# Economic order quantity (EOQ)

## Definition and explanation

**Economic order quantity** (**EOQ**) is the order size that minimizes the sum of ordering and holding costs related to raw materials or merchandise inventories. In other words, it is the optimal inventory size that should be ordered with the supplier to minimize the total annual inventory cost of the business. Other names used for economic order quantity are optimal order size and optimal order quantity.

The economic order quantity is computed by both manufacturing companies and merchandising companies. Manufacturing companies compute it to find the optimal order size of raw materials inventory and merchandising companies compute it to find the optimal order size of ready to use merchandise inventory.

### The ordering and holding costs

The two significant factors that are considered while determining the economic order quantity (EOQ) for any business are the *ordering costs* and the *holding costs*.

A brief explanation of both the costs is given below:

#### Ordering costs

The **ordering costs** are the costs that are incurred every time an order for inventory is placed with the supplier. Examples of these costs include telephone charges, delivery charges, invoice verification expenses and payment processing expenses etc. The total ordering cost usually varies according to the frequency of placing orders. Mostly, it is directly proportional to the number of orders placed during the year which means If the number of orders placed during the year increases, the annual ordering cost will also increase and if, on the other hand, the number of orders placed during the year decreases, the annual ordering cost will also decrease.

#### Holding costs

The **holding costs** (also known as carrying costs) are the costs that are incurred to hold the inventory in a store or warehouse. Examples of costs associated with holding of inventory include occupancy of storage space, rent, shrinkage, deterioration, obsolescence, insurance and property tax etc. The total holding cost usually depends upon the size of the order placed for inventory. Mostly, the larger the order size, the higher the annual holding cost and vice versa. The total holding cost is some time expressed as a percentage of total investment in inventory.

**The economic order quantity is the level of quantity at which the combined ordering and holding cost is at the minimum level.**

### Relation between the ordering and holding cost:

There is an inverse relationship between ordering cost and holding cost. Keeping the annual demand constant if for example the number of orders decreases, the ordering cost will also decrease but the holding cost will rise and vice versa.

## Economic order quantity formula

The following formula is used to determine the economic order quantity (EOQ):

*Where,*

- D = Demand per year
- Co = Cost per order
- Ch = Cost of holding per unit of inventory

## Example

The material DX is used uniformly throughout the year. The data about annual requirement, ordering cost and holding cost of this material is given below:

- Annual requirement: 2,400 units
- Ordering cost: $10 per order
- Holding cost: $0.30 per unit

**Required:** Determine the economic order quantity (EOQ) of material DX using above data.

### Solution

The economic order quantity for material DX is 400 units. Now, we can compute the number of orders to be placed per year, annual ordering cost, annual holding cost and combined annual ordering and holding cost as follows:

#### Number of orders per year

= Annual demand/EOQ

= 2,400 units/400 units

= 6 orders per year

#### Ordering cost

= Number or orders per year × Cost per order

= 6 orders × $10

= $60

#### Holding cost

= Average units × Holding cost per unit

= (400/2) × 0.3

= $60

#### Combined ordering and holding cost at economic order quantity (EOQ):

= Ordering cost + Holding cost

= $60 + $60

= $120

**Notice that both ordering cost and holding cost are $60 at economic order quantity. The holding cost and ordering cost at EOQ tend to be the same.**

### Tabular determination of economic order quantity (EOQ)

Under tabular approach of determining economic order quantity, the combined ordering and holding cost is computed at different number of orders and their respective order quantities. This approach is also known as trial and error approach of determining economic order quantity.

This approach is illustrated below using the same data as used in the above example:

*Average units × Holding cost per unit: 1,200 units × 0.30 = $360

Notice that the quantity of 400 units with 6 annual orders and a combined ordering and holding cost of $120 is the most economical quantity to order. Other order quantities that result in more or less than six orders per year are not so economical. For example, if only one order for the whole annual requirement of 2,400 units is placed, the combined ordering and holding cost comes to $370 which is far higher than the cost at economic order quantity of 400 units.

