# Economic Order Quantity (EOQ)

Economic order quantity is the size of an order that minimizes both the purchasing costs and the inventory carrying costs. When making purchasing decisions, it is necessary to consider the cost of the purchase as well as the cost of holding the inventory purchased. EOQ is the exact order quantity that minimizes the combination of these two costs.

Larger order sizes minimize purchasing costs. So as order sizes increase, purchasing costs go down. However, larger orders increase inventory levels. And as inventory increases, carrying costs go up. So the two costs move inversely to one another. Mathematically, the point at which the two costs are minimized is the point at which the two costs are equal.

There is an equation for computing the exact EOQ. The equation requires three input variables. The first is an estimate of the number of units of inventory required per year. This is the number of units the company needs for the entire year. The second variable is the estimated cost of placing an order. The third variable is the estimated cost of holding one unit of inventory for a year. These inventory holding costs include costs such as storage, handling, and insurance.

## Economic Order Quantity Equation

Economic order quantity equals the square root of: two times the annual requirement times the cost per order, divided by the annual holding cost per unit.

EOQ = √ ((2 x R x C) / H)

R = Annual requirement of units of inventory
C = Cost per order
H = Annual holding cost per unit of inventory

### Economic Order Quantity Example

Here is a simple example. Let’s say a widget company estimates, based on historic data, that it will need 600,000 widgets for the upcoming year in order to meet consumer demand.

The company previously found the most reliable supplier with the best quality widgets for the best price – finding the best supplier is an entirely separate decision from the optimal order quantity. The cost of an order from the supplier is \$10 per order.

The widget company also determined, based on historic data, that the cost of holding one widget in storage for a year is \$0.20 per widget. Now we have the necessary variables to compute the EOQ.

7,745.97 = √ ((2 x 600,000 x 10) / .20)

So as you can see, the economic order quantity is 7,745.97, which we’ll round up to 7,746. The widget company should place orders for 7,746 widgets from the supplier. This turns out to mean that the widget company will make about 77 orders from the supplier during the year. ### Source:

Barfield, Jesse T., Michael R. Kinney, Cecily A. Raiborn. “Cost Accounting Traditions and Innovations,” West Publishing Company, St. Paul, MN, 1994

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