# Economic Order Quantity (EOQ)

Economic order quantity (EOQ) is the order quantity of inventory that minimizes the total cost of inventory management.

Two most important categories of inventory costs are ordering costs and carrying costs. Ordering costs are costs that are incurred on obtaining additional inventories. They include costs incurred on communicating the order, transportation cost, etc. Carrying costs represent the costs incurred on holding inventory in hand. They include the opportunity cost of money held up in inventories, storage costs, spoilage costs, etc.

Ordering costs and carrying costs are quite opposite to each other. If we need to minimize carrying costs we have to place small order which increases the ordering costs. If we want minimize our ordering costs we have to place few orders in a year and this requires placing large orders which in turn increases the total carrying costs for the period.

We need to minimize the total inventory costs and EOQ model helps us just do that.

Total inventory costs = Ordering costs + Holding costs |

By taking the first derivative of the function we find the following equation for minimum cost

EOQ = SQRT(2 × Quantity × Cost Per Order / Carrying Cost Per Order) |

## Example

ABC Ltd. is engaged in sale of footballs. Its cost per order is $400 and its carrying cost unit is $10 per unit per annum. The company has a demand for 20,000 units per year. Calculate the order size, total orders required during a year, total carrying cost and total ordering cost for the year.

__Solution__

EOQ = SQRT(2 × 20,000 × 400/10) = 1,265 units

Annual demand is 20,000 units so the company will have to place 16 orders (= annual demand of 20,000 divided by order size of 1,265). Total ordering cost is hence $64,000 ($400 multiplied by 16).

Average inventory held is 632.5 ((0+1,265)/2) which means total carrying costs of $6,325 (i.e. 632.5 × $10).

Written by Obaidullah Jan, ACA, CFA