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# Learning Curves - PowerPoint PPT Presentation

Learning Curves. Stephen R. Lawrence Associate Professor of Operations Leeds School of Business University of Colorado Boulder, CO 80309-0419. [email protected] Leeds.colorado.edu/faculty/lawrence. Learning Curves.

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### Learning Curves

Stephen R. LawrenceAssociate Professor of Operations

Boulder, CO 80309-0419

• As experience increases, costs decline. For each doubling of cumulative unit production, costs decrease by some percentage

• Learning on the part of labor (methods improvement)

• Changes in production methods and tools

• Improved product design

• Changes in layout and process flow

• Standardization

kn = k1 n b

n = cumulative unit outputkn=cost of the nth item

k1= cost of the first item

r = rate of learning

b = learning parameter

b = log r / log 2

Consider two start-up firms making similar new products.

If firm A produces at twice the rate of firm B, what will be

the relative costs of the two firms after 2 years?

k1= \$100 per unit (both firms)

r= 0.8 (80 percent learning curve)

nA = 1000 (after two years)

nB= 500 (after two years)

First – find b:

r = 0.8

b = log r / log 2

= log 0.8 / log 2

= 0.0969 / 0.301

= -0.3219

Consider two start-up firms making similar new products.

If firm A produces at twice the rate of firm B, what will be

the relative costs of the two firms after 2 years?

k1= \$100 per unit (both firms)

b = -0.3219 (80 percent learning curve)

nA= 1000 (after two years)

nB= 500 (after two years)

k1000 = k1 nAb = 100 (1000) -0.3219 = \$10.82 / unit

k500 = k1 nBb = 100 (500) -0.3219 = \$13.53 / unit

Firm 1 will have a 25% cost advantage over Firm 2 !

Faster learning means lower costs and competitive advantage

Costper

Unit

Slower Learning

Faster Learning

Number of Units Produced

Faster learning can offset initial cost disadvantages

Costper

Unit

Number of Units Produced

Faster learning can offset a late market start

Costper

Unit

Number of Units Produced

Learning Curves:Another Example

Your snow board manufacturing company is taking off and has received an order for 80 boards of a new design. The first board took 46 hours to produce (!), but you are learning quickly, and the 10th board took only 24 hours to produce. What is your rate of learning? How many hours do you estimate the 80th board will take to manufacture?