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© 2008 Prentice Hall, Inc. E – 1
Operations ManagementOperations ManagementModule E – Module E – Learning CurvesLearning Curves
PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer/Render Heizer/Render Principles of Operations Management, 7ePrinciples of Operations Management, 7eOperations Management, 9e Operations Management, 9e
© 2008 Prentice Hall, Inc. E – 2
OutlineOutline Learning Curves in Services and Learning Curves in Services and
ManufacturingManufacturing
Applying the Learning CurveApplying the Learning Curve Arithmetic ApproachArithmetic Approach
Logarithmic ApproachLogarithmic Approach
Learning-Curve Coefficient ApproachLearning-Curve Coefficient Approach
Strategic Implications of Learning Strategic Implications of Learning CurvesCurves
Limitations of Learning CurvesLimitations of Learning Curves
© 2008 Prentice Hall, Inc. E – 3
Learning ObjectivesLearning Objectives
When you complete this module you When you complete this module you should be able to:should be able to:
1.1. Define a learning curveDefine a learning curve
2.2. Use the arithmetic concept to Use the arithmetic concept to estimate timesestimate times
3.3. Compute learning curve effects with Compute learning curve effects with the logarithmic and learning-curve the logarithmic and learning-curve coefficient approachescoefficient approaches
4.4. Describe the strategic implications of Describe the strategic implications of learning curveslearning curves
© 2008 Prentice Hall, Inc. E – 4
Learning CurvesLearning Curves
Based on the premise that people and Based on the premise that people and organizations become better at their organizations become better at their tasks as the tasks are repeatedtasks as the tasks are repeated
Time to produce a unit decreases as Time to produce a unit decreases as more units are producedmore units are produced
Learning curves typically follow a Learning curves typically follow a negative exponential distributionnegative exponential distribution
The rate of improvement decreases The rate of improvement decreases over timeover time
© 2008 Prentice Hall, Inc. E – 5
Learning Curve EffectLearning Curve Effect
Figure E.1Figure E.1
Co
st/t
ime
per
rep
etit
ion
Co
st/t
ime
per
rep
etit
ion
Number of repetitions (volume)Number of repetitions (volume)00
© 2008 Prentice Hall, Inc. E – 6
Learning CurvesLearning Curves
T x LT x Lnn = Time required for the n = Time required for the nthth unit unit
wherewhere TT == unit cost or unit time of the first unitunit cost or unit time of the first unitLL == learning curve ratelearning curve ratenn == number of times T is doublednumber of times T is doubled
First unit takes First unit takes 1010 labor-hours labor-hours70%70% learning curve is present learning curve is presentFourth unit will require doubling twice — Fourth unit will require doubling twice — 11 to to 2 2 to to 44
Hours required for unit Hours required for unit 4 = 10 x (.7)4 = 10 x (.7)22 = 4.9 = 4.9 hourshours
© 2008 Prentice Hall, Inc. E – 7
Learning Curve ExamplesLearning Curve Examples
Table E.1Table E.1
ExampleExampleImproving Improving
ParametersParametersCumulative Cumulative ParameterParameter
Learning-Learning-Curve Curve SlopeSlope (%)(%)
Model -T Ford Model -T Ford productionproduction
PricePrice Units producedUnits produced 8686
Aircraft Aircraft assemblyassembly
Direct labor-hours Direct labor-hours per unitper unit
Units producedUnits produced 8080
Equipment Equipment maintenance maintenance at GEat GE
Average time to Average time to replace a group of replace a group of partsparts
Number of Number of replacementsreplacements
7676
Steel Steel productionproduction
Production worker Production worker labor-hours per labor-hours per unit producedunit produced
Units producedUnits produced 7979
© 2008 Prentice Hall, Inc. E – 8
Learning Curve ExamplesLearning Curve Examples
Table E.1Table E.1
ExampleExampleImproving Improving
ParametersParametersCumulative Cumulative ParameterParameter
Learning-Learning-Curve Curve SlopeSlope (%)(%)
Integrated Integrated circuitscircuits
Average price per Average price per unitunit
Units Units producedproduced
7272
Handheld Handheld calculatorcalculator
Average factory Average factory selling priceselling price
Units Units producedproduced
7474
Disk memory Disk memory drivesdrives
Average price per Average price per bitbit
Number of bitsNumber of bits 7676
Heart Heart transplantstransplants
1-year death rates1-year death rates Transplants Transplants completedcompleted
7979
© 2008 Prentice Hall, Inc. E – 9
Uses of Learning CurvesUses of Learning Curves
Internal:Internal: labor forecasting, labor forecasting, scheduling, establishing scheduling, establishing costs and budgetscosts and budgets
External:External: supply chain negotiationssupply chain negotiations
Strategic:Strategic: evaluation of company and evaluation of company and industry performance, industry performance, including costs and pricingincluding costs and pricing
© 2008 Prentice Hall, Inc. E – 10
Arithmetic ApproachArithmetic Approach
Simplest approachSimplest approach
Labor cost declines at a constant rate, Labor cost declines at a constant rate, the learning rate, as production doublesthe learning rate, as production doubles
Nth Unit ProducedNth Unit Produced Hours for Nth UnitHours for Nth Unit
11 100.0100.0
22 80.080.0 = (.8 x 100)= (.8 x 100)
44 64.064.0 = (.8 x 80)= (.8 x 80)