The application of tabular approach is not common as it is more time consuming as compared to formula approach. Moreover, in some situations, it provides only an estimate of economic order quantity and is therefore not as accurate as the formula approach. If a question regarding economic order quantity is asked in the examination, the students should avoid using tabular (trial and error) approach; rather they should use the formula approach which is comparatively less time consuming and which also provides the most accurate answer.

## Example 2

The John Sports Inc. purchases tennis balls at $20 per dozen from its suppliers. The John Sports will sell 34,300 dozens of tennis balls evenly throughout the year. The total cost to handle a purchase order is $10. The insurance, property tax and rent for each dozen tennis balls in the average inventory is $0.40. The company wants a 5% return on average inventory investment.

**Required**:

- Compute the economic order quantity.
- Compute the total annual inventory expenses to sell 34,300 dozens of tennis balls if orders are placed according to economic order quantity computed in part 1.

### Solution

#### 1. Economic order quantity:

*$0.40 + ($20 × 5/100) = $1.4

#### 2. Total annual inventory expenses to sell 34,300 dozens of tennis balls:

= Annual ordering cost + Annual holding cost

= (Number of orders × Cost per order) + (Average units × Holding cost per unit)

= (*49 orders × $10) + [(700/2) × 1.4]

= $490 + $490

= $980

*Number of orders to be placed: 34,300/700 = 49 orders

## Underlying assumptions of economic order quantity (EOQ)

The computation of economic order quantity (EOQ) is based on the following assumptions:

- The total number of units to be consumed during the period is known with certainty.
- The total ordering cost remains constant throughout the period.
- The inventory cost remains constant throughout the period.
- There are no cash or quantity discounts available.
- The whole quantity of ordered inventory is delivered in one batch.
- The optimal quantity for each invariable or stock item is computed separately.
- The lead time does not fluctuate and the order is received on time with the total order quantity.

The assumptions described above are also known as the limitations of economic order quantity (EOQ).

15 Comments on Economic order quantity (EOQ)Found this material useful. The presentation simplified eoq and made it readily understandable. Thanks for the good work.

Nice write ups

Thanks for the explicit explanation.

You have put the Economic Order Quantity in an understandable way as possible thank you very much

Maximum consumption 600 units per month

Minimum consumption 100 units per month

Normal consumption 300 units per month

Yearly consumption 3600 units

Storage cost 50% of stock value

ORdering cost 400 per order

Price of material 64 per unit

Calculate average stock level

Minimum stock level nd maximum stock level and re order level?

can u hlp.m

Thank you for the simplified explanation

There is no mention of lead time , please include the same

Average usage =20 units per day

minimum usage=120 units per day

maximum usage=260 units per day

lead time 20-26 days

demand is 25 per working days, ordering cost $150 per order,items cost $3 and carrying cost are 12% per year.there are 250 working day in a year.

calculate: re- order level

minimum level

maximum level

economic order quantity

please help me .

what is the implication of price increase or price fluctuations on the EOQ?

annual consumption 36000

purchase price per units 5400

order cost per order 1500

inventory carrying cost is 20% of the average inventory

calculate economic order quantity

Useful for my Assignment (Operation Management)

Minimum lead time =4weeks

Maximum lead time=6weeks

Cost of material=#20per unit

Maximum usage per week=15 unit

Manimum usage per week=50 unit

Minimum usage per week=50 unit

Yearly usage =4000 unit

Carrying cost=5% of stock value

Ordering cost=#3 per order

Plz if u can help me out, am having the exams tomorrow and I don’t have any idea

Please I need an urgent help with the following problem:

The demand for an item is 44,000 units per annum, the ordering cost is $50 per order. The holding cost per item is $2.5 per annum and the price per unit of the item is $10. The supplier offers a discount rate of 3% for orders between 10,000 to 31,999 and 8% discount rate for orders of 32,000 and above.

You’re required to determine the best quantity to order

Awesome!!!

Thanks so much

Pls can you help me with this

The annual requirement of an item is 72000 units, each costing #36. Every order cost #1200 and inventory carting charges are 20% of the average inventory per annum.

Required:

1. Solve for EOQ using the formula

2. Calculate total inventory cost

worderfull job, its a good job