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Economic order quantity (EOQ) and EPQ

Enter annual demand, the cost of each setup or order, the item cost and holding cost to get the economic lot, total cost, average inventory and the setup needed for smaller lots.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Preliminary estimate
Demand and costs
Replenishment
Calculate from history (paste from Excel)

Paste the demand of each period to calculate annual demand.

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—Economic lot size
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Total cost versus lot size

Annual setup cost, holding cost and total. The bottom of the curve is shallow: lots up to 30% off cost almost the same.

Tap the chart to see the values.

Inventory profile with the economic lot

Inventory over three cycles: it builds up during production and falls with consumption.

Tap the chart to see the values.

The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Purchase (Harris): Q* = √(2 · D · S ÷ (i · C))
Production (Taft): Q* = √(2 · D · S ÷ (i · C · (1 − D/P)))
Annual total cost: TC(Q) = D/Q · S + Q/2 · (1 − D/P) · i · C
All-units quantity discount: for each break j, Qj = max(√(2DS ÷ (i Cj)), break minimum); TCj = D · Cj + D/Qj · S + Qj/2 · i · Cj; pick the lowest TCj
Setup needed for lot Qd: S = Qd² · i · C · (1 − D/P) ÷ (2 · D)

Assumptions and limits

  • Constant, known demand, no stockouts, no quantity discounts and setup cost independent of lot size.
  • Holding cost includes capital, storage, insurance, losses and obsolescence.
  • For items with variable demand, add safety stock (another calculator in this group).

Standards and technical documents

  • Harris, F. W. How many parts to make at once. Factory, The Magazine of Management, 10(2), 1913
  • Taft, E. W. The most economical production lot. Iron Age 101, 1918
  • Silver, E. A.; Pyke, D. F.; Thomas, D. J. Inventory and Production Management in Supply Chains, 4th ed. CRC, 2017
  • ASCM (APICS) Dictionary, 17th ed.

U.S. regulations

  • ASC 330 (Inventory) and IRC §263A: inventory valuation and capitalization of costs
  • OSHA 29 CFR 1910.176: handling and storage of materials

Frequently asked questions

How do you calculate the economic order quantity?

Use Q* = √(2 · D · S ÷ (i · C)). With demand of 24,000 units per year, a $280 order cost, a $12 item and 18% holding cost, EOQ is about 2,500 units.

What is the difference between EOQ and EPQ?

With EOQ the lot arrives at once. With EPQ it is produced gradually while being consumed, so peak inventory is lower and the economic lot is larger by the factor 1 ÷ √(1 − D/P).

How does SMED change the economic lot?

The economic lot grows with the square root of setup cost. Cutting setup by 75% halves the lot without raising total cost.