- Enter setup/changeover cost per batch (labor + downtime).
- Enter holding cost per unit per period.
- Enter demand rate in units per period.
- Click Calculate to see economic batch quantity (EBQ).
The EBQ Formula
Understanding Batch Size Optimization
Batch size is one of the most consequential decisions in manufacturing. Too large and you carry excess inventory, extend lead times, and hide quality problems. Too small and you spend all your time on changeovers instead of production. The Economic Batch Quantity (EBQ) finds the mathematical sweet spot.
But here is the lean insight: instead of accepting whatever EBQ the formula gives you, reduce the setup cost to make smaller batches economical. This is exactly what SMED accomplishes.
EBQ: 7,071
EBQ: 3,873
EBQ: 2,236
Real-World Example
Annual demand is 50,000 units. Setup cost is $250 per batch. Holding cost is $5 per unit per year.
Batches per year = 50,000 / 2,236 = 22.4 batches
Avg inventory = 2,236 / 2 = 1,118 units
Total cost = (22.4 x $250) + (1,118 x $5) = $5,590 + $5,590 = $11,180/year
If SMED reduces setup cost to $75: EBQ drops to 1,225 units (45% smaller batches).
The Setup-Inventory Tradeoff
| Setup Cost | EBQ | Batches/Year | Avg Inventory |
|---|---|---|---|
| $500 | 3,162 | 16 | 1,581 units |
| $250 | 2,236 | 22 | 1,118 units |
| $100 | 1,414 | 35 | 707 units |
| $25 | 707 | 71 | 354 units |
How Lean Thinking Flips the Formula
The Square Root Relationship
EBQ is proportional to the square root of setup cost. This means you must cut setup cost by 75% to halve the batch size. It also means the first 50% reduction in setup cost only reduces EBQ by 29%. Lean manufacturers keep pushing SMED because each further reduction yields compounding benefits through smaller batches.
✅ Small Batch Benefits
- Less WIP on the floor
- Shorter lead times (Little's Law)
- Faster quality feedback loops
- Better response to demand changes
❌ Large Batch Problems
- High inventory carrying costs
- Long lead times and slow response
- Quality problems hidden in WIP
- Obsolescence risk on large stocks
🎯 Key Takeaway
The EBQ formula tells you the optimal batch size given current setup costs. But lean manufacturing challenges you to reduce those setup costs and unlock smaller, more flexible batch sizes. Use SMED to shrink changeovers, then recalculate EBQ — the compounding benefits of smaller batches flow through your entire value stream.
Frequently Asked Questions
What is economic batch quantity (EBQ)?
EBQ is the batch size that minimizes total annual cost — the sum of setup costs and holding costs. Too small = too many setups. Too large = too much inventory. EBQ finds the sweet spot.
How is EBQ different from EOQ?
EOQ (Economic Order Quantity) is for purchased items — it balances ordering cost vs holding cost. EBQ is for manufactured items — it balances setup/changeover cost vs holding cost. The formula is structurally similar.
Why do lean manufacturers want smaller batches?
Smaller batches reduce WIP, shorten lead times, improve quality feedback loops, and increase flexibility. Rather than accepting large EBQ, lean manufacturers reduce setup cost (via SMED) to make smaller batches economical.
How does setup cost reduction affect batch size?
EBQ is proportional to the square root of setup cost. Cutting setup cost by 75% (via SMED) cuts EBQ by 50%. This is why changeover reduction is foundational to lean manufacturing.
What costs should I include in holding cost?
Capital cost (interest on tied-up cash), storage space, insurance, obsolescence risk, handling, and damage. A common rule of thumb is 20-30% of unit cost per year.
Is the EBQ formula still relevant in lean manufacturing?
Yes, but lean thinking flips the approach. Instead of accepting a large EBQ, lean asks: how do we reduce setup cost to make the desired small batch size economical? SMED is the primary tool for this.
Track this automatically every shift
SymplProcess captures production data, computes KPIs, and trends everything over time — no spreadsheets, no manual math.
Try SymplProcess Free →