88 51.251.2 = (.8 x 64)= (.8 x 64)
1616 41.041.0 = (.8 x 51.2)= (.8 x 51.2)
© 2008 Prentice Hall, Inc. E – 11
Logarithmic ApproachLogarithmic Approach
Determine labor for any unit, TDetermine labor for any unit, TN N , by, by
TTNN = T = T11((NNbb))
wherewhere TTNN == time for the Ntime for the Nthth unit unit
TT11 == hours to produce hours to produce
the first unitthe first unitbb == ((log of the learning log of the learning raterate)/()/(log log 2) 2)
== slope of the slope of the learning curvelearning curve
© 2008 Prentice Hall, Inc. E – 12
Logarithmic ApproachLogarithmic Approach
Determine labor for any unit, TDetermine labor for any unit, TN N , by, by
TTNN = T = T11((NNbb))
wherewhere TTNN == time for the Ntime for the Nthth
unitunitTT11 == hours to produce hours to produce
the first unitthe first unitbb == ((log of the log of the learning ratelearning rate)/()/(log log 2)2)
== slope of the slope of the learning curvelearning curve
LearningRate (%) b
70 – .515
75 – .415
80 – .322
85 – .234
90 – .152Table E.2Table E.2
© 2008 Prentice Hall, Inc. E – 13
Logarithmic ExampleLogarithmic Example
Learning rate Learning rate = 80%= 80%First unit took First unit took 100100 hours hours
TTNN == TT11((NNbb))
TT33 == (100 (100 hourshours)(3)(3bb))
== (100)(3(100)(3loglog .8/ .8/loglog 2 2))
== (100)(3(100)(3–.322–.322))
== 70.2 70.2 labor hourslabor hours
© 2008 Prentice Hall, Inc. E – 14
Coefficient ApproachCoefficient Approach
TTNN == TT11CC
wherewhere TTNN == number of labor-number of labor-hours required to produce the hours required to produce the NNthth unit unit
TT11 == number of labor-number of labor-hours required to produce the hours required to produce the first unitfirst unit
CC == learning-curve learning-curve coefficient found in coefficient found in Table E.3Table E.3
© 2008 Prentice Hall, Inc. E – 15
Learning-Curve CoefficientsLearning-Curve CoefficientsTable E.3Table E.3
70%70% 85%85%
UnitUnitNumberNumber
(N)(N) Unit TimeUnit Time Total TimeTotal Time Unit TimeUnit Time Total TimeTotal Time
11 1.0001.000 1.0001.000 1.0001.000 1.0001.000
22 .700.700 1.7001.700 .850.850 1.8501.850
33 .568.568 2.2682.268 .773.773 2.6232.623
44 .490.490 2.7582.758 .723.723 3.3453.345
55 .437.437 3.1953.195 .686.686 4.0314.031
1010 .306.306 4.9324.932 .583.583 7.1167.116
1515 .248.248 6.2746.274 .530.530 9.8619.861
2020 .214.214 7.4077.407 .495.495 12.40212.402
© 2008 Prentice Hall, Inc. E – 16
Coefficient ExampleCoefficient Example
First boat required First boat required 125,000125,000 hours hoursLabor cost = Labor cost = $40$40/hour/hourLearning factor = Learning factor = 85%85%
TTNN == TT11CC
TT44 == (125,000 (125,000 hourshours)(.723))(.723)
== 90,37590,375 hours for the 4 hours for the 4thth boat boat
90,37590,375 hours x hours x $40/$40/hour hour = $3,615,000= $3,615,000
TTNN == TT11CC
TT44 == (125,000 (125,000 hourshours)(3.345))(3.345)
== 418,125418,125 hours for all four boats hours for all four boats
© 2008 Prentice Hall, Inc. E – 17
Coefficient ExampleCoefficient Example
Third boat required 100,000 hoursThird boat required 100,000 hoursLearning factor = 85%Learning factor = 85%
100,000100,000
.773.773= 129,366= 129,366 hours hours
New estimate for the first boatNew estimate for the first boat
© 2008 Prentice Hall, Inc. E – 18
Strategic ImplicationsStrategic Implications
To pursue a strategy of a steeper curveTo pursue a strategy of a steeper curvethan the rest of the industry, a firm can:than the rest of the industry, a firm can:
1.1. Follow an aggressive pricing policyFollow an aggressive pricing policy
2.2. Focus on continuing cost reduction Focus on continuing cost reduction and productivity improvementand productivity improvement
3.3. Build on shared experienceBuild on shared experience
4.4. Keep capacity ahead of demandKeep capacity ahead of demand
© 2008 Prentice Hall, Inc. E – 19
Industry and Company Industry and Company Learning CurvesLearning Curves
Figure E.2Figure E.2
Pri
ce p
er u
nit
(lo
g s
cale
)P
rice
per
un
it (
log
sca
le)
Accumulated volume (log scale)Accumulated volume (log scale)
Gross profit Gross profit marginmargin
LossLoss
((aa))
((cc))
((bb))
Company cost
Company cost
Industry price
Industry price
© 2008 Prentice Hall, Inc. E – 20
Limitations of Learning Limitations of Learning CurvesCurves
Learning curves differ from company Learning curves differ from company to company as well as industry to to company as well as industry to industry so estimates should be industry so estimates should be developed for each organizationdeveloped for each organization
Learning curves are often based on Learning curves are often based on time estimates which must be accurate time estimates which must be accurate and should be reevaluated when and should be reevaluated when appropriateappropriate
© 2008 Prentice Hall, Inc. E – 21
Limitations of Learning Limitations of Learning CurvesCurves
Any changes in personnel, design, or Any changes in personnel, design, or procedure can be expected to alter the procedure can be expected to alter the learning curvelearning curve
Learning curves do not always apply to Learning curves do not always apply to indirect labor or materialindirect labor or material
The culture of the workplace, resource The culture of the workplace, resource availability, and changes in the process availability, and changes in the process may alter the learning curvemay alter the learning curve