Linear
Programming
McGraw-Hill/Irwin
Technical
Supplement 3
Learning
Curves
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Objectives
1. Explain the learning curve concept
2. Identify different uses of learning curves in
operations management
3. Calculate the estimated time required to do a task
for a given learning curve
TS3-2
Concepts
Overview of
Learning Curves
• Learning curve is an equation that can be used
to estimate a rate of improvement in tasks
• Resource needs are reduced as people learn
through repetition
–Time to assemble a product
–Cost to fabricate an item
• Resource requirement is reduced by certain
percentage each time cumulative output is
doubled
TS3-3
The Learning Curve
1
0.9
Tn = T1 (nb)
0.8
Time per unit
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Cumulative repetitions
Where:
• Tn = time required to complete the nth task
• r = learning rate percentage
• b = ln(r)/ln(2)
TS3-4
Example
T1 = 100 minutes
T2 = 80 minutes
T4 = 64 minutes
• What would be the time required to produce the
eighth part?
T8 = (100)(8-0.322) = 51.2 minutes
since b= ln(0.80)/ln(2) = -0.322
TS3-5
Learning Curve Table
TS3-6
Factors that Impact Learning Rate
• Incentives and rewards
• Supporting resources for experimentation
• Training
• Tools and technology
• Culture
TS3-7
How OM Managers Use Learning Curves
• Setting goals and expectations
• Capacity planning
• Costing
• Changes to product and process designs
TS3-8
Summary
• Learning curve estimation is a powerful planning
tool
–Helps to identify resources needed to accomplish a
production program
–Can be used to set goals and assess progress
• Wide application given that underlying drivers of
learning are present
TS3-9