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Short answer
The EOQ calculation finds the order size that minimises yearly ordering cost plus holding cost: Q* = √(2AD/h), where A is the fixed cost per order, D is annual demand and h is the yearly holding cost per unit. With D = 1,000 units, A = $12 and h = $0.25, Q* is about 310 units, costing $77.46 a year before the price of the goods.
What economic order quantity means
Economic order quantity (EOQ) is the order size at which the combined yearly cost of placing orders and holding stock is lowest. It is also called the EOQ model, and the “classical” or “basic” version rests on a short list of assumptions. In the University of Iowa lecture notes on the model (Dennis Bricker, Department of Mechanical and Industrial Engineering), these are:
- demand is at a constant, known rate;
- lead time is known and not random;
- a replenishment arrives all at once;
- no shortages are allowed;
- the product cost does not depend on the order quantity, so there are no quantity discounts and the product cost can be left out of the optimisation.
Because stock is used at a constant rate and each delivery arrives just as stock reaches zero, average inventory is Q/2, and the holding cost is taken as proportional to that average.
The EOQ formula and what each term is
Total yearly cost, excluding the product price, is C(Q) = ½·Q·h + A·D/Q: a holding term that rises with order size and an ordering term that falls with it. The total is bowl-shaped, and its minimum sits where the two curves cross.
| Symbol | Meaning | Alternative notation |
|---|---|---|
| D | Annual demand (units per year) | D |
| A | Fixed cost of placing one order | S (setup or order cost) |
| h | Holding cost per unit per year, = holding cost rate i × unit value v | H |
| Q* | Economic order quantity = √(2AD/h) | √(2DS/H) |
| C(Q*) | Minimum yearly ordering plus holding cost = √(2ADh) | – |
The second notation comes from the University of Lisbon (ISEG) operations-management exercise solutions, which write the same result as Q* = √(2DS/H). Textbooks and software differ on letters, so check which symbol a source uses for the ordering cost before plugging numbers in.
Worked EOQ calculation
The Iowa notes use D = 1,000 units a year, a holding cost of 25% of a $1.00 unit value (so h = $0.25) and A = $12 per order.
- Multiply: 2 × 12 × 1,000 = 24,000.
- Divide by h: 24,000 ÷ 0.25 = 96,000.
- Take the square root: Q* = √96,000 = 309.8, about 310 units.
- Minimum yearly cost: √(2 × 12 × 1,000 × 0.25) = √6,000 = $77.46.
At Q* the ordering and holding costs are equal, about $38.73 each. The next table compares order sizes for this example. The 200-unit and 50-unit rows are from the Iowa notes; the 310-unit and 500-unit rows are calculated here from the same formula C(Q) = ½·Q·h + A·D/Q.
| Order size Q | Orders per year | Ordering cost | Holding cost | Total |
|---|---|---|---|---|
| 50 | 20.0 | $240.00 | $6.25 | $246.25 |
| 200 | 5.0 | $60.00 | $25.00 | $85.00 |
| 310 (EOQ) | 3.2 | $38.71 | $38.75 | $77.46 |
| 500 | 2.0 | $24.00 | $62.50 | $86.50 |
Why the answer is forgiving
The cost curve is flat near its minimum. The ISEG exercise solutions give a general ratio: if Q0 is the optimum, the cost at another quantity Q relative to the optimum is C/C0 = ½(Q0/Q + Q/Q0). In their example (20,000 litres a year, €90 per order, €2.40 holding cost per litre), the EOQ is 1,225 litres, and ordering 1,200 instead costs only about 0.02% more in ordering plus holding cost.
The same ratio applied to the Iowa example shows that a 200-unit order, roughly a third below the optimum, costs about 10% more than the minimum ($85.00 against $77.46). The practical reading, which is this page’s interpretation rather than a claim from either source: rounding Q* to a convenient pack or case size usually matters far less than getting A, D and h roughly right.
