Economic Production Quantity Calculator
The economic production quantity — the batch size that minimises setup plus holding cost when items are produced at a finite rate and consumed while they are made — with the cycle length, maximum inventory and yearly cost.
The EOQ assumes a whole order arrives at once; when you make the parts yourself they arrive gradually while demand draws them down, so inventory never reaches the full batch.
How the economic production quantity calculator works
The EOQ assumes a whole order arrives at once; when you make the parts yourself they arrive gradually while demand draws them down, so inventory never reaches the full batch. The EPQ corrects for that with the ratio of demand to production rate: Q = √(2DS ÷ (H(1 − D ÷ P))). The faster you can make them relative to demand, the closer it sits to the EOQ.
Formula: Q* = √(2 D S ÷ (H (1 − D ÷ P))); max inventory = Q (1 − D ÷ P)
Worked examples
| Inputs | Economic production quantity | Note |
|---|---|---|
| Demand 24,000, rate 96,000, setup 400, holding 2.50 | 3,200 units | 3,200 units, 7.5 batches a year |
| A busy line: rate only 1.5× demand | 4,800 units | 4,800 units |
| Cheap setup: 50 | 1,131 units | 1,131 units |
FAQFrequently asked questions
How is this different from the EOQ?
The EOQ assumes the whole order arrives at once; the EPQ has the batch arriving over the run while demand consumes it, so average inventory is lower and the optimum batch is larger by 1 ÷ √(1 − D/P).
What if I can make far faster than demand?
Then D ÷ P is small and the EPQ is close to the EOQ; the correction only matters when the line is busy — at P = 2D the batch is 41% larger than the EOQ.
What should the setup cost include?
The labour and machine time of the changeover, any scrap during start-up, and cleaning — everything that would not be spent if the batch were twice as big. Reducing it (SMED) is what shrinks batches.
Does this handle several products on one line?
Not directly — each product’s EPQ assumes the line is free when its run is due. For a shared line use the economic lot scheduling approach, or check that the run lengths fit inside the cycle.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- OSHA — the US workplace safety administration
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.