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Economic Batch Quantity (EBQ / EPQ) Calculator
Calculate the exact financial equilibrium between machine setup changeover costs and inventory holding carrying charges. Optimise production run sizes with verified finite rate manufacturing equations.
Industrial EBQ & EPQ Optimisation
Economic Batch Quantity (EBQ / EPQ) Calculator
Balance machine setup changeover costs against inventory holding costs using verified Camp-Harris and finite production rate models.
Select Manufacturing Industry Preset:
Demand & Production Model
Replenishment pace and annual quantity
6,000 units/yr
units
Daily Demand Rate (d)
24.0 units/day
85 units/day
units/day
Machine Setup & Changeover (S)
Cost incurred every time a new batch is set up
$220.00
$/setup
Unit Cost & Holding Rate (H)
Capital, storage, insurance and obsolescence
$48.00
$/unit
24% / yr
% / year
Derived Annual Holding Cost (H):$11.52 / unit / year
Recommended Run Size (EPQ Model)
565units / batch
Annual Runs
10.6 runs/yr
Every 23.5 working days
Run Duration
6.6 days
53 spindle hrs
Peak Inventory (Imax)
405 units
Avg: 203 units
Annual Setup Cost
$2,336
10.6 × $220
Annual Holding Cost
$2,333
203 × $11.52
Minimum Total Policy Cost (Setup + Holding):
$4,669.08 / yr
Total Cost Curve & Equilibrium Point
Setup costs decline with larger runs, while inventory holding costs climb linearly.
Setup Holding Total
Small Batches (High Setup Penalty)Optimal Run EquilibriumLarge Batches (High Storage Cost)
Lean SMED Batch Reduction Target
How much must machine setup time decrease to run smaller batches economically?
Desired Batch Size Reduction:50% Smaller
10% (Minor Lean gain)50% (Halved Batch Size)80% (Rapid Flow)
Target Lean Batch Size
283 units
Reduces WIP holding risk by 50%
Required Setup Reduction
-75%
Setup must drop to $55.19 (30 mins)
Key Lean Insight: Under the square-root relationship, cutting batch size in half requires a 75% reduction in changeover time to prevent unit cost increases.
Batch Size Scenario & Cost Trade-Off Comparison
Evaluate financial trade-offs between smaller lean runs, optimal EBQ, and large production runs.
| Run Strategy | Batch Size (Q) | Runs / Year | Annual Setup | Annual Holding | Total Policy Cost | Cost Delta | WIP Capital |
|---|---|---|---|---|---|---|---|
Lean Agility Batch (50% EBQ)Fast Lead Time & Low WIP | 283 | 21.2 | $4,664 | $1,170 | $5,834 | +$1,165 (+25.0%) | $4,874 |
Economic Batch Quantity (EBQ / EPQ)Minimum Total Cost Equilibrium | 565 | 10.6 | $2,336 | $2,336 | $4,672 | Baseline $0 | $9,731 |
Double Batch (200% EBQ)Over-Batched / Excess Stock | 1,130 | 5.3 | $1,168 | $4,671 | $5,839 | +$1,170 (+25.1%) | $19,463 |
Custom User BatchCurrent Shop Floor Practice | 500 | 12.0 | $2,640 | $2,067 | $4,707 | +$38 (+0.8%) | $8,612 |
Visual Production Scheduling
Schedule optimum batch queues visually in Synctile
Eliminate whiteboard chaos and spreadsheet calculations. Drag and drop work orders onto machine timelines while automatically grouping similar setups to minimise changeover downtime.
Grounded Operations Science
The Mathematics of Economic Production Batch Sizing
Every production manager faces an unavoidable operational conflict: running large batches reduces machine changeover downtime and spreads setup costs over more units, but drastically inflates inventory storage costs, warehouse congestion, and working capital requirements. Conversely, running tiny batches slashes inventory carrying costs but causes machines to sit idle during frequent setups.
The Economic Production Quantity (EPQ), originally formulated by E.W. Taft in 1918 as an extension of Ford W. Harris's 1913 Economic Order Quantity (EOQ) model, determines the exact mathematical batch size that minimises total annual variable costs.
The Finite Production Rate EPQ Formula
Core EBQ / EPQ Equation:
Q* = √[ (2 × D × S) / ( H × (1 - d/p) ) ]
Where Q* is the optimum run size, D is annual demand, S is setup cost, H is unit holding cost per year, d is daily consumption, and p is daily machine production rate.
Annual Setup Cost
(D / Q) × S
Decreases hyperbolically as batch size Q increases because fewer setups are performed each year.
Annual Holding Cost
[ (Q / 2) × (1 - d/p) ] × H
Increases linearly with batch size Q. The term (1 - d/p) reflects inventory consumed during active production.
Why EOQ Fails in Manufacturing: The Finite Production Factor
Traditional purchasing formulas assume supplier deliveries arrive instantaneously at the dock (EOQ). In manufacturing, parts leave the spindle or moulding press gradually over several days.
