# Economic order quantity (EOQ)

Economic order quantity is a mathematical model which helps in identifying the optimum level of order size which will result in minimum costs associated with inventory. Remember, the aim is to minimize the costs associated with inventory.

Varying the order size has implications on the ordering costs as well as on holding costs of inventory. So, for deciding what should be the order size of inventory procurement, relevant costs will be the ordering costs and the holding costs. However, not all holding costs are relevant. If we breakdown the holding costs, they are both fixed holding costs (such as wages and salaries of store keepers, rental of warehouse etc.) and variable holding costs (such as opportunity cost of capital tied up). Varying order size will not have any effect on fixed holding costs, therefore, relevant costs for EOQ model are ordering costs and variable holding costs.

## Formula Where
O = Ordering cost per order
D = Annual demand
H = Holding cost per unit, per anum

## Assumptions

EOQ model uses some assumptions which are highlighted below:

• Annual demand for inventory is constant and the entity is well aware of the inventory requirements for the year
• Ordering cost per order is constant
• Holding cost per unit per anum is constant
• Lead time is constant and the entity knows the lead time accurately
(Lead time is the time taken between placing an order and receiving an order)
• No bulk discounts are on offer

Effect of above mentioned assumptions is that purchase price of inventory will remain same irrespective of the order size as there are no bulk discounts on offer. That makes the purchase price irrelevant. So the order size that minimizes the sum of total ordering costs and total holding costs will be the economic order quantity. The following example will help to better understand EOQ model.

## Example – EOQ

XYZ Company is involved in the purchase and sale of PRODUCT-A. Purchase price of one unit of Product-A is \$300. Annual demand of this product is 300,000 units. Ordering cost of one order is \$50 whereas annual inventory holding cost is 10% of purchase price.

Find the economic order quantity of PRODUCT-A.

Arranging the data:
Ordering cost = \$50 per order
Annual demand = 300,000 units
Holding cost = 10% of \$300 = \$30 per unit per anum

Using the EOQ Formula:  EOQ = 1,000 units

No. of orders = annual demand / order size = 300,000 / 1,000 = 300 orders

Recalling the purpose of this formula, i.e. to minimize costs associated with inventory. Let’s calculate total costs with EOQ and some other order sizes.

If the order size is 1,000 units, i.e. EOQ:

 USD (\$) Ordering cost — \$50 x 300 orders 15,000 Holding cost — \$30 x 500 (average inventory i.e. EOQ/2) 15,000 30,000

If the order size is 980 units:

 USD (\$) Ordering cost — \$50 x 307 orders 15,350 Holding cost — \$30 x 490 (average inventory i.e. 980/2) 14,700 30,050

If the order size is 1,020 units:

 USD (\$) Ordering cost — \$50 x 295 orders 14,750 Holding cost — \$30 x 510 (average inventory i.e. 1,020/ 2) 15,300 30,050

From the above scenarios, it can be seen that when order size is changed, whether increased or decreased, as compared to EOQ, total costs associated with inventory increase. Hence, EOQ is the most optimum level of order size for procurement of inventory.

## Optimum order quantity if price discounts are offered

Recall the assumptions of EOQ model. In EOQ model, it is assumed that purchase price will remain constant throughout the year. What if this is not the case? What if the supplier offers bulk purchase discount? In this case, purchase costs will become relevant along with ordering costs and holding costs.

Remember, the aim is to minimize the costs associated with inventory. In this scenario, the most optimum order size will be either of the following:

• Economic order quantity; or
• The minimum order quantity above which price discount is offered

Total costs are calculated at these quantities and the order size that results in least costs will be the optimum order quantity. The following example will help in understanding this concept.

## Example – EOQ with price discounts

XYZ Company is involved in the purchase and sale of PRODUCT-A. Purchase price of one unit of Product-A is \$300. Annual demand of this product is 300,000 units. Ordering cost of one order is \$50 whereas annual inventory holding cost is 10% of purchase price.

This is the same example, used above to illustrate EOQ, but this time, supplier offers following discounts on purchase price:

• \$ 2 per unit if 1,500 or more units are ordered
• \$ 5 per unit if 2,000 or more units are ordered

Required: Find the most optimum order quantity of PRODUCT-A.