Business & Commerce
Intermediate

Economic Order Quantity (EOQ)

The order size that minimizes total inventory ordering and holding costs.

Formula

EOQ=2DSHEOQ = \sqrt{\dfrac{2DS}{H}}

Variables

EOQOptimal order quantity
DAnnual demand
SCost per order
HHolding cost per unit/yr

Example

D=10000, S=$50, H=$5: EOQ ≈ 447 units

How it works

Economic Order Quantity (EOQ) tells you the order size that balances two opposing costs: ordering too often raises setup/order costs, while ordering too much raises storage and capital costs. It comes from minimizing the total annual inventory cost, where ordering cost falls as order size increases and holding cost rises as order size increases. The square-root formula gives the point where these two cost effects are optimally traded off.

When to use it

Use EOQ when a business repeatedly buys or produces the same item, demand is fairly steady, and each order has a fixed cost. It is especially useful for stock planning in retail, wholesale, manufacturing, and warehouse management.

Worked example, step by step

Annual demand, D = 24,000 units Cost per order, S = $80 Holding cost per unit per year, H = $2 EOQ = √(2DS / H) EOQ = √(2 × 24,000 × 80 / 2) EOQ = √(3,840,000 / 2) EOQ = √1,920,000 EOQ ≈ 1,386 units Final answer: The optimal order quantity is about 1,386 units per order.

Common mistakes to avoid

  • Using monthly demand with annual holding cost without converting units to the same time period
  • Confusing holding cost per unit per year with the purchase price of the item
  • Rounding too early and carrying the rounded value through the whole calculation

Did You Know?

EOQ, derived in 1913, is one of the oldest operations-research formulas still used in supply chains today.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026