Manufacturing Operations & SCM Lab

EPQ Production Batch Lab

Calculate Economic Production Quantity (EPQ), finite production run lengths, max inventory build-up, and setup vs holding cost trade-offs in a free lab.

Batch Model Operations Schedule EPQ Theory FAQ

Manufacturing Presets

Load calibrated plant operations.

Step 1: Production Rates, Setup & Holding Costs

Production Schedule & Cost Parameters

Demand & Production Capacity

Setup & Inventory Carrying Cost

$
$
%
Optimal EPQ Batch Size
1,474 units
vs. Instant EOQ: 1,162 units
Production Run Length
5.9 days
Cycle: 15.4 days (16.3 runs/yr)
Peak Inventory (I_max)
908 units
Buildup Factor: 61.6%
Total Annual Variable Cost
$14,601
Setup: $7,330 | Hold: $7,271

Production Batch & Inventory Schedule

Operational Parameter Optimized Value Strategic Context

Production Planning & Operations Research

Mastering the Economic Production Quantity

The EPQ model extends the classical EOQ formula to manufacturing environments where production occurs gradually over time rather than arriving in an instant batch.

  • Simultaneous Production & Demand: During the run period ($t_p$), units are produced at rate $p$ while being consumed at rate $d$. The net inventory build rate is $(p - d)$.
  • Peak Inventory ($I_{max}$): Reaches its maximum exactly when machine production ceases, equal to $EPQ imes (1 - d/p)$.
  • Holding Cost Efficiency: Because peak inventory is lower than the full batch $EPQ$, holding costs are reduced compared to instant purchasing.
  • Setup vs. Holding Trade-off: Larger batches spread fixed machine changeover costs over more units but increase warehouse storage costs.

Compare purchasing inventory in the Inventory EOQ Lab.

EPQ Mathematical Formulas

Essential production formulas

Daily Demand (d) = Annual Demand (D) ÷ Work Days (W)

Holding Cost per Unit (H) = Unit Cost (C) × Holding Rate (%)

EPQ = sqrt[ (2 × D × S) ÷ (H × (1 - d/p)) ]

Max Inventory (I_max) = EPQ × (1 - d/p)

Run Duration (t_p) = EPQ ÷ p

Cycle Time (T) = EPQ ÷ d

Total Cost (TC) = (D ÷ EPQ) × S + (I_max ÷ 2) × H

Balance line cycle times in the Takt Time Lab.

FAQ

EPQ and batch production questions

What is Economic Production Quantity (EPQ)?

Economic Production Quantity (EPQ), also called Economic Lot Size (ELS), determines the optimal manufacturing batch size that minimizes total annual machine setup and inventory holding costs when production occurs gradually rather than instantaneously.

How does EPQ differ from basic EOQ?

Basic EOQ assumes infinite instantaneous delivery of an entire order batch. EPQ accounts for finite production rates where items are consumed simultaneously while being manufactured, reducing peak inventory by (1 - d/p) and yielding a larger optimal batch size.

How do you calculate the production run duration?

Production Run Length (t_p) = EPQ ÷ Daily Production Rate (p). This represents the exact number of operating days the manufacturing line must run to complete one batch.

What is the maximum inventory level in an EPQ system?

Maximum Inventory (I_max) = EPQ × (1 - d/p), where d is the daily demand rate and p is the daily production rate. Peak inventory occurs exactly when the production run finishes.

Can I export EPQ production batch audits to CSV?

Yes. You can export complete annual demands, production rates, setup costs, holding costs, EPQ batch sizes, run durations, and cost breakdowns as a UTF-8 CSV spreadsheet with formula injection defense.

Is this tool certified industrial engineering software?

No. This tool provides educational operations research simulations for industrial management analysis without certified manufacturing engineering warranties.

Continue Exploring Operations & Quality Tools

Explore our Operations & Quality Hub, calculate purchasing lot sizes in the Inventory EOQ Lab, balance assembly lines in the Takt Time Lab, or evaluate project networks in the Critical Path Lab.