By Gary Hewamadduma ACMA, CPA, CGMA, MBA, B.Sc.(Hons) in Computer Engineering

The economic order quantity is the optimum quantity of an inventory item to be purchased per order in order to minimize the “ordering cost” and “carrying cost”.

Most likely, a simple google search will show the general formula used for calculating EOQ. But how is it derived?

Let’s say,

Cost per order = c

Annual demand = d

Carrying (Holding) cost per unit = h

Order Quantity = q

Apart from the purchase cost of units (assuming you have no control over that, and there are no bulk discounts), you have to incur holding costs and order costs, in order to deal with your inventory.

So, your objective should be to minimize the combined total of ‘holding cost’ and ‘order cost’

That means, at the optimal level there is no difference in holding cost and order cost.

holding cost – order cost = 0

So, at the optimal order quantity point (EOQ point)

holding cost = order cost

Holding cost per unit (h) x average units = Cost per order (c ) x No. of orders

Assuming; the average number of units = half the order size and no. of orders are equal to annual demand divided by order quantity;

h x ½ q = c x d/q

q = SQRT of (2.c.d / h)

## Limitations of Using EOQ

The above calculation assumes that consumer demand is constant. It rarely is the case. However, you can tweak other variables like marketing spend to make up for possible variations.

The calculation also assumes that both ordering and holding costs remain constant. In practice, bulk discounts, order expense variations, and much more come into effect. For the sake of calculation, you can change the annual figures to a specific period to minimize the error.