# Economic order quantity

*Management accounting*.

(EOQ).

The optimal size of orders and frequency for ordering stocks or raw materials based on the periodic demand (D), the fixed ordering cost (F) and the periodic holding cost (H) of the item of stock in question.

Expressed as a formula:

EOQ = (2FD / H)^{(1/2)}

Where:

F = the Fixed cost per order (eg £20)

D = the annual Demand, or usage, of the item (eg 100 units)

H = annual Holding cost per unit of the item (eg £40)

**Example 1**

In this case:

EOQ = (2FD / H)^{(1/2)}

= (2 x £20 x 100 / £40)^{(1/2)}

= 10 units per order.

With this size of order, the average number of orders per year would be

100 / 10 = 10 orders.

Total annual ordering costs

= 10 orders x £20/order

= £200.

Average stock levels would be

10 / 2 = 5 units.

Total annual stock holding costs

= 5 units x £40/unit

= £200.

Grand total costs

= £200 + £200

**= £400.**

**Example 2**

Total costs would be greater with any other number of units per order (other than the EOQ of 10 units calculated above), for example:

*With 9 units per order,*

the average number of orders per year would be

100 / 9 = 11.111 orders.

Total annual ordering costs

= 11.111 orders x £20/order

= £222.

Average stock levels would be

9 / 2 = 4.5 units.

Total annual stock holding costs

= 4.5 units x £40/unit

= £180.

Grand total costs

= £222 + £180

**= £402.**

*With 11 units per order,*

the average number of orders per year would be

100 / 11 = 9.0909 orders.

Total annual ordering costs

= 9.0909 orders x £20/order

= £182.

Average stock levels would be

11 / 2 = 5.5 units.

Total annual stock holding costs

= 5.5 units x £40/unit

= £220.

Grand total costs

= £180 + £222

**= £402.**