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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


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


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


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


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


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


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


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


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


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)



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



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


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


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


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


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


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


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


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


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


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

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