# Economic Order Quantity Formula: What It Is and How to Use It

## Article by Matt Kenyon on August 3, 2021

If you’ve been longing for a little EOQ guidance, read on for a concise primer on what the economic order quantity formula is, how you can use it to calculate your optimal order quantity and the inherent limitations to the model that you need to keep in mind.

## What Is Economic Order Quantity Formula? Part I: History & Theory

The economic order quantity formula was first presented by a fascinating character in business-world history: Ford Whitman Harris, an inventor, patent attorney, and engineer who had no formal education beyond high school, and yet in 1913 managed to find a simple (well, relatively) solution to this notorious inventory management struggle.

Harris’s economic order quantity formula proceeds from assuming that there are cost tradeoffs associated with holding inventory and that those tradeoffs can be identified.

It then follows that a business that can calculate the optimal number of items to order will minimize the overall levels of operational costs it incurs.

His model almost immediately became the dominant paradigm for order-quantity analysis for at least half a century.

Though several increasingly complicated variations to the basic formula have been engineered over the years, the original model still serves the vast majority of businesses today.

## What Is the Economic Order Quantity Formula? Part II: Practice

And now, get out those calculators, because it’s time to actually do some math.

This is the basic equation for calculating the economic or optimal order quantity:

Where:

Q = Economic Order Quantity (in units)

A = Ordering Cost (\$ per order)

D = Annual Demand (in units)

I = Inventory Carrying Cost (a percent of average inventory value expressed as a decimal fraction)

C = Item Cost (\$ per unit)

### A Note on These Values:

Keep in mind that the formula only purports to work if you know all these values with certainty, or at least that any variations are reasonably and accurately anticipated and estimated.

So before you solve for Q, make sure all of your figures are precise and up-to-date. A tech-based inventory management system, like the one offered by SkuVault, can help generate those solid numbers for you at a moment’s notice.

#### A few notes on Ordering Cost:

• The ordering cost is the average dollar amount of one order
• The ordering cost includes both fixed and variable costs incurred to process an order

#### The Inventory Carrying Cost may include:

• Storage costs
• Handling costs
• Information processing
• Insurance
• Obsolescence
• Shrinkage
• Opportunity costs (that is, lost business opportunities due to financial resources tied up in physical inventory)

#### A note on Item Cost:

• The product value must be real to generate an accurate representation of the costs of carrying inventory over time

## Plugging in the Numbers: An Example of a Standard EOQ Calculation

Let’s take a quick look at an example to see how to put the EOQ formula into practice.

#### Example Data to Plug Into EOQ Formula

Variable Value
D = Annual Demand 4000 units
A = Ordering cost (\$ per order) \$80
I = Inventory carrying cost as a percent of the value of average inventory level 16 percent
C = Item cost (product value) \$100 per unit

Take the formula we expressed above and plug in the values from the example data…

Et voila! You should order 200 units per order to minimize your operational costs.

## Inventory Types to Have on Hand

No matter how lean of an operation a retailer might run, they’re always going to need to hold a certain amount of inventory. There are at least three main types of inventory that businesses perennially need to have on hand:

• Cycle stock, or inventory held to meet the average daily, weekly, or monthly product demand.
• Safety stock, or extra inventory held to meet sudden or unexpected surges in demand.
• Speculative stock, which is inventory held to safeguard against product shortages or price increases.

Deciding to hold inventory might sound daunting for younger and smaller enterprises with more precarious cash flows. The costs associated with investing in stock and storing and managing it can be painfully burdensome.

But the fact is, no matter a business’s age or size, and despite any other unique variables it might face, one common maxim holds for all:

Pay to hold inventory, save on higher costs elsewhere.

That is, retailers need to hold inventory, despite the storage fees and so forth, in order to minimize certain operational costs and maximize profits.

Here’s where it gets tricky: how much inventory does any given business need to hold? Ordering too little or too much inventory can both inflict some serious financial damage—let’s take a look at each scenario.

