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

2. 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

3. Learning Curve Model k n = k 1 n b n = cumulative unit output k n = cost of the n th item k 1 = cost of the first item r = rate of learning b = learning parameter b = log r / log 2

4. Example: Learning Curves k 1 = $100 per unit (both firms) r = 0.8 (80 percent learning curve) n A = 1000 (after two years) n B = 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 = 0.8 b = log r / log 2 = log 0.8 / log 2 = 0.0969 / 0.301 = -0.3219

5. Example: Learning Curves k 1 = $100 per unit (both firms) b = -0.3219 (80 percent learning curve) n A = 1000 (after two years) n B = 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? k 1000 = k 1 n A b = 100 (1000) -0.3219 = $10.82 / unit Firm 1 will have a 25% cost advantage over Firm 2 ! k 500 = k 1 n B b = 100 (500) -0.3219 = $13.53 / unit

6. Competing with Learning Cost per Unit Number of Units Produced Slower Learning Faster Learning Faster learning means lower costs and competitive advantage

7. Competing with Learning Cost per Unit Number of Units Produced Faster learning can offset initial cost disadvantages

8. Competing with Learning Cost per Unit Number of Units Produced Faster learning can offset a late market start

9. 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 10 th board took only 24 hours to produce. What is your rate of learning? How many hours do you estimate the 80 th board will take to manufacture?

10. Learning Curve Spreadsheet