouses which centralizes to one warehouse can theoretically reduce inventory carried in stock by 55 percent.
•This will of course result in large savings in inventory carrying cost which will be slightly offset by more rapid transport to meet current delivery service levels.
•It is recognized that the inventory tends to increase as the number of locations increase.
•While the reduction of inventory and number of locations for keeping finished products are desired, the companies must do so without reducing service to customers.
•The square root law determines the extent to which inventory reduces by reducing the number of locations.
•An important assumption is the total customer demand remains same.
•The Square Root Law states that the total inventory in a future number of warehouses is determined by multiplying the total inventory at the existing warehouses by the square root of number of future warehouses divided by number of existing warehouses. Mathematically, it is represented as under:
•L = [(L1) x {Ö (W2÷ W1) }], where
•L= Total inventory in future warehouses
•L1= Total inventory in existing warehouses
•W1= Number of existing warehouses
• W2 = Number of future warehouses.
•For example, In a company there are 40 warehouses and the existing inventory is 2,00,000 units. If the number of warehouses are reduced to 10 what will be impact on total inventory.
•L1= 2,00,000
•W1= 40
•W2= 10
\L= [(2,00,000) x {Ö (10÷ 40 )}] = 1,00,000
•Thus, inventory will consist of 1,00,000 units giving a reduction of 50%.
•Conversely, if the number of warehouses are increased, the total inventory will increase.
•Assumptions are
(1)Inventory transfer from one warehouse to other is not done.
(2)Lead time does not vary.
(3)Customer service level does not change from any warehouse.
(4)Demand level is well distributed from all warehouse.
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