Economic Production Quantity Calculator

Calculator Inputs

Use yearly units for demand and production rate. The calculator adjusts production speed for scrap before computing EPQ.

Annual Demand (units/year)

Annual Production Rate (units/year)

Setup Cost per Run ($)

Unit Production Cost ($)

Holding Rate (% of unit cost)

Annual Holding Cost per Unit ($)

Working Days per Year

Safety Stock (units)

Scrap Rate (%)

Lot Size Rounding Increment

Lead Time (days)

Plotly Graph

The chart shows one complete EPQ cycle. Inventory rises during production, then falls under demand until the next setup begins.

Example Data Table

Example Item	Value
Annual Demand	24,000 units/year
Annual Production Rate	40,000 units/year
Setup Cost	$180.00
Unit Cost	$12.00
Holding Rate	18%
Working Days	300 days/year
Safety Stock	200 units
Scrap Rate	2%
Round Increment	50 units
Lead Time	5 days
Example Rounded EPQ	3,250 units
Example Maximum Inventory	1,260.20 units
Example Relevant Annual Cost	$3,122.25

Formula Used

Economic Production Quantity:

EPQ = √[(2 × D × S ÷ H) × (Pₑ ÷ (Pₑ − D))]

Where:

D = annual demand
S = setup cost per production run
H = annual holding cost per unit
Pₑ = effective production rate after scrap adjustment

Supporting formulas:

Effective Production Rate = P × (1 − Scrap Rate)
Maximum Inventory = Q × (1 − D ÷ Pₑ)
Average Inventory = Safety Stock + Maximum Inventory ÷ 2
Annual Setup Cost = (D ÷ Q) × S
Annual Holding Cost = Average Inventory × H
Relevant Annual Cost = Annual Setup Cost + Annual Holding Cost

How to Use This Calculator

Enter yearly demand and yearly production capacity using the same unit basis.
Provide setup cost and unit cost for one production run and one unit.
Enter either annual holding cost per unit or use holding rate.
Add safety stock, scrap rate, working days, lead time, and rounding increment.
Press Calculate EPQ to display the result section above the form.
Review lot size, inventory levels, timing, and annual cost impact.
Use the export buttons to save results as CSV or PDF.

FAQs

1. What does EPQ measure?

EPQ estimates the most economical production lot size when replenishment occurs gradually during manufacturing rather than arriving all at once.

2. How is EPQ different from EOQ?

EOQ assumes inventory is received immediately. EPQ assumes production and demand happen at the same time, so inventory builds progressively.

3. Why must production rate exceed demand?

If production cannot outpace demand, inventory never builds. In that case, the classic EPQ model no longer applies correctly.

4. What happens when I enter scrap rate?

The calculator reduces usable production speed by the scrap percentage. That lowers effective output and can increase the recommended lot size.

5. Should I enter holding rate or holding cost?

You can use either. If annual holding cost per unit is provided, it takes priority. Otherwise, the tool calculates it from unit cost and holding rate.

6. Why is there a rounding increment?

Factories often run in practical batch multiples. Rounding adjusts the mathematical EPQ to a usable operational quantity.

7. Does safety stock change EPQ?

Safety stock does not change the EPQ formula itself. It increases average inventory, holding cost, and reorder planning requirements.

8. Can I use monthly data instead of yearly data?

Yes. Use any time period you want, but keep demand, production rate, and holding assumptions on the same consistent basis.