Economic Production Quantity (EPQ) Calculator
The best batch size for items you make yourself — balancing set-up cost against holding cost while stock builds up gradually — with the cycle, run length and yearly cost.
Results
What this tool does
The economic order quantity assumes a whole order arrives at once; when you produce the goods yourself, stock builds up gradually, at the production rate minus the rate of demand. That makes the stock peak lower than the batch size by the factor (1 − D ÷ P), and the best batch is bigger than the EOQ: EPQ = √[2DS ÷ (H(1 − D ÷ P))]. As the production rate grows far beyond demand the factor tends to 1 and the formula becomes the ordinary EOQ. It needs production to be faster than demand, otherwise the machine can never catch up.
Formula
EPQ = √[2 D S ÷ (H (1 − D ÷ P))] · max stock = EPQ × (1 − D ÷ P)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
d | Annual demand | — |
p | Production rate per year (while running) | — |
s | Set-up cost per production run | — |
h | Holding cost per unit per year | — |
Q | Economic production quantity | — |
MX | Highest stock level during the cycle | — |
RN | Production runs per year | — |
CD | Days between the starts of two runs | d |
RD | Days of production in each run | d |
TC | Yearly set-up plus holding cost | — |
Worked example
- Annual demand12,000
- Production rate per year (while running)48,000
- Set-up cost per production run200
- Holding cost per unit per year2
- Economic production quantity1789
- Highest stock level during the cycle1342
- Production runs per year6.71
- Days between the starts of two runs54.4 d
- Days of production in each run13.6 d
- Yearly set-up plus holding cost2683
Limitations
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.