EOQ: Economic Order Quantity in 13 Minutes
The economic order quantity (EOQ) is the order size that keeps total inventory cost as low as possible. Order too often and ordering costs pile up; order too much at once and holding costs pile up. EOQ finds the balance point, where annual ordering cost equals annual holding cost.
Economic order quantity explained simply
The economic order quantity (EOQ) is the order size that minimizes total ordering and holding cost: EOQ = √(2DS ÷ H). At EOQ, yearly ordering cost equals yearly holding cost. In the example, the store should order 500 units, 20 times a year, for a total cost of $2,000.
What this EOQ lesson covers
- What ordering costs and holding costs are
- How to calculate EOQ with the square root formula
- How to find the number of orders per year and total inventory cost
- Why ordering cost equals holding cost at the EOQ
EOQ formulas, explained
- D
- annual demand in units
- S
- cost per order
- H
- holding cost per unit per year
- Q
- order quantity
- D ÷ Q
- number of orders per year
- Q ÷ 2
- average inventory
How to calculate EOQ step by step (worked example)
A store sells 10,000 units a year. Each order costs $50 to place, and holding one unit for a year costs $4. What is the EOQ and the total annual ordering and holding cost?
- EOQ = √(2 × 10,000 × $50 ÷ $4) = √250,000 = 500 units.
- Orders per year = 10,000 ÷ 500 = 20 orders.
- Annual ordering cost = 20 × $50 = $1,000.
- Annual holding cost = (500 ÷ 2) × $4 = $1,000.
- Total = $1,000 + $1,000 = $2,000.
Answer: Order 500 units at a time, 20 times a year, for a total ordering and holding cost of $2,000.
Ordering cost vs holding cost
| Ordering cost | Holding cost | |
|---|---|---|
| What it covers | Placing and receiving each order | Storage, insurance, capital tied up |
| Bigger orders make it | Lower (fewer orders) | Higher (more stock on hand) |
| Formula per year | (D ÷ Q) × S | (Q ÷ 2) × H |
| At EOQ (500 units) | $1,000 | $1,000 |
Harder EOQ questions
What if the cost per order doubles to $100?
EOQ = √(2 × 10,000 × 100 ÷ 4) ≈ 707 units. EOQ rises with the square root, so doubling order cost raises the order size by about 41%, not 100%.
How costly is ordering 400 instead of 500?
Ordering cost = 25 × $50 = $1,250 and holding cost = 200 × $4 = $800, total $2,050, only 2.5% more. The total cost curve is flat near the EOQ, so being a little off doesn't hurt much.
Common EOQ questions
What is the EOQ formula?
EOQ equals the square root of two times annual demand times the cost per order, divided by the annual holding cost per unit. It gives the order size that minimizes the combined cost of ordering and holding inventory.
How do you calculate the number of orders per year with EOQ?
Divide annual demand by the EOQ. For example, with annual demand of 10,000 units and an EOQ of 500, the company places 20 orders a year. Dividing the days in a year by that number gives the time between orders.
Why are ordering cost and holding cost equal at EOQ?
Ordering cost falls as order size grows, while holding cost rises. In the basic EOQ model, total cost is lowest exactly where the two curves cross, so at the EOQ annual ordering cost equals annual holding cost.
What are the assumptions of the EOQ model?
The basic model assumes steady, known demand, a fixed cost per order, a constant holding cost per unit, no quantity discounts, instant delivery of the full order and no stockouts. Real life bends these, which is why extensions like discounts and safety stock exist.