How this instrument works
Economic order quantity is the batch size that minimizes the combined expense of two costs pulling in opposite directions: placing purchase orders too often, which racks up a fixed fee every time, and placing them too rarely, which ties up cash and shelf space in stock sitting idle. A warehouse planner, a small retailer restocking a fast-moving SKU, and a manufacturer buying raw material all face the identical trade-off, and the formula finds the single batch size where neither expense dominates the other.
The square-root shape comes straight out of calculus. Total annual expense is the ordering side (demand divided by batch size, times cost per order) plus the holding side (batch size divided by two, times holding cost per unit); setting the derivative of that sum to zero produces EOQ = √(2DS⁄H). Because the batch size sits inside a square root, doubling demand does not double the ideal batch — it multiplies the result by √2, about 1.41 — an outcome that surprises anyone used to plain linear scaling.
The model assumes demand and lead time stay steady, replenishment arrives all at once, and the price per unit never changes with batch size — assumptions that strain fast in practice. A supplier discount past some threshold, a seasonal spike, or a long unpredictable lead time all push the real best batch away from the textbook figure, so treat this output as a starting estimate to round toward a practical shipment, not a target to fill four decimal places.
- Enter Annual demand, units — the total quantity you expect to sell or use across the year.
- Set Cost per order, $ — the fixed cost of placing one purchase order, whatever its size.
- Set Annual holding cost per unit, $ — what it costs to store, insure, and finance one unit for a year.
- Read Economic order quantity, units — the batch size that minimizes the two costs combined.
- Change Annual demand, units on its own and watch the readout move by a square root, not a straight multiple.
Worked example — the 10,000-unit warehouse
A parts distributor pulls 10,000 units of a single SKU off the shelf every year, pays $50 to process and receive each purchase order no matter its size, and reckons $2 a year to hold one unit in the warehouse — a blend of shelf space, insurance, and the return that capital would earn elsewhere. Enter a demand of 10,000, an order cost of $50, and a holding cost of $2, and the sheet returns an economic order quantity of 707.1068 units.
At roughly 707 units a batch, the distributor places about 14.14 orders a year — close to one every twenty-six days — and both sides of the trade-off land at $707.11: the ordering side (14.14 × $50) matches the holding side (707.1 ⁄ 2 × $2) almost exactly, which is the defining feature of the minimum. Rounding to a supplier's 700-unit case pack barely moves the total, since the expense curve sits flat near its floor.
Questions
What exactly does the economic order quantity tell me?
It gives the batch size, in units, that minimizes the sum of two costs — the fixed fee of placing purchase orders and the expense of holding stock in inventory. Order less than the EOQ and you place orders too often, paying more in cumulative fees; order more and you tie up cash and space holding units you don't need yet. Treat the figure as a target batch size, not a purchase mandate.
Why does quadrupling demand only double the order quantity?
Because the formula is a square root of demand, not a straight multiple of it. Two quantities that both grow with batch size sit on opposite sides of the equation — the ordering side falls as batches get bigger, the holding side rises — and their balance point scales at the square root of demand. Multiply annual demand by four and the ideal batch grows by exactly two, so fast-growing operations that skip rechecking the number tend to under-order relative to their new volume.
Where does the holding cost per unit come from?
It bundles several charges into one yearly figure: warehouse space and utilities, insurance, spoilage or obsolescence risk, and the return the tied-up cash could otherwise earn, often called the cost of capital. Firms typically estimate it as a share of the item's unit price, commonly 15 to 30 percent a year, though the true figure varies sharply by industry and by how perishable or fragile the goods are.
Is EOQ the same as the reorder point?
No — they answer different questions. Economic order quantity sets how many units to order each time; the reorder point sets when to place that order, based on how much stock gets used during the supplier's lead time plus any safety buffer. A warehouse typically runs both together: order the EOQ amount whenever inventory falls to the reorder point.
Does the formula account for bulk discounts?
Not on its own — the base version assumes the price per unit stays fixed no matter how large the order, which volume discounts violate directly. If a supplier cuts the price past some threshold, the true cost-minimizing batch can sit above the plain EOQ figure; that variant is normally solved by comparing total expense at each discount tier separately, rather than by adjusting this formula.
What happens if the answer comes out as a fraction, like 707.1?
Round to whatever unit the supplier actually ships — a case, a pallet, or a whole item — since fractional units rarely exist on a loading dock. The expense curve near the minimum is shallow, so rounding 707.1 up to a 710-unit case or down to a 700-unit lot changes the total yearly cost by only a sliver of a percent.
References
- NC State Poole College of Management — Economic Order Quantity (EOQ) Model Tutorial
- U.S. Small Business Administration — Manage your finances
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.