# Economic Order Quantity: Definition, EOQ Formula, Calculation

## What is Economic Order Quantity?

The company’s reputation and profitability are always at stake if it has too much or too little inventory on hand. 43% of business owners have considered “overbuying inventory” as a challenge, whereas 36% said the same for “underbuying inventory”.

To provide a solution to this, in 1913, Ford W. Harris designed a model of “Economic Order Quantity (EOQ)” through an explanation. This was later turned to a mathematical equation by R.H. Wilson, a consultant who applied it extensively.

The Economic Order Quantity is a very good approach for efficient inventory management, though not the only step that a merchant can take, but can certainly make an impact.

## EOQ Formula

Variables:

T = Total annual inventory cost
P = Purchase unit price, unit production cost
Q = Order quantity
Q* = Optimal order quantity
D = Annual demand quantity
K = Fixed cost per order, setup cost
h = Annual holding cost per unit, also known to be carrying or storage cost

The single-item EOQ formula helps find the minimum point of the following cost function:

Total Cost = Purchase Cost or Production Cost + Ordering Cost + Holding Cost

Where,

• Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P × D
• Ordering cost: This is the cost of placing orders: each order has a fixed cost K, and we need to order D/Q times per year. This is K × D/Q
• Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is h × Q/2

To determine the minimum point of the total cost curve, calculate the derivative of the total cost with respect to Q (assume all other variables are constant) and set it equal to zero (0):

Solving for Q gives Q* (the optimal order quantity):

Therefore,

Can also be written as,

## Example of Economic Order Quantity (EOQ)

Let’s assume, a retail clothing shop is into men’s jeans and sells roughly around 1000 pairs of jeans every year. It takes \$5 for the shop to hold a pair of jeans for the entire year, and the fixed cost to place an order is \$2.

As per the EOQ formula, the calculation of the above-mentioned scenario is below:

EOQ = Sq. root [(2 * 1000 pairs * \$2 order cost) / (\$5 carrying cost)]

Therefore, EOQ = 28.3 pairs.

The ideal order quantity for the shop will be 28 pairs of jeans. Simple!

## Factors that affect Economic Order Quantity

• Reorder Point
It is the time when there occurs a need to reorder another set of stock or replenish the existing stock. EOQ always assumes that you order the same quantity at each reorder point.
• Purchase order lead time
This is the time period from placing the order until the ordering is delivered. EOQ assumes that the lead time is understood.
• Purchasing cost per unit
The cost per unit never changes, over the period of time, even though the quantity of the order is changed. EOQ always assumes that you pay the same amount per product, every time.
• Stockouts
There are no chances for stockouts. You have to always maintain enough inventory to avoid stockout costs. This clearly states that you always have to strictly monitor your customer demand along with your inventory levels, carefully.
• Quality costs
EOQ never focuses on the quality costs, rather the carrying costs.
• Demand
It’s about how much the customer wants the product for a specific time period.
• Relevant ordering cost
The cost per purchase order.
• Relevant carrying cost
The cost involved in the entire maintenance and carrying the stock, for the specific period.

## How to Implement EOQ

1. Gather Data:
Collect the necessary data for the EOQ calculation. This includes the annual demand for the product (D), the ordering cost per order (S), and the holding cost per unit per year (H).
2. Understand Assumptions:
Be aware of the assumptions underlying the EOQ model, such as constant demand, fixed ordering costs, and constant holding costs.
3. Calculate EOQ
Depending on your specific situation, you may need to make adjustments to the basic EOQ model. For example, if there are quantity discounts offered by suppliers, incorporate these discounts into the calculation. Adjustments might also be necessary for factors like storage limitations, seasonality, or variations in demand.
5. Evaluate Reorder Point:
Once you have the EOQ, calculate the reorder point. The reorder point is the inventory level at which a new order should be placed. It is determined by multiplying the demand rate per period by the lead time in periods.
6. Monitor Inventory Levels:
Implement a system to regularly monitor and update inventory levels. This involves keeping track of the actual demand, lead times, and inventory on hand. Adjust the reorder point and reorder quantity as needed based on actual performance.
7. Use Technology:
Leverage inventory management software systems that can automate the calculation and tracking of EOQ. These tools can streamline the process and provide real-time insights into inventory levels.

## Importance of Economic Order Quantity (EOQ)

The Economic Order Quantity is a quantity designed to assist companies to not over- or under-stock their inventories and minimize their capital investments on the products that they are selling. The cost of ordering an inventory touches down with an increase in ordering in bulk. However, as the seller wishes to grow the size of the inventory, the carrying costs also increase.

The EOQ is exactly the point that optimizes both of these costs i.e. cost of ordering and the carrying costs which are inversely related.

Now, with this…

• The business owners can easily order the right quantities and reduce the ordering and carrying costs. This will eventually result in either profits or a balanced business.
• Decision making can be made smoother, with less time and effort wasted.
• Right vendors can be chosen, with the right packages to save costs and earn better profits.

## Why should you be calculating EOQ?

There are several benefits of calculating EOQ that can impact your business. It shows and lets you maintain your supply chain while keeping the costs down.

### Minimize Inventory Costs

There are high chances of booming storage costs if you plan to store any extra inventory. High inventory costs depend majorly on how you order, if there is anything that is damaged, the number of products that lie there not getting sold. If you are constantly re-ordering products that have a very low velocity, EOQ can help you analyze how much to order in a certain period.

### Minimize Stockouts

By calculating how much inventory you need on how much you are planning to sell, EOQ will help you avoid stock-outs without having too much inventory on hand for too long. It can definitely be surprising enough to see that ordering in small quantities can be way more cost-effective, but this can turn the other way as well – calculating EOQ for your products can help.

## Limitations of Economic Order Quantity (EOQ)

1. Gather Data:
Collect the necessary data for the EOQ calculation. This includes the annual demand for the product (D), the ordering cost per order (S), and the holding cost per unit per year (H).
2. Understand Assumptions:
Be aware of the assumptions underlying the EOQ model, such as constant demand, fixed ordering costs, and constant holding costs.
3. Calculate EOQ