What is Economic Order Quantity (EOQ)?
Why Is EOQ Important?
EOQ matters because ordering cost and holding cost pull in opposite directions, and the right order size minimizes their combined total. Ordering too little means placing orders frequently, which drives up total ordering cost. Ordering too much means holding excess inventory, which drives up total carrying cost. EOQ sits at the exact crossover point where the two costs are equal — and their sum is at its lowest.
Without EOQ, buyers typically default to round-number order quantities or supplier minimums, both of which can be substantially more expensive than optimal. A company ordering twice the EOQ pays roughly 25% more in total annual inventory cost than one ordering at EOQ. At high volume or with expensive goods, that premium becomes material within a single quarter.
EOQ also improves decision quality beyond cost. It provides a defensible, formula-derived order size that teams can align on, audit, and update consistently — rather than relying on gut feel or outdated convention. It integrates directly with the reorder point, which answers the complementary question of when to order.
How Does EOQ Work?
EOQ is derived by setting the first derivative of the total annual cost function equal to zero. Total annual cost equals annual ordering cost plus annual holding cost: TC = (D/Q) × S + (Q/2) × H. Minimizing TC with respect to Q gives the EOQ formula.
At the EOQ quantity, annual ordering cost and annual holding cost are exactly equal to each other — this is the mathematical condition for the minimum. Ordering cost = (D ÷ EOQ) × S; Holding cost = (EOQ ÷ 2) × H. If you calculate both for the EOQ result, they will always match.
The square root in the formula has an important practical implication: EOQ is far less sensitive to input changes than linear intuition suggests. Doubling annual demand (D) increases EOQ by only 41% (√2 ≈ 1.41), not 100%. This means moderate demand fluctuations have a small effect on the optimal order size, and using last period's EOQ as a starting point remains defensible even when demand shifts somewhat. For the full derivation with each step shown, see the EOQ formula guide.
EOQ Example
A warehouse stocks a fastener with annual demand of 12,000 units, a $50 ordering cost per purchase order, and a holding cost of $3 per unit per year.
Enter your demand, ordering cost, and holding cost — get EOQ, order frequency, and the cost curve instantly.
What Factors Affect EOQ?
Three inputs determine EOQ. Each must be measured accurately — inaccurate inputs produce a result that is mathematically correct but operationally wrong.
| Factor | Symbol | Unit | Effect on EOQ | Common pitfalls |
|---|---|---|---|---|
| Annual demand | D | units / year | Higher D → larger EOQ (√ relationship) | Using seasonal demand as annual demand; forgetting to annualize weekly/monthly figures |
| Ordering cost | S | $ / order | Higher S → larger EOQ | Omitting internal labor to process the PO; excluding inbound freight and supplier setup charges |
| Holding cost | H | $ / unit / year | Higher H → smaller EOQ | Counting only storage rent while ignoring capital opportunity cost, insurance, damage, and obsolescence — typically 20–30% of unit value |
Unit price is notably absent from the EOQ formula because EOQ minimizes cost attributable to ordering and holding decisions, not the purchase price itself. When price varies with quantity (quantity discounts), EOQ must be supplemented with a break-point analysis that compares total annual cost at each price tier.
Common EOQ Mistakes
EOQ calculated on last year's demand is only as good as how closely last year resembles the coming year. Demand that has shifted by 20% or more will produce an order size that over- or under-orders by roughly 10%. Refresh the demand input whenever sales forecasts are updated.
The most common error in EOQ is using only the warehouse rent line as holding cost. The full holding rate includes capital opportunity cost (the cost of money tied up in inventory), insurance, shrinkage, damage, and obsolescence risk. The true rate is typically 20–30% of unit value per year. A holding cost that is 50% too low inflates EOQ by 41%, leading to chronic over-ordering.
EOQ minimizes cost under the assumption of constant demand and instantaneous replenishment. Real demand varies, and lead times are rarely zero. EOQ says nothing about how much safety stock to hold. Pair EOQ with a safety stock calculation to protect against variability.
EOQ is a snapshot, not a permanent setting. As suppliers change their ordering costs, as holding cost rates shift with interest rates, and as demand evolves, the optimal quantity changes. A simple rule: recalculate EOQ at least annually and immediately whenever any input changes by more than 10%.
Frequently Asked Questions
Is EOQ the same as reorder point?
No. EOQ is how much to order; the reorder point is when to order. EOQ sets the order size that minimizes total inventory cost, while the reorder point triggers a new order based on average demand during lead time plus safety stock. The two answers together define a complete replenishment policy — you need both.
What assumptions does the EOQ model make?
EOQ assumes constant annual demand, a fixed cost per order, a fixed holding cost per unit per year, instantaneous replenishment, no quantity discounts, and no planned stockouts. When demand is seasonal, lead time is variable, or the supplier offers volume discounts, treat EOQ as a starting approximation and adjust with safety stock and break-point analysis.
How often should I recalculate EOQ?
Recalculate EOQ at least once per year and immediately whenever any input changes by more than 10–15%. A 10% change in ordering cost or holding cost shifts EOQ by roughly 5%, which is small enough to ignore in most cases. A 25% demand increase shifts EOQ by about 12%, which is worth updating at meaningful order volumes.
Can EOQ be used with quantity discounts?
Not directly — EOQ assumes a constant unit price. When a supplier offers a discount above a minimum order size, calculate EOQ at the standard price first, then compare total annual cost (ordering + holding + purchase price) at the EOQ quantity versus the minimum discount quantity. Choose the option with the lower total annual cost.
What is the difference between EOQ and lot sizing?
EOQ is one lot-sizing method, designed for stable continuous demand. Other methods — Periodic Order Quantity (POQ), Lot-for-Lot (LFL), and Wagner-Whitin — handle variable or lumpy demand patterns better. EOQ minimizes cost precisely under its assumptions; the others trade cost optimality for a better fit with irregular demand schedules, such as those driven by MRP requirements.