EPQ
Optimal production lot size.
These tools are provided for educational and operational guidance only. Results are estimates and may not reflect all factors in your business. Always review calculations and use your own professional judgement before making decisions.
What is this tool?
The Economic Production Quantity (EPQ) calculator extends EOQ to situations where you produce and consume at the same time. It finds the optimal production lot size that balances setup costs with holding costs when items are produced in batches rather than delivered all at once.
Formula
The EPQ formula used here is:
EPQ = √( (2 × D × S) / (H × (1 − D / P)) )
- D = demand rate.
- S = setup cost per production run.
- H = holding cost per unit.
- P = production rate (must be greater than D).
Because production occurs over time, inventory builds up more slowly than in EOQ, which is why the (1 − D / P) term appears in the denominator.
Example
Suppose annual demand D = 12,000, setup cost S = 50, holding cost H = 2, and production rate P = 30,000.
First compute 1 − D / P = 1 − 12,000 / 30,000 = 0.6.
Plugging into the formula gives an EPQ of several hundred units (the calculator will show the exact number).
Operationally, this tells you how big each production batch should be so that you are not constantly stopping and starting the line, but also not building excessive work‑in‑process and finished goods.
When should you use this tool?
- When you produce items in-house instead of buying them fully finished.
- When production happens in batches with a significant setup or changeover cost.
- When demand is reasonably stable and production capacity is higher than demand.
- When you want to compare different batch sizes and production rates.
How this tool helps your business
- Reduces total production and inventory costs by optimizing lot sizes.
- Supports better capacity planning and changeover scheduling.
- Helps avoid both frequent small setups and bloated work‑in‑process inventories.
- Gives production and planning teams a clear, quantitative target for batch sizing.
Related tools
- EOQ Calculator – compare EPQ results with classic EOQ when you purchase instead of produce.
- Safety Stock Calculator – add variability buffers on top of your EPQ-based production plan.
- Inventory Turnover Calculator – monitor how efficiently inventory moves under your EPQ policy.
Frequently Asked Questions
When should I use EPQ instead of EOQ?
Use EPQ when you produce items internally in batches and inventory builds up during production. Use EOQ when you purchase items that arrive all at once from suppliers.
What happens if production rate is close to demand?
As P approaches D, the denominator becomes small and EPQ grows very large, reflecting that slow production cannot support frequent small batches without excessive cost.
Can I ignore setup cost in this model?
If setup cost is negligible, the optimal batch size shrinks and you may move toward make-to-order. EPQ is most useful when setup or changeover costs are meaningful.
Should I round EPQ to whole batches or days?
Yes. Treat the EPQ result as a guideline and round to practical batch sizes, while keeping an eye on capacity constraints and changeover schedules.