How to use the economic production quantity calculator
- Enter the annual demand for the item and the annual production rate of the line.
- Enter the setup cost for one production run and the holding cost per unit per year.
- Read the economic production quantity, the runs per year and the highest stock on hand.
- Compare the total yearly cost with the cost at the simple EOQ size, shown in the table.
Formula
EPQ = square root of (2 x demand x setup cost / (holding cost x (1 - demand / production rate)))
highest stock = EPQ x (1 - demand / production rate)
setup cost per year = setup cost x demand / EPQ
holding cost per year = holding cost x highest stock / 2
At the best run size the setup cost per year and the holding cost per year are equal. As the production rate grows very large, EPQ approaches the EOQ.
A press that makes four times demand
Demand is 12,000 units a year and the press can make 48,000. A run costs $90 to set up and holding costs $1.50 per unit per year. Demand over production rate is 0.25, so EPQ = square root of (2 x 12,000 x 90 / (1.50 x 0.75)) = square root of 1,920,000 = 1,385.6 units.
That means 8.66 runs a year, with a highest stock of 1,385.6 x 0.75 = 1,039.2 units. Setup costs $779.42 a year and holding costs $779.42, for a total of $1,558.85. Running the line at the simple EOQ size of 1,200 units instead would cost $1,575.00 a year, because the EOQ formula ignores the units used while a run is under way.
EPQ and EOQ
The EOQ Calculator assumes an order arrives all at once. When a line makes the item itself, stock builds up gradually during the run and falls when the run ends, so the average stock is lower and the best run is larger. The two formulas meet when the production rate is far above demand.
Once you have a run size, size the loop with the Kanban Card Quantity Calculator and decide when to start a run with the Reorder Point Calculator.
Where the answer bends
Setup costs that fall with practice, limited warehouse space and a line shared by many items all change the real best quantity. Treat the formula as a starting point and test nearby run sizes. The cost curve is flat near the minimum, so a modest change in run size costs little.
Assumptions and limits
- Demand is constant and known, and the production rate is constant while the line runs.
- The production rate must be higher than demand, or stock could never build up.
- Setup cost and holding cost per unit do not change with the run size.
- Run days use a 365 day year; capacity limits and several items on one line are not modeled.
- No stockouts are allowed in the model.
Frequently asked questions
What does the production rate mean?
It is how many units the line could make in a year if it only made this item. It is not the units you plan to make.
Why is the total cost higher at the EOQ size?
EOQ assumes the whole batch arrives at once, so it overestimates average stock for a line that fills the batch gradually. Using it for a production run gives a run size away from the minimum cost.
What happens when production is only just above demand?
The factor 1 minus demand over rate gets small, so the best run becomes very large and the highest stock grows too. In practice you may make the item almost continuously.
How do I choose the holding cost?
Include the cost of capital, storage, insurance and spoilage per unit per year. Use your own figures.