1. Operations Management
Module E – Learning Curves
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 6e
Operations Management, 8e
© 2006 Prentice Hall, Inc.

2. Outline Learning Curves In Services And Manufacturing
Applying The Learning Curve
Arithmetic Approach
Logarithmic Approach
Learning-Curve Coefficient Approach
Strategic Implications of Learning Curves
Limitations of Learning Curves

3. Learning Objectives
When you complete this module, you should be able to:
Identify or Define:
What a learning curve is
Examples of learning curves
The doubling concept

4. Learning Objectives
When you complete this module, you should be able to:
Describe or Explain:
How to compute learning curve effects
Why learning curves are important
The strategic implication of learning curves

5. Learning Curves
Based on the premise that people and organizations become better at their tasks as the tasks are repeated
Time to produce a unit decreases as more units are produced
Learning curves typically follow a negative exponential distribution
The rate of improvement decreases over time
This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.

6. Learning Curve Effect Cost/time per repetition
Number of repetitions (volume)
This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.
Figure E.1

7. Learning Curves T x Ln = Time required for the nth unit
where T = unit cost or unit time of the first unit
L = learning curve rate
n = number of times T is doubled
First unit takes 10 labor-hours
70% learning curve is present
Fourth unit will require doubling twice — 1 to 2 to 4
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
Hours required for unit 4 = 10 x (.7)2 = 4.9 hours

8. Learning Curve Examples
Improving Parameters
Cumulative Parameter
Learning-Curve Slope
(%)
Model -T Ford production
Price
Units produced 86
Aircraft assembly
Direct labor-hours per unit 80
Equipment maintenance at GE
Average time to replace a group of parts
Number of replacements 76
Steel production
Production worker labor-hours per unit produced 79
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
Table E.1

9. Learning Curve Examples
Improving Parameters
Cumulative Parameter
Learning-Curve Slope
(%)
Integrated circuits
Average price per unit
Units produced 72
Hand-held calculator
Average factory selling price 74
Disk memory drives
Average price per bit
Number of bits 76
Heart transplants
1-year death rates
Transplants completed 79
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
Table E.1

10. Uses of Learning Curves
Internal: labor forecasting, scheduling, establishing costs and budgets
External: supply chain negotiations
Strategic: evaluation of company and industry performance, including costs and pricing
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

11. Arithmetic Approach Simplest approach
Labor cost declines at a constant rate, the learning rate, as production doubles
Nth Unit Produced
Hours for Nth Unit 1
100.0 2
80.0 = (.8 x 100) 4
64.0 = (.8 x 80) 8
51.2 = (.8 x 64) 16
41.0 = (.8 x 51.2)
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

12. Logarithmic Approach Determine labor for any unit, TN , by TN = T1(Nb)
where TN = time for the Nth unit
T1 = hours to produce the first unit
b = (log of the learning rate)/(log 2) =
slope of the learning curve
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

13. Logarithmic Approach Determine labor for any unit, TN , by TN = T1(Nb)
Learning
Rate (%) b 70
– .515 75
– .415 80
– .322 85
– .234 90
– .152
where TN = time for the Nth unit
T1 = hours to produce the first unit
b = (log of the learning rate)/(log 2)
= slope of the learning curve
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
Table E.2

14. Logarithmic Example Learning rate = 80% First unit took 100 hours
TN = T1(Nb)
T3 = (100 hours)(3b)
= (100)(3log .8/log 2)
= (100)(3–.322)
= 70.2 labor hours
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

15. Coefficient Approach TN = T1C
where TN = number of labor-hours required to produce the Nth unit
T1 = number of labor-hours required to produce the first unit
C = learning-curve coefficient found in Table E.3
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

16. Learning-Curve Coefficients
Table E.3
70% 85%
Unit
Number
(N) Time Unit Time Total Time Unit Time Total Time
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

17. Industry and Company Learning Curves
Price per unit (log scale)
Accumulated volume (log scale)
Industry price
(a)
(c)
(b)
Company cost
Loss
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
Gross profit margin
Figure E.2

18. Coefficient Example First boat required 125,000 hours
Labor cost = $40/hour
Learning factor = 85%
TN = T1C
T4 = (125,000 hours)(.723)
= 90,375 hours for the 4th boat
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
90,375 hours x $40/hour = $3,615,000
TN = T1C
T4 = (125,000 hours)(3.345)
= 418,125 hours for all four boats

19. Coefficient Example Third boat required 100,000 hours
Learning factor = 85%
New estimate for the first boat
100,000
.773
= 129,366 hours
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

20. Strategic Implications
To pursue a strategy of a steeper curve
than the rest of the industry, a firm can:
Follow an aggressive pricing policy
Focus on continuing cost reduction and productivity improvement
Build on shared experience
Keep capacity ahead of demand
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

21. Limitations of Learning Curves
Learning curves differ from company to company as well as industry to industry so estimates should be developed for each organization
Learning curves are often based on time estimates which must be accurate and should be reevaluated when appropriate
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

22. Limitations of Learning Curves
Any changes in personnel, design, or procedure can be expected to alter the learning curve
Learning curves do not always apply to indirect labor or material
The culture of the workplace, resource availability, and changes in the process may alter the learning curve
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.