### Costs Associated With Not Holding Enough Inventory:

• Lost sales from going out-of-stock
• Sudden increases in vendor prices
• Transportation (ordering smaller amounts of product more frequently is more expensive)

### Costs Associated With Holding Too Much Inventory:

• Unnecessarily high storage and warehouse management costs
• Excessively high initial inventory investment cost
• Lost opportunities due to too much capital being tied up in inventory

Somewhere in between these two cases, though, lies a “just right” Goldilocks of a number—the number representing precisely how much stock to hold to avoid the above-listed costs.

Figuring out that optimal order quantity is the keystone to an efficient inventory management system.

By far and away, the most popular tool to calculate that amount is the economic order quantity (EOQ) formula, a tool that businesses around the world have relied on for the past hundred-plus years.

You’ve probably run into this standard square-root formula before or at least encountered its name: the basic EOQ model and its subsequent variations appear in elementary textbooks for students of business, accounting, industrial engineering, management science, and so forth.

Of course, just because it’s so omnipresent in the business world doesn’t mean that the calculation is that straightforward or intuitive to use—don’t worry if you need to study up!

## Limitations of the Economic Order Quantity Formula

The basic economic order quantity formula operates on certain assumptions that just won’t be true for many businesses, such as the assumption that:

• Demand is known and constant
• There are no inventory shortages
• Inventory is replenished in just one shipment
• The only relevant costs are for ordering and holding

Furthermore, there’s a host of complexities that this relatively simple formula can’t reflect, but which will play an essential role in inventory management, such as a business’s ordering capacity, warehouse capacity, or capital constraints.

Nor can the EOQ formula account for the multitude of external factors that can influence a retailer’s inventory purchasing decisions, like anticipated wholesale price increases or discounts obtained when buying in bulk.

### A Note of Caution About the EOQ

Keep in mind that Harris only intended his economic order quantity formula to be used as one tool in a robust inventory management system. It can certainly act as a practical guide, but it shouldn’t be used indiscriminately or treated as a miraculous cure-all.

Here’s what Harris said in his own words in that famed 1913 paper (emphasis added):

Every manufacturer, in putting through an order, encounters the problem of finding the most economical quantity to make at once. This is a general problem and admits of a general solution. Up to a certain point, mathematics answers it definitely, as with a thoroughly standardized product like automobile parts in a large plant. It is not put forth, however, that any mere mathematical formula can be depended upon entirely to determine how much stock should be carried or put through on an order. This is a matter that calls in each case for a trained judgment, for which there is no substitute. With special orders and under the emergencies that are constantly arising, the mathematical formula will, of course, give only approximate results, which must be tempered with judgment, based on knowledge of the factors involved in economical production and grasp of wise business policy.

In cases of minor importance a trained judgment . . . will determine the size of lots with sufficient accuracy. Where larger quantities are involved and conditions are standard, an estimate with its chances of mistakes should scarcely be final. Application of the mathematical formula is then warranted at least as a check upon the judgment. Given the size of lot which by mathematical theory is cheapest, the manager can the better supply such corrections as seem important.”

## Tools to Help Efficiently Calculate an Accurate EOQ

Even accounting for the above restrictions—and Harris’s warning about the limited applicability of his model—the basic EOQ formula, used judiciously, can still be a real boon to business leaders.

The model gives them a scientific benchmark when making complex, potentially overwhelming inventory purchasing decisions.

But studies have found that far too many retailers are making those purchasing decisions based on their “gut feeling” or a possibly arbitrary “rule of thumb” passed on from a predecessor.

Why might that be the case? Researchers have found that, for many businesses, gathering the necessary quantitative data that the EOQ formula demands is a real source of difficulty, to the point where it bars them from relying on this approach altogether.

And this is where inventory management software comes into play. SkuVault’s powerful reporting and filtering capabilities, for instance, allow businesses to instantly generate detailed reports on sales, ordering history, inventory levels, inventory performance, and more.

Thus, making the data-gathering process for calculating your EOQ dramatically more comfortable, faster, and above all, more accurate.

SkuVault also offers data-driven inventory forecasting capabilities to compare your carefully calculated EOQ and make even more finely honed purchasing and operations decisions.

We’d love to show you more about how SkuVault can help you gain control of your inventory management and maximize your eCommerce profitability. Contact our team today for a live demo or to talk further.