Manufacturing Batch Size Calculator
The Batch Size That Minimizes Total Cost
Ordering or producing in large batches spreads setup cost over more units, but it also means more inventory sitting in holding cost while it waits to be used. Economic Order Quantity (EOQ) and its production variant, Economic Production Quantity (EPQ), find the batch size where those two opposing costs are balanced — not the biggest batch possible, and not the smallest, but the one that minimizes total cost.
The Formulas
Economic Production Quantity: Q = √((2 × D × S) / (H × (1 − D/P)))
D = Annual Demand, S = Setup Cost per Order, H = Holding Cost per Unit, P = Production Rate
Worked Examples
| Model | Extra input | Calculation | Batch size |
|---|---|---|---|
| EOQ | — | √((2 × 10,000 × 50) / 2) | 707.11 units |
| EPQ | Production rate 15,000/yr | √((2 × 10,000 × 50) / (2 × 0.3333)) | 1,224.74 units |
EPQ produces a larger batch than EOQ for the same demand and cost inputs, because it accounts for the batch being consumed gradually while it's still being produced — a factor EOQ assumes away by treating the order as arriving all at once.
Where This Matters
- EOQ — fits purchased materials or components ordered from a supplier and received in a single delivery.
- EPQ — fits items manufactured in-house, where production and consumption can happen simultaneously rather than the whole batch arriving at once.
- Balancing setup and holding costs — both formulas exist to avoid the two failure modes of guessing: batches too small (excess setup cost from frequent changeovers) or too large (excess capital tied up in inventory).
How to Use This Calculator
- Choose the mode: Economic Order Quantity (EOQ) or Economic Production Quantity (EPQ).
- Enter Annual Demand, Setup Cost per Order, and Holding Cost per Unit.
- For EPQ, also enter the Production Rate (units/year), which must exceed annual demand.
- Select Calculate to see the cost-minimizing batch size.
Related Calculations
Once a batch size is set, work out the resulting per-unit cost with the Manufacturing Unit Cost Calculator, or check the pace needed to keep up with demand using the Takt Time Calculator.