Logistics & Supply Chain
Intermediate

Economic Order Quantity

Order size that minimises the combined cost of ordering and holding stock.

Formula

Q=2DSHQ = \sqrt{\frac{2DS}{H}}

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Variables

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

Example

D=10000, S=50, H=2: Q = √500000 ≈ 707 units

How it works

Economic Order Quantity finds the batch size that balances two opposing costs: placing orders too often and keeping too much inventory for too long. As order quantity rises, ordering costs fall because fewer orders are needed, but holding costs rise because more stock sits in storage. The formula comes from setting these two cost tendencies against each other and choosing the quantity where their combined annual cost is lowest.

When to use it

Use this when you know the annual demand for an item and can estimate both the fixed cost per order and the yearly cost of holding one unit in stock. It is most useful for inventory planning in retail, manufacturing, and procurement when demand is fairly steady and stock is replenished in batches.

Worked example, step by step

Annual demand D = 24,000 units Cost per order S = 80 Holding cost per unit per year H = 4 Step 1: Substitute into the formula Q = √((2DS)/H) Q = √((2 × 24,000 × 80) / 4) Step 2: Calculate the numerator 2 × 24,000 × 80 = 3,840,000 Step 3: Divide by H 3,840,000 / 4 = 960,000 Step 4: Take the square root Q = √960,000 ≈ 980 Final answer: The EOQ is about 980 units per order.

Common mistakes to avoid

  • Using monthly demand or monthly holding cost without converting everything to the same time period
  • Treating H as a percentage instead of a cost per unit per year
  • Forgetting that EOQ gives the optimal order size, not the number of orders per year

Did You Know?

The EOQ model dates to 1913 and still underpins inventory software a century later.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026