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**Economic Order Quantity –**If you’re running a business, it’s critical to know how much inventories you should buy or produce. By calculating EOQ, we will be able to understand how much quantity a business should order or produce.

source: defense.gov

We note from above, that even the US Department of Defense is using Economic Order Quantity contracting strategy for the U.S. Services.

In this article, we will go through EOQ in detail, the definition of EOQ, its importance, how we can calculate economic order quantity, and a practical EOQ example to illustrate EOQ.

Let’s get started.

## What is Economic Order Quantity (EOQ)?

The word ‘optimal’ is key.

It helps the company decide how much to produce or purchase.

That means economic order quantity can be defined as a formula through which a company can find out how much it has to produce or order by lowering the carrying cost or holding cost and ordering cost.

The equation is derived from a simple equation.

The equation is –

Total Cost = Purchase Cost + Ordering Cost + Holding Cost

But how would we derive the Economic Order Quantity formula from the above function?

We will understand that in the next section.

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### Economic Order Quantity Formula

We know the function of the total cost.

In that function, we can’t change the purchase cost; because purchase cost would be what the supplier or the vendor will decide.

That means all we can low down are ordering cost and carrying the cost.

But they are two separate costs.

Let’s say that you decide that you will order in bulk so that the ordering cost gets lower. But there is a disadvantage of that approach. If you order in bulk, maybe you would be able to lower down the ordering cost, but your carrying cost would be higher.

So, to solve this issue, our approach would be to set a level where the ordering cost and the carrying cost would be equal. It means beyond this level, either the carrying cost or the ordering cost would be higher or lower.

That means in this case, we get –

Ordering Cost = Carrying Cost

We can break down the ordering cost and the carrying cost further.

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Ordering cost = Annual Order / Ordering Quantity * Cost per Order

Carrying cost = ½ * Ordering Quantity * Carrying cost per unit

(**Note:** In material cost, it is assumed that at least the half of ordering quantity should be the carrying cost.)

So, putting the break-down of ordering cost and carrying cost into the equation, we get –

Annual Order / Ordering Quantity * Cost Per Order = ½ * Ordering Quantity * Cost per Order

Or, A / OQ * O = ½ * OQ * C

Or, 2A * O / OQ = OQ * C (By multiplying with 2 in the both sides)

Or, 2A * O = OQ ^{2 }* C

Or, 2A * O / C = OQ ^{2}

Or, OQ = √2A * O / C

And here’s how we come up with this Formula (EOQ).

### Importance of Economic Order Quantity

Before we go with the practical Economic Order Quantity examples, let’s understand the importance of EOQ.

### Significances of Economic Order Quantity or EOQ

- To business owners, lowering costs can greatly help in generating profits. By calculating Economic Order Quantity, the business owners would be able to order the right quantities and then they would be able to reduce the ordering and the carrying costs. And that will result in more profits.
- By using this, the business owners would be able to take decisions regarding materials (and orders) quickly which will result in less time and effort wasted. As a result, the processes would get improved.
- By using Economic Order Quantity, the business owners can choose the right vendors and can avail better packages to save costs and to earn better profits.

### Examples

We will look at two practical Economic Order Quantity examples.

The first one would be simple where all information will be given. And the next one would be a bit more advanced and complex.

Let’s get started.

**Economic Order Quantity Examples #1**

**Bing-Bong Company wants to find out the EOQ. It has the following information –**

**Annual Demand – 100,000 units****Ordering Cost – $20,000****Carrying Cost – $10,000**

**Find out the EOQ for Bing-Bong Company.**

This is one of the quite a simple Economic Order Quantity examples.

All we need to do is to take the Economic Order Quantity formula and feed the data into it.

EOQ Formula = √2AO/C

Or, EOQ = √2 * 100,000 * 20,000 / 10,000

Or, EOQ = √400000 = 632.45 units = 633 units (approx.)

In the next example, we will use the fundamentals so that it becomes clear.

**Economic Order Quantity Examples#2**

**Hong-Yong Inc. has given you the information to find out the EOQ. You have put the paper in your pocket; but due to heavy rain, some of the information has gone missing. Here’re a few things you still could glance your eyes on –**

**Annual demand – 400,000 units.****Carrying cost – $5 per unit.****Order costs per unit – $10 per unit.**

**You couldn’t discover the total ordering costs and the total carrying costs by any means. You need to use the information you have and find out the EOQ.**

In this Economic Order Quantity examples, we need to go back to the fundamentals to find out the EOQ.

Since we don’t have all the information for feeding into the Economic Order Quantity formula, we should start with the balancing act between ordering costs and carrying costs.

We know that at EOQ,

Ordering costs = Carrying Costs

Or, Annual Demand / Ordering Quantity * Cost per Order = ½ * Ordering Quantity * Carrying Costs per unit

Or, A / OQ * O = ½ * OQ * C

Or, 400,000 / OQ * 10 = ½ * OQ * 5

Or, 400,000 * 10 = ½ * OQ ^{2 }* 5

Or, OQ ^{2 }= 40, 00,000 * 2 / 5

Or, OQ ^{2 }= 16, 00, 000

Or, OQ = 1264.9 units = 1265 units.

From the above Economic Order Quantity examples, it’s clear how you can calculate EOQ even when you don’t have the information about the total ordering costs and total carrying costs.

All you need to pay heed to is the fundamentals.

### Recommended Readings –

This has been a guide to Economic Order Quantity or EOQ, EOQ formula, EOQ examples. You can learn more about Corporate Finance and Accounting from the below suggested articles –