1. Learning Curves Dr. Everette S. Gardner, Jr.

2. Learning Curves2 Learning curve concepts Predicts reduction in manufacturing costs or direct labor hours as cumulative production increases Based on empirical evidence rather than theory

3. Learning Curves3 Price of Model T, 1909-1923 (in 1958 dollars) 85% slope 1909: 18,000 units $3,300 1923: 8,000,000 units $950 1910 1911 1912 1913 1914 1915 1918 1920 1921 1923 Thousands of $.8 1 2 3 1909 4 5 6 10,000 100,000 1,000,000 Cumulative units produced

4. Learning Curves4 An 80% learning curve Unit Man hours 1 ST 1000 2 ND 1000 X.80 800 4 TH 800 X.80 640 8 TH 640 X.80 512 16 TH 512 X.80 410 32 ND 410 X.80 328

5. Learning Curves5 An 80% learning curve (cont.) 10 20 30 40 50 1000 800 600 400 200 0 Man-hours per unit Cumulative units produced 1st unit 2nd 4th 8th 16th 32nd

6. Learning Curves6 The log - linear method Exponential form: y x = kx n Where x = unit number y x = man-hrs. to produce x th unit k = hrs. to produce first unit n = log b / log 2 b = learning rate (80%, etc.) expressed as decimal (.8, etc.) Logarithmic equation: log y x = log k – n (log x) Learn.xls

7. Learning Curves7 The log - linear method (cont.) y x log y x Cum. units Cum. units (x) (log x)

8. Learning Curves8 Example calculations y x = kx n, n = log b / log 2 For 80% LC, b =.80 n = log.80 / log 2 = -.3219 Assume k = 1000 y 1 = 1000 (1) -.3219 = 1000 (1) = 1000 y 2 = 1000 (2) -.3219 = 1000 (.80) = 800 y 3 = 1000 (3) -.3219 = 1000 (.7021) = 702 y 4 = 1000 (4) -.3219 = 1000 (.6400) = 640 y 100 = 1000 (100) -.3219 = 1000 (.2270) = 227

9. Learning Curves9 1 10 100 1000 b = 90% b = 80% b = 70% Man-hours per unit Cumulative units produced Typical learning curves where k = 1 (one hour required for first unit) 1.00.10.01.001

10. Learning Curves10 Forces behind the learning curve 1. Increased labor efficiency 2. Process innovations and methods improvements 3. Substitution effects 4. Product redesign 5. Standardization 6. Economies of scale 7. Shared experience

11. Learning Curves11 Estimating learning curve parameters The concept applies to an aggregation rather than to individual operations First unit hours rarely known in time to develop curve – must estimate far in advance Slope can be estimated by least-squares regression Comparisons should always be made to similar products/processes – industry data usually available Extensive pre-production planning should result in lower, flatter curve

12. Learning Curves12 Estimating learning curve parameters (cont.) Man-hrs. / unit Cumulative units Little planning Extensive planning

13. Learning Curves13 Manufacturing strategy and the learning curve Capacity expands automatically Break-even points reduced automatically Worker compensation plans should account for learning effects The learning curve is a strategic, not a tactical concept – cannot be used as a short-range operating control A learning curve strategy can reduce the ability to innovate At some point, the learning curve will “plateau”

14. Learning Curves14 Manufacturing strategy and the learning curve (cont.) Man-hrs. / unit Cumulative units b < 1.0 b = 1.0

15. Learning Curves15 Learning curve applications Production planning / EOQ planning Price forecasting Petrochemicals Consumer durable goods Competitive bidding Income reporting in accounting Planning warranty maintenance Washers / dryers Televisions Forecasting industrial accidents Petroleum industry Mining Forecasting automobile accidents on new roadways