The EOQ Formula and a Worked Example
Ordering more at once means fewer orders (lower ordering cost) but more stock on the shelf (higher holding cost). Annual total cost for an order size Q is
TC(Q) = (D ÷ Q) × S + (Q ÷ 2) × H
where D is annual demand, S the fixed cost of one order and H the cost of holding one unit for a year. Setting the derivative to zero gives Q* = √(2DS ÷ H), the square-root formula Ford Whitman Harris published in 1913. At Q*, ordering cost equals holding cost.
- H = 25% × $20 = $5 per unit per year.
- Q* = √(2 × 12,000 × $75 ÷ $5) = √360,000 = 600 units.
- Orders per year = 12,000 ÷ 600 = 20, one every 365 ÷ 20 = 18.3 days.
- Ordering cost = 20 × $75 = $1,500; holding cost = 600 ÷ 2 × $5 = $1,500; total $3,000.
- Reorder point = daily demand × lead time + safety stock = 12,000 ÷ 365 × 7 + 100 = 330.1, rounded up to 331 units.
Total Cost Around the EOQ
The curve is flat near the bottom: ordering 25% more than the EOQ (750) costs about 2.5% extra and 25% less (450) about 4.2%, so rounding to a case or pallet size is fine, preferably upward. Ordering a third of the EOQ costs two-thirds more.
What Moves the EOQ
Because of the square root, doubling demand raises the EOQ by only about 41%, and cutting the order cost to a third shrinks it by about 42%. Expensive items carry high holding costs, so they are ordered in smaller lots more often.
Mistakes and Edge Cases
- Leaving out part of the holding cost. It is not just warehouse rent: include the cost of the money tied up, insurance, handling, shrinkage and obsolescence, which is why it is usually stated as a percentage of unit cost.
- Counting variable costs as order cost. S is the cost that does not change with quantity: purchase-order processing, a delivery fee, receiving. Freight that scales with units belongs in the unit cost.
- Ignoring quantity discounts. If the supplier takes 2% off orders of 1,000 or more, compare total cost including the purchase price: at 600 units and $20 the year costs $243,000, at 1,000 units and $19.60 it costs $238,550. The discount wins here even though 1,000 is far above the EOQ.
- Using EOQ for seasonal or perishable items. The model assumes steady demand and no shelf life; for holiday stock or food, plan by period and expiry instead.
- Forgetting safety stock in the reorder point. Lead time times average demand only covers an average week; safety stock covers the weeks that run high.
What This Calculator Does Not Model
It uses the classic Harris model: constant demand, a fixed order cost, constant unit price and delivery of the whole order at once. Quantity discounts, minimum order quantities, production runs that deliver gradually (the economic production quantity model), backorders, multiple items sharing a truck, and statistical safety-stock levels are outside it; enter safety stock yourself. For a full inventory policy across many items, an operations or supply-chain specialist can set service levels from your demand data.
Frequently Asked Questions
What is the EOQ formula?
EOQ = √(2DS/H): D is annual demand in units, S the cost of placing one order and H the cost of holding one unit for a year.
What counts as holding cost?
The cost of capital tied up in inventory plus storage, insurance, handling, shrinkage and obsolescence. It is often expressed as a percentage of unit cost per year; enter your own estimate.
What counts as ordering cost?
The fixed cost of each order regardless of quantity: purchase-order processing, a flat delivery charge, receiving and inspection.
How do I calculate the reorder point?
Daily demand × lead time in days + safety stock. With 12,000 units a year, a 7-day lead time and 100 units of safety stock, it is 331 units.
Why are ordering and holding costs equal at the EOQ?
Ordering cost falls and holding cost rises as the order size grows; the total is lowest where the two lines cross, which for this model is exactly where they are equal.
What happens if I order more than the EOQ?
Total cost rises slowly at first: 25% above EOQ adds about 2.5%. It only pays to order much more when a price break or freight saving outweighs the extra holding cost.
Does EOQ work for a small online store?
Yes for steady sellers with a fixed reorder cost; less so for new, seasonal or fast-changing products, where demand is the bigger unknown.
How to Use This Calculator
- Enter annual demand — units sold or used per year, from last year’s sales or a forecast.
- Enter order and unit costs — the fixed cost of placing one order and the price per unit.
- Set the holding cost — as a percentage of unit cost per year (capital, storage, insurance, shrinkage).
- Compare an order size and set lead time — your current order quantity, the supplier’s lead time in days and the safety stock you keep.
- Read the results — EOQ, orders per year and cycle length, ordering and holding cost, the comparison and the reorder point.
📚 Sources & References- [1] Erlenkotter, D. (1990). Ford Whitman Harris and the Economic Order Quantity Model. Operations Research 38(6):937-946 (reprints Harris 1913). ideas.repec.org
- [2] Erlenkotter, D. (1989). An early classic misplaced: Ford W. Harris’s EOQ model. Management Science 35(7):898-900. ideas.repec.org
- [3] Operational Research: Methods and Applications (2023), section 3.12 Inventory (EOQ = √(2kλ/h)); Petropoulos et al., arXiv:2303.14217. arxiv.org
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