How formula of EOQ is derived?

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It is one of the oldest classical production scheduling models. The model was developed by Ford W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, and K. Andler are given credit for their in-depth analysis.[i]
In cost accounting economic ordering quantity is that quantity that minimizes the total holding costs and ordering costs. These two costs react inversely to each other. When we increase order size, then fewer orders are required to meet demand ,this results in decline in the ordering cost, whereas the average amount of inventory on hand will increase, resulting in an increase in carrying costs.

EOQ formula is based on certain assumptions[ii]:

i. Demand for the product is known and constant.

ii. Lead time is known and constant.

iii. The receipt of inventory is instantaneous.

iv. Quantity discounts are not availed.

v. Stock outs and shortages are not considered.

 

Derivation of EOQ Formula    

Let



Now, as shown in the following figure, the relationship between ordering cost and carrying cost in inverse, in turn in a convex total cost curve.


As given in the above figure, we can find the optimal order quantity where the total cost curve is at a minimum and this happens where the carrying cost curve intersects the ordering cost curve. In other words, we can find optimal value of  by equating ordering cost with carrying cost.


Alternatively, we can derive the formula for economic ordering quantity by differentiating the total cost curve with respect to Q , setting the resulting function equal to zero and solving for Q :


So, these are two methods for deriving economic ordering quantity formula. Hopes this will helps students. Thank you.

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