stephen r. lawrence associate professor of operations leeds school of business university of...
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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
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