Stephen R. LawrenceAssociate Professor of OperationsLeeds School of BusinessUniversity of ColoradoBoulder, CO 80309-0419

Stephen.Lawrence@Colorado.eduLeeds.colorado.edu/faculty/lawrence

Learning Curves

Learning Curves

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

Learning Curve Model

kn = k1 n b

n = cumulative unit output kn = cost of the nth item

k1 = cost of the first item

r = rate of learning b = learning parameterb = log r / log 2

Example: Learning Curves

k1 = $100 per unit (both firms)

r = 0.8 (80 percent learning curve)

nA = 1000 (after two years)

nB = 500 (after two years)

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?

First – find b: r = 0.8b = log r / log 2 = log 0.8 / log 2 = 0.0969 / 0.301 = -0.3219

Example: Learning Curves

k1 = $100 per unit (both firms) b = -0.3219 (80 percent learning curve)nA= 1000 (after two years)nB = 500 (after two years)

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?

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

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

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

Competing with Learning

CostperUnit

Number of Units Produced

Slower Learning

Faster Learning

Faster learning means lower costs and competitive advantage

Competing with Learning

CostperUnit

Number of Units Produced

Faster learning can offset initial cost disadvantages

Competing with Learning

CostperUnit

Number of Units Produced

Faster learning can offset a late market start

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?

Learning Curve Spreadsheet