Operations
Management
Module E –
Learning Curves
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 7e
Operations Management, 9e
© 2008 Prentice Hall, Inc.
E–1
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
© 2008 Prentice Hall, Inc.
E–2
Learning Objectives
When you complete this module you
should be able to:
1. Define a learning curve
2. Use the arithmetic concept to
estimate times
3. Compute learning curve effects with
the logarithmic and learning-curve
coefficient approaches
4. Describe the strategic implications of
learning curves
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E–3
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
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E–4
Cost/time per repetition
Learning Curve Effect
0
Number of repetitions (volume)
Figure E.1
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E–5
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
Hours required for unit 4 = 10 x (.7)2 = 4.9 hours
© 2008 Prentice Hall, Inc.
E–6
Learning Curve Examples
Example
Model -T Ford
production
Aircraft
assembly
Equipment
maintenance
at GE
Steel
production
Improving
Parameters
Price
Direct labor-hours
per unit
LearningCurve
Cumulative
Slope
Parameter
(%)
Units produced
86
Units produced
80
Average time to
Number of
replace a group of
replacements
parts
Production worker
Units produced
labor-hours per
unit produced
76
79
Table E.1
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E–7
Learning Curve Examples
LearningCurve
Slope
(%)
72
Example
Integrated
circuits
Handheld
calculator
Improving
Parameters
Average price per
unit
Average factory
selling price
Cumulative
Parameter
Units
produced
Units
produced
Disk memory
drives
Average price per
bit
Number of bits
76
Heart
transplants
1-year death rates
Transplants
completed
79
74
Table E.1
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E–8
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
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E–9
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
2
100.0
80.0 = (.8 x 100)
4
64.0 = (.8 x 80)
8
16
© 2008 Prentice Hall, Inc.
51.2 = (.8 x 64)
41.0 = (.8 x 51.2)
E – 10
Logarithmic Approach
Determine labor for any unit, TN , by
TN = T1(Nb)
where
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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
E – 11
Logarithmic Approach
Determine labor for any unit, TN , by
TN = T1(Nb)
Learning
where
b
TN = time for the
T1 = hours to produce70
the first unit
– .515
b = (log of the learning rate)/(log 2)
75
– .415
= slope of the learning curve
80
– .322
NthRate
unit(%)
Table E.2
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85
– .234
90
– .152
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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
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E – 13
Coefficient Approach
TN = T1C
where
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TN = number of labor-hours required
to produce the Nth unit
T1 = jumlah jam kerja yang
dibutuhkan untuk memproduksi
unit pertama
C = Coefficient kurva belajar spt
ditampilan di tabel E.3
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Learning-Curve Coefficients
Table E.3
70%
85%
Unit
Number
(N)
Unit Time
Total Time
Unit Time
Total Time
1
1.000
1.000
1.000
1.000
2
.700
1.700
.850
1.850
3
.568
2.268
.773
2.623
4
.490
2.758
.723
3.345
5
.437
3.195
.686
4.031
10
.306
4.932
.583
7.116
15
.248
6.274
.530
9.861
20
.214
7.407
.495
12.402
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E – 15
Learning-Curve Coefficients
Table E.3
70%
80%
Unit
Number
(N)
Unit Time
Total Time
Unit Time
Total Time
1
1.000
1.000
1.000
1.000
2
.700
1.700
.800
1.800
3
.568
2.268
.702
2.502
4
.490
2.758
.640
3.142
.512
5.346
8
10
.306
4.932
.477
6.315
15
.248
6.274
.418
8.511
20
.214
7.407
.381
10.485
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E – 16
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
90,375 hours x $40/hour = $3,615,000
TN = T1C
T4 = (125,000 hours)(3.345)
= 418,125 hours for all four boats
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E – 17
Coefficient Example
Third boat required 100,000 hours
Learning factor = 85%
New estimate for the first boat
100,000
= 129,366 hours
.773
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E – 18
Strategic Implications
To pursue a strategy of a steeper curve
than the rest of the industry, a firm can:
1. Follow an aggressive pricing policy
2. Focus on continuing cost reduction
and productivity improvement
3. Build on shared experience
4. Keep capacity ahead of demand
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E – 19
Price per unit (log scale)
Industry and Company
Learning Curves
Figure E.2
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Loss
(c)
(b)
Gross profit
margin
(a)
Accumulated volume (log scale)
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Limitations of Learning
Curves
 Learning curves differ from company
to company as well as industry to
industry so estimates should be
developed for each organization
 Learning curves are often based on
time estimates which must be accurate
and should be reevaluated when
appropriate
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E – 21
SEKIAN
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E – 22
Limitations of Learning
Curves
 Any changes in personnel, design, or
procedure can be expected to alter the
learning curve
 Learning curves do not always apply to
indirect labor or material
 The culture of the workplace, resource
availability, and changes in the process
may alter the learning curve
© 2008 Prentice Hall, Inc.
E – 23
• Dibutuhkan waktu 28.718 jam untuk
menyelesaikan lokomotif kedelapan
pada sebuah perusahaan
manufaktur. Jika faktor pembelajaran
adalah 80% berapa lama yang
dibutuhkan untuk memproduksi
lokomotif kesepuluh. Dan berapa
total biaya untuk memproduksi 10
lokomotif jika upah perjam US$ 20
© 2008 Prentice Hall, Inc.
E – 24