Operations management 12th stevenson ch07 learning curves

Interesting Characteristics of Learning The learning effect is predictable  Every doubling of repetitions results in a constant percentage decrease in the time per repetition... Learn

Learning Curves

Supplement 7

McGraw-Hill/Irwin

Supplement 7: Learning Objectives

 You should be able to:

Learning Curves

 Learning curve

 The degree of improvement is a function of the task being done

Short, routine tasks will show modest improvement relatively quickly

Longer, more complex tasks will show improvement over a longer interval

Learning

The Learning Effect

Effort expended prior to the start of work

 Changes made after production has begun

Changes in work methods

Changes in tooling and equipment

 Managerial factors

Improvements in planning, scheduling, motivation, and control

Interesting Characteristics of Learning

 The learning effect is predictable

 Every doubling of repetitions results in a constant percentage decrease in the

time per repetition

Learning Curves: On a Log-Log Graph

Learning Percentage

 90% learning percent means 10% decrease in unit time with

each doubling of repetition

 80% learning percent means 20% decrease in unit time with

each doubling of repetition

 Question: What does 100% learning percent imply?

7

8 5.12 (.8)(6.4) = (.8)(.8)(.8)(10) = (.8) 3 (10) 1.28 9

Learning Illustrated

 Each time cumulative output doubles, the time per unit for that amount should be approximately

equal to the previous time multiplied by the learning percentage

 If the first unit of a process took 100 hours and the learning rate is 90%:

Unit Unit Time (hours)

Unit Times: Formula Approach

logarithm natural

for the stands

ln

percentage rate

learning

2 ln

ln

unit first

for Time

unit

th for

Time

where

1 1

T

n T

n T

T

n

b n

Example: Formula Approach

 If the learning rate is 90, and the first unit took 100 hours to complete, how

long would it take to complete the 25th unit?

hours 3068

61

25 100

25

100

15200

2 ln

90 ln 25

Unit Times: Learning Factor Approach

 The learning factor approach uses a table that shows two things for selected

learning percentages:

complete a given number of units.

Example: Learning Factor Approach

 If the learning rate is 90, and the first unit took 100 hours to complete, how

long would it take to complete the 25th unit?

 How long would it take to complete the first 25 units?

hours 3

61

613

771 ,

1

713

7 1

Learning Curves Example S-2

 A contract calls for the production of 20 jets The initial unit

required 400 days of direct labor The learning percent is 80%

Learning Curves Example S-2

 Q1: Calculate the time of the 5th unit

b = ln(.8) / ln(2) = -.3219

n b = 5 (-.3219) = 5956

T5 = (400)(.5956) = 238.24

Learning Curves Example S-2

 Q1: Calculate the time of the 5th unit

using the learning Curve Coefficients table (7S-1, page 346)

n b = 596 (Unit Time for 85% and n = 5)

T 5 = (400)(.596) = 238.4

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

Unit Time

Total Time

Learning Curves Example S-2

 Q2 – Expected time for the 20th jet

T20 = (400) X (.381) = 152.4 labor days

 Q3 – Expected total time for all 20 jets

T1-20 = (400) X (10.485) = 4,194 labor days

 Q4 – Average time per jet:

Average time = 4,194/20 = 209.7 labor days

Learning Curves Example

 Given T2 = 10 and 80% learning percent, find the expected time for the 5th unit

T2 = 10 = T1 X (.8)

T1 = 10 / 8 = 12.5

T5 = 12.5 X 0.596 = 7.45

Learning Curve Applications

 Useful application areas:

Cautions and Criticisms

1 Learning rates may differ from organization to organization and by type of work

Base learning rates on empirical studies rather than assumptions where possible

2 Projections based on learning curves should be regarded as approximations of actual

times

3 Because time estimates are based on the first unit, care should be taken to ensure

that the time is valid

4 It is possible that at some point the curve might level off or even tip upward

Cautions and Criticisms

5 Some of the improvements may be more apparent than real: improvements in times

may be caused by increases in indirect labor costs

6 In mass production situations, learning curves may be of initial use in predicting how

long it will take before the process stabilizes

 The concept does not usually apply because improvement in time per unit is almost imperceptible

Cautions and Criticisms

7 Users of learning curves fail to include carryover effects from previous experiences

8 Shorter product life cycles, flexible manufacturing, and cross-functional workers can

affect the ways in which learning curves may be applied

Operations Strategy

 Learning curves have strategic implications for:

 As volume increases, operations is able to move quickly down the learning curve

Reduced cost  improved competitive advantage

 Can lead to more realistic time estimates, thus leading to more accurate capacity needs

assessment