# Economic Order Quantity

Economic Order Quantity, also described as (EOQ), is a measurement used in the field of Logistics, Operations and Supply Chain Management. In short, EOQ is a tool you can use to determine the volume and frequency of orders needed to satisfy a specific level of demand while minimizing your cost per order. If your assumptions don’t hold exactly true, economic order quantity can be a good indicator of whether or not current order quantities are reasonable.

## Why Is Economic Order Quantity Important?

The Economic Order Quantity is a set point designed to help companies minimize the cost of ordering and holding inventory. The cost associated with ordering inventory decreases when the volume of orders increase, this due to the economies of scale. Despite that, as inventory grows, the cost of holding your inventory increases. The point that minimizes both of these related costs is EOQ.

## The EOQ Formula

The Economic Order Quantity formula is calculated by minimizing the total cost per order by setting the first order derivative to zero. The components of the formula that make up the total cost per order are the cost of holding inventory and the cost of ordering that inventory. The key notations in understanding the EOQ formula are as follows:

## Components of the EOQ Formula:

• A: Annual Quantity Demanded
• B: Volume per Order
• C: Ordering Cost (Fixed Cost)
• D: Unit Cost (Variable Cost)
• E: Holding Cost (Variable Cost)
• F: Carrying Cost (Interest Rate)

(1) Ordering Cost

You can calculate the number of orders you have annually by dividing your annual demand by the volume per order. The formula would be calculated as such:

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Number of Orders = A/B

(2) EOQ formula

For all orders with a fixed cost that is independent of the number of units (C) the annual ordering cost can be found by multiplying the number of orders by this fixed cost. It’s calculated as;

Annual Ordering Cost = A/B x C

(3) Holding Cost

Holding inventory will usually have additional costs you have to account for. These cost can direct costs, such as financing the storage, opportunity cost, investments tied up, etc.  Due to this, the holding cost per unit is defined as cost per unit multiplied by the interest rate, as below.

E=FD

Assuming demand is constant, the quantity of stock can be seen constantly depleting over time. When inventory reaches zero, an order is placed and inventory is restored. Due to this, the holding cost of the inventory is calculated by finding the sum product of the inventory at any instant and the holding cost per unit.

Annual Holding Cost = B/2 x E

(4) Total Cost and the Economic Order Quantity

Summing the two costs together will give you the annual total cost of orders. To find the optimal quantity that reduces this cost, the annual total cost is differentiated with respect to B.

Annual Total Cost (TC) = A/B x C + B/2 X E

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