**Formula of EOQ (Table of Contents)**

## What is EOQ Formula?

The EOQ stands for economic order quantity, EOQ formula calculates by reducing the cost of per order by setting order derivative to zero. In simple language, we can say that the EOQ equation helps to find a volume of production or order by decreasing holding cost and ordering cost.

**Total cost = Purchase cost + Ordering cost + Holding cost**

The components for calculation of EOQ equation are the cost of holding and cost of ordering.

#### #1 – Holding Cost

Holding cost is the cost of a holding of inventory in storage. It is the direct cost which needs to be calculated to find the best opportunity whether to store inventory or instead of it invest it somewhere else. Assuming demand to be constant.

** H = i*C**

Where,

- H= Holding cost
- i= Carrying cost
- C= Unit cost

Here as demand is constant inventory will decrease with usage when it reduces to zero order placed again.

#### #2 – Ordering Cost

Ordering cost is the cost of placing an order to the supplier for inventory. The number of order is calculated by annual quantity demanded divided by volume per order.

**Number of orders = D / Q**

Where,

- D = Annual quantity demanded
- Q = Volume per order
- Annual Ordering Cost

An annual ordering cost is the number of order multiply by ordering cost.

**Annual ordering cost = (D * S) / Q**

Where,

- S = Ordering cost

#### #3 – Annual Holding Cost

Annual holding cost is sum product of volume per order and holding cost which can be written as.

**Annual Holding Cost= (Q * H) / 2**

#### #4 – Total Cost

Sum of two costs gives an annual total cost of an order.

By adding annual ordering cost and annual holding cost we get below equation.-

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**Annual Total Cost or Total Cost = Annual ordering cost + Annual holding cost**

**Annual Total Cost or Total Cost = (D * S) / Q + (Q * H) / 2**

To find EOQ – Economic Order Quantity Formula, differentiate total cost by Q.

EOQ Equation = DTC / DQ

### Examples of EOQ Formula (with Excel Template)

Let’s see some examples of EOQ equation to understand it better.

#### EOQ Formula – Example #1

**Let’s take an example to calculate EOQ – Economic Order Quantity for a pen manufacturing company where company’ annual quantity demanded is 400, holding cost is $2 and the ordering cost is $1. Now we will put these values in the above equation.**

In the below-given figure, we have shown the calculation for EOQ equation for a pen manufacturing company.

**So, the calculation for EOQ ^{2 }= (2*400*1)/2**

Therefore ,EOQ =20.

#### EOQ Formula – Example #2

**Let us understand this with an example. A company names Den Pvt. Ltd. wants to know EOQ as it is a tool to calculate volume and frequency of order required for minimizing the cost of per order.**

In below-given table is the data for the calculation of EOQ – Economic Order Quantity Formula for company Den Ltd.

Take below assumption.

By keeping above values in the below tabular equation we get total cost with a combination of different volume.

Through the above data, we get below the graph.

From it, we can clearly see EOQ is 250. EOD set point where minimize the cost of inventory.

#### EOQ Formula – Example #3

**A company manufactures steel boxes for that it needs steel to calculate quantity required EOD need to be calculated.**

Taking below Assumptions:-

- Ordering Cost = $10 per order
- Annual quantity demanded = 2000 units
- Holding cost = $1 per unit

In the below-given figure, we have shown the calculation of EOQ equation for manufacturing company.

**So, the calculation for EOQ ^{2}^{=}(2*2000*10)/1**

EOQ = (40000)^{1/2}

Therefore ,EOQ = 200

Further, we will calculate holding cost, ordering cost, and the number of orders per year and combine ordering and holding cost at economic order quantity.

- Numbers of orders per year

The below table shows the calculation of the number of orders per year.

**A number of orders per year = Annual quantity demanded/ EOQ.**

So, the calculation of EOQ for numbers of orders per year is =2000/200

Therefore, a number of orders per year =10

- Ordering Cost

The below table shows the calculation of the Ordering cost.

**Ordering cost = Number of orders per year * cost per order**

So, the calculation of EOQ for ordering cost is = 10*10

Therefore, ordering cost = 100

- Holding Cost

The below table shows the calculation of the Holding cost.

**Holding cost = Average unit * Holding cost per unit**

So, the calculation of EOQ – Economic Order Quantity Formula for holding cost is = (200/2) * 1

Therefore, holding cost = 100

- Combine ordering and holding cost at economic order quantity

The below table shows the calculation of the combine ordering and holding cost at economic order quantity

**Ordering cost + Holding Cost**

So, the calculation for combine ordering and holding cost at economic order quantity formula is = 100 + 100

Here, holding cost and ordering cost is same i.e. $100.

Therefore, combine ordering and holding cost at economic order quantity formula is= 200

Let’s see the table how we can derive the same.

From this table, we also get EOQ = 200.

### Relevance and Uses

**Cash flow planning-**EOQ formula is used to minimize the cost of inventory and save cash.- Reordering Point- This formula is used to calculate reordering point i.e. point at which one gets a trigger to order inventory.
- It helps the company to reduce waste.
- It helps to minimize storage and holding cost.

### Recommended Articles

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