EOQ explained: the trade-off, the maths, and when to ignore it

Every order size is a bet against itself. Order in large batches and you pay to store, insure and finance stock you will not touch for months. Order in small ones and you pay the buyer, the carrier and the receiving dock over and over. EOQ — the economic order quantity — is the batch size where those two costs are lowest added together. It is a hundred-year-old model, it is wrong about several things, and it is still the right place to start on a stable purchased item.

Economic order quantity (EOQ)

The order quantity that minimises the sum of annual ordering cost and annual inventory holding cost, ignoring the purchase price of the goods. Purchase price drops out because buying 90,000 units a year costs the same whether they arrive in four deliveries or forty.

The EOQ formula and the cost it minimises

EOQ = √(2DS ÷ H)

Total relevant cost = (D ÷ Q) × S  +  (Q ÷ 2) × H
                      ordering cost      holding cost

The second line is the one worth understanding. Ordering cost falls as Q rises, because you place fewer orders. Holding cost rises as Q rises, because average inventory is half the order quantity. EOQ is where those two lines cross, and the square-root formula is simply the algebraic solution to that crossing point.

A worked example

A make-to-stock manufacturer buys one machined component. Annual demand is 90,000 units. The purchasing team costs $340,000 a year fully loaded and processes about 3,400 order lines, so $100 per order is a defensible S. The part costs $8.00 and the company's carrying rate is 25%, so H = $8.00 × 25% = $2.00 per unit per year.

This buyer currently orders 9,000 at a time, ten times a year, because that is a full pallet layer and it always has been. Ordering cost is 10 × $100 = $1,000 and holding cost is 4,500 × $2.00 = $9,000, so total relevant cost is $10,000 against $6,000 at EOQ. The habit costs $4,000 a year on this one component and parks $36,000 of average stock instead of $12,000.

The cost curve is flat, and that is liberating

EOQ answers look precise. They are not, and they do not need to be, because the total cost curve is almost flat near its minimum. Here is the same component at multiples of EOQ.

There is a neat identity hiding in that table. Order k times EOQ and total cost rises by a factor of (k + 1÷k) ÷ 2. At k = 2 that is (2 + 0.5) ÷ 2 = 1.25, exactly the 25% penalty shown. At k = ½ it is (0.5 + 2) ÷ 2 = 1.25 as well — which is why ordering half of EOQ and twice EOQ cost the same. At k = 1.5 it is (1.5 + 0.667) ÷ 2 = 1.083, an 8.3% penalty.

The practical consequence: round EOQ to a case pack, a pallet or a supplier minimum without guilt. What matters is knowing whether you are near the bottom of the curve or sitting at three times EOQ, where the penalty is 67%.

EOQ moves with the square root of demand

Because demand sits under a square root, EOQ is far less sensitive to forecast error than people expect. Double annual demand from 90,000 to 180,000 and EOQ becomes √(2 × 180,000 × 100 ÷ 2) = √18,000,000 = 4,243 units — a 41% increase, not 100%. Orders per year rise from 30 to 42, so frequency absorbs most of the growth, not batch size.

Two consequences follow. A 20% forecast miss changes EOQ by about 10%, which the flat curve discounts to under 1% of cost — so EOQ does not need a good forecast. And growth raises inventory turns on its own, because average inventory grows more slowly than demand does. If your turns fall while volume grows, order policy is not the cause; inventory turnover: how to read it covers what usually is.

Where the EOQ assumptions break

EOQ assumes a world with one item, constant demand, one fixed ordering cost, one price, unlimited storage and instant replenishment. Real distribution and manufacturing violate every one of those. Knowing which assumption you are breaking tells you what to do instead.

Quantity discounts: doing the comparison properly

This is where EOQ gets misused most often, in both directions. Buyers either ignore price breaks entirely, or take every break offered because the saving is visible and the carrying cost is not. The only honest test is total annual cost including the purchase price.

Same component. The supplier offers 1% off — $7.92 instead of $8.00 — on orders of 22,500 units, which is a quarter's demand. At that price, holding cost per unit becomes $7.92 × 25% = $1.98.

Check it from the other direction: the discount saves $0.08 × 90,000 = $7,200 on purchase price and $2,600 on ordering cost, but adds $19,275 of holding cost. Net $9,475 worse, which matches the table. The break would need to be about 2.3% before it paid for itself here — and even then you would be accepting a quarter's worth of obsolescence risk on a machined part.

The manufacturing variant: EOQ for a production run

If you make the item rather than buy it, stock does not arrive in one instant — it builds while you produce and drains while you consume. The economic production quantity corrects for that with one extra term: EPQ = EOQ × √(p ÷ (p − d)), where p is the daily production rate and d the daily demand rate. At 90,000 units over 250 working days, d = 360 a day. If the cell produces 1,200 a day, p ÷ (p − d) = 1,200 ÷ 840 = 1.4286, whose square root is 1.1952, so EPQ = 3,000 × 1.1952 = 3,586 units — a 19% longer run, because peak inventory only reaches the net accumulation rather than the full batch. As p approaches d, that multiplier explodes, which is the arithmetic telling you the constraint is capacity, not batch size.

Getting D, S and H out of your ERP

The formula takes ten seconds; the inputs take a week. Annual demand has to be demand rather than shipments, on a consistent unit of measure, excluding intercompany transfers and one-off project buys. Ordering cost is an internal costing exercise — total purchasing cost divided by order lines placed is a defensible first pass, and better than the $50 someone typed in 2019. Holding cost is a policy decision that belongs to finance, because it silently sets how much stock the whole business carries.

Ask ERPray for "units issued and purchase order line count by item for the last 12 months, top 100 items by usage value" and you have D and the order frequency you are actually running, computed live from your own account with the query shown underneath so you can confirm what counted as an issue. Then check the resulting policy is deliverable with the reorder point calculator before anyone edits an item record.