EOQ with quantity discounts and minimum order quantities
The basic formula assumes the unit price is the same at every order size. When a supplier prices in tiers, the ISEG solutions work it as follows: compute the EOQ at the lowest tier price, check whether that quantity is actually feasible within that tier’s range, and then compare total cost including the purchase price across the candidate quantities. In their example (D = 86,000, holding cost 30% of price, A = 10, tiers at 10, 9.5, 9 and 7), the EOQ at the lowest price is about 906, which falls inside the top tier (more than 900), so it is feasible. See also the CASRAI entry on minimum order quantity (MOQ), which limits the order sizes available in the first place.
Reorder point and lead time
EOQ says how much to order, not when. The ISEG notes pair it with the reorder point, ROP = lead time × daily demand. In their second exercise (annual demand 72,000, ordering cost 10, holding cost 1), Q* = 1,200 and a 4-day lead time at 288 units a day gives ROP = 4 × 288 = 1,152. The same exercise shows a fixed batch of 1,000 costs 1,220 a year against 1,200 at the EOQ, and a batch of 1,500 costs 1,230. A par level serves a similar trigger role in practice.
Where EOQ does and does not fit lab and clinic supplies
The CDC and the Association of Public Health Laboratories’ Next Generation Sequencing Quality Initiative publish a “Summary of Inventory Management Processes” template for laboratories. It gives no EOQ formula and does not endorse one. What it does say is relevant to the assumptions above: laboratories should keep proper stock levels, monitor reagent expiration dates, set a minimum stock level that triggers a reorder (the “critical amount”), consider the time to order and receive supplies, and rotate stock by expiry using shortest-life-first-out and first-in-first-out rules. It notes that stock should cover unexpected events without overstocking and wasting reagents through expiration.
| EOQ assumption (Iowa notes) | Lab supply room check |
|---|---|
| Constant, known demand | Volume that swings by run or project breaks it; the CDC template asks labs to establish minimum stock for an appropriate time period. |
| Known, non-random lead time | The CDC template says to account for ordering and receiving time and to adjust when supply-chain issues appear. |
| No shortages allowed | The CDC template’s critical amount is the lowest stock level that triggers an alert to reorder. |
| Holding cost proportional to average stock | Expiry is not in the basic model. Reagents that expire put a ceiling on useful order size; this is an inference from the two sources, not a CDC statement. |
| No quantity discounts | Use the tiered procedure above when a supplier prices by volume. |
For related practice, see the CASRAI pages on chemistry stockroom management, just-in-time inventory and the comparison of laboratory inventory management software.
Common misunderstandings
- EOQ is not the cheapest purchase. The basic model leaves the product price out; it minimises ordering plus holding cost only.
- EOQ is not a reorder trigger. It sets the order size; the reorder point depends on lead time and demand.
- A precise answer is not a precise decision. Because the curve is flat, an inexact A or h changes the result far less than the decimals suggest, but the inputs still need to be measured honestly.
- The basic model does not cover discounts or expiry. Both need extra steps, as above.
FAQ
What is the EOQ formula?
Q* = √(2AD/h), or √(2DS/H) in other notation: twice the annual demand times the cost per order, divided by the yearly holding cost per unit, all under a square root.
What is the EOQ model?
It is the basic inventory model that balances ordering cost against holding cost under constant demand, known lead time, no shortages and a price that does not vary with quantity.
What is economic order quantity in simple terms?
It is the order size that makes the sum of yearly ordering and holding costs as small as possible. In the worked example above it is about 310 units.
Sources
- Bricker, D. “EOQ model”, lecture slides (dated 01/27/03), Department of Mechanical and Industrial Engineering, University of Iowa: user.engineering.uiowa.edu/~dbricker/Lecture_Slides/EOQ_Model.pdf (checked 2026-10-30).
- ISEG, University of Lisbon. “Inventory Management Exercises Solutions”, Production and Operations Management 2023/24: fenix.iseg.ulisboa.pt (checked 2026-10-30).
- CDC and APHL Next Generation Sequencing Quality Initiative. “Summary of Inventory Management Processes”: cdc.gov/lab-quality (checked 2026-10-30). The template is written for CLIA next-generation-sequencing, research and surveillance laboratories.