EOQ
Purchasing EOQ (Instantaneous)
Assumes all Q parts arrive at once into the warehouse. Peak inventory equals Q, and average inventory equals Q / 2.
Application: Purchased raw bar stock, fasteners, and off-the-shelf components.
EPQ
Manufacturing EPQ (Gradual)
Units are shipped or consumed while the machine is running. Peak inventory reaches only Q × (1 - d/p), reducing holding costs.
Application: In-house CNC machining, injection moulding, stamping, and assembly runs.
Lean Manufacturing Strategy
How to Shrink Batch Sizes with SMED Quick Changeovers
In lean manufacturing (Toyota Production System), large batches are treated as a root cause of waste. They conceal defective parts, prolong customer lead times, and create erratic boom-and-bust cycles across work centres.
However, arbitrarily mandating smaller batches without reducing setup time is dangerous: it causes machine downtime to surge and total unit manufacturing costs to escalate. The lean solution is SMED (Single-Minute Exchange of Die):
The Square-Root Law of Lean Batching
Because batch size scales with the square root of setup cost, reducing batch size by 50% requires a 75% reduction in machine setup time. Reducing batch size by 80% requires a 96% reduction in setup time.
Step-by-Step Calculation Example: Precision CNC Job Shop
Let us walk through a practical scenario for a precision engineering facility producing hydraulic valve manifolds:
Step 1: Gather Parameters
• Annual Demand (D): 6,000 manifolds/year
• Working Days (N): 250 days/year → Daily Consumption (d) = 6,000 / 250 = 24.0 units/day
• Daily Production Rate (p): 85 manifolds/day
• Machine Setup Cost (S): 2 hours changeover × ($75 machine + $35 labour) = $220.00 / setup
• Unit Production Cost (C): $48.00 / unit
• Annual Holding Rate (i): 24% / year → H = $48.00 × 0.24 = $11.52 / unit / year
Step 2: Compute Finite Production Factor
Factor = (1 - d/p) = (1 - 24 / 85) = 1 - 0.2824 = 0.7176
Step 3: Calculate Economic Batch Quantity (Q*)
Q* = √[ (2 × 6,000 × 220) / (11.52 × 0.7176) ] = √[ 2,640,000 / 8.2668 ] = √[ 319,350 ] = 565 units
• Number of Runs/Year: 6,000 / 565 = 10.6 runs
• Run Duration: 565 / 85 = 6.6 working days per batch
• Annual Setup Cost: 10.6 × $220 = $2,336
• Annual Holding Cost: (565 / 2) × 0.7176 × $11.52 = $2,335
• Notice that Annual Setup Cost and Annual Holding Cost balance perfectly at equilibrium!
Frequently Asked Questions
What is the difference between EOQ and EBQ (EPQ)?
Economic Order Quantity (EOQ) assumes instantaneous delivery where the entire batch arrives at once into stock. Economic Batch Quantity (EBQ), also known as Economic Production Quantity (EPQ), accounts for finite manufacturing rates where items are produced gradually and consumed simultaneously during the production run. Because parts are shipped or consumed while the machine is still running, peak inventory is lower, which permits slightly larger production runs than pure EOQ.
What mathematical formula governs Economic Batch Quantity (EBQ)?
The classic EBQ formula is Q* = sqrt((2 * D * S) / (H * (1 - d/p))), where D is annual demand, S is setup cost per changeover, H is annual holding cost per unit per year, d is daily consumption rate, and p is daily machine production rate. The term (1 - d/p) represents the finite production adjustment factor.
How is the inventory holding cost rate (H) calculated?
Annual holding cost rate H typically ranges from 18% to 30% of unit production cost per year. It combines the cost of working capital (interest rate on cash tied up in stock), warehouse space and utilities, property insurance, material handling labour, and risks of scrap, damage, and obsolescence.
How does SMED (Single-Minute Exchange of Die) affect batch sizing?
Under the square-root law of batch sizing, batch size is directly proportional to the square root of setup cost. If you reduce setup time by 75% via SMED, the optimal economic batch size is cut in half without increasing total unit manufacturing costs, unlocking shorter customer lead times and 50% less work-in-process inventory.
Why is running oversized batches dangerous for high-mix manufacturers?
Large batches tie up substantial working capital, congest floor space, lengthen customer lead times, and magnify quality risks. If a tool wears or a dimension drifts, an entire large batch may become scrap before the defect is identified at downstream assembly.
How does Synctile help operations teams execute optimum batch scheduling?
Calculating batch size is only the first step. Synctile provides drag-and-drop visual production boards that sequence batch runs across machine cells, group compatible setups to minimise changeover delays, and provide operators with live digital work queues.
Visual Production Scheduling Software
Schedule optimum batch queues visually in Synctile
Stop juggling spreadsheets and guessing run sizes. Synctile equips your shop floor with visual drag-and-drop planning, live machine dispatch queues, and automatic setup grouping.