For getting the EOQ formula we shall use the subsequent symbols:

U = annual usage/demand

Q = quantity ordered

F = cost per order

C = per cent carrying cost

P  = price per unit

TC = total costs of ordering and carrying

Specified the above assumptions and symbols, the net costs of ordering and carrying inventories are equivalent to

TC = U/Q × F + Q/2 × P ×C

In the equation, the initial term on the right-hand side is the ordering cost, acquired as the product of the number of orders (U/Q) and the cost per order (F) and the next term on the right-hand side is the carrying cost, acquired as the product of the average value of inventory holding (QP/2) and the percentage carrying cost C.

The total cost of ordering and carrying is minimized as:

Q =    √(2FU/PC)

That can be acquired by putting the first derivative of TC regarding Q and equating this with zero.

dTC/dQ = ( - UF/ Q² )+ (PC/2) = 0

- 2UF + Q²PC = 0

Q² PC + 2UF

Q² =  2UF/ PC

Q =    √(2UF/ PC)

Suppose here the second derivative condition is satisfied:

The formula embodied in the equation is the EOQ formula. This is a helpful tool for inventory management. This tells us what must be the order size for the purchase of items and what must be the size of production run for manufactured items.

The EOQ model may be demonstrated with the assist of the subsequent data relating to the Ace Company.

U = annual sales = 20,000 units

F = fixed cost per order =Rs. 2,000

P = purchase price per unit = Rs. 12

C = carrying cost= 25 per cent of inventory value.

Plugging in these values in eq. (2) we determine that:

Q = √(2 × 2,000× 20, 000)/( 12×0.25)

= 5.164