1. Learning Curve Analysis
Supplement G
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

2. Learning Curve
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3. Learning Curve
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0 –
| | | | | |
Cumulative units produced
Process time per unit (hr)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

4. Learning Curve
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0 –
| | | | | |
Learning curve
Cumulative units produced
Process time per unit (hr)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

5. Learning Curve
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0 –
| | | | | |
Learning curve
Cumulative units produced
Process time per unit (hr)
Learning period
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6. Learning Curve
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0 –
Learning curve
Process time per unit (hr)
Learning period
Standard time
| | | | | |
Figure G.1
Cumulative units produced
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

7. The 80% Learning Curve
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

8. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
Labor hours required for first unit = 50,000
Learning rate = 80%
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

9. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

10. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
k40 = 50,000(40)(log 0.8)/(log 2)
Labor hours required for first unit = 50,000
Learning rate = 80%
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

11. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
k40 = 50,000(40)-0.322
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

12. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
k40 = 50,000( )
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

13. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
k40 = 15,244 hours
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

14. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
k40 = 15,244 hours
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

15. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
k40 = 15,244 hours
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

16. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Cumulative average labor hours =
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

17. The 80% Learning Curve Labor hours required for first unit = 50,000
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Cumulative average labor hours =
Labor hours required for first unit = 50,000
Learning rate = 80% n
. .
Table H.1
80% Learning Rate
(n = cumulative production)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

18. The 80% Learning Curve Labor hours required for first unit = 50,000
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Cumulative average labor hours = 50,000( ) n
. .
Table H.1
80% Learning Rate
(n = cumulative production)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

19. The 80% Learning Curve Labor hours required for first unit = 50,000
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Cumulative average labor hours = 21,492 hours n
. .
Table H.1
80% Learning Rate
(n = cumulative production)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

20. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
Labor hours required for first unit = 50,000
Learning rate = 80%
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

21. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

22. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Second unit = 50,000(80%)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

23. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Second unit = 40,000 hours
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

24. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Fourth unit = 40,000(80%)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

25. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Labor hours required for first unit = 50,000
Learning rate = 80%
Fourth unit = 32,000 hours
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

26. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Example G.1
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

27. Direct labor hours per locomotive (thousands)
The 80% Learning Curve
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | |
Cumulative units produced
Direct labor hours per locomotive (thousands)
Figure G.2
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

28. Estimating Labor Requirements
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

29. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

30. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units n
. .
Table H.1
90% Learning Rate
(n = cumulative production)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

31. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 n
. .
Table H.1
90% Learning Rate
(n = cumulative production)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

32. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 n
. .
Table H.1
90% Learning Rate
(n = cumulative production)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

33. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810 n
. .
Table H.1
90% Learning Rate
(n = cumulative production)
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

34. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500
2 30,000( ) = 26,035
3 30,000( ) = 23,983
4 30,000( ) = 22,224
5 30,000( ) = 20,727
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35. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035
3 30,000( ) = 23,983
4 30,000( ) = 22,224
5 30,000( ) = 20,727
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36. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983
4 30,000( ) = 22,224
5 30,000( ) = 20,727
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37. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

38. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1:
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

39. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1: 57,000 – 0 = 57,000 hours
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

40. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1: 57,000 – 0 = 57,000 hours
Month 2: 130,175 – 57,000 = 73,175 hours
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

41. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1: 57,000 – 0 = 57,000 hours
Month 2: 130,175 – 57,000 = 73,175 hours
Month 3: 239,830 – 130,175 = 109,655 hours
Month 4: 400,032 – 239,830 = 160,202 hours
Month 5: 621,810 – 400,032 = 221,778 hours
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42. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1: 57,000 – 0 = 57,000 /150
Month 2: 130,175 – 57,000 = 73,175 /150
Month 3: 239,830 – 130,175 = 109,655 /150
Month 4: 400,032 – 239,830 = 160,202 /150
Month 5: 621,810 – 400,032 = 221,778 /150
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43. Estimating Labor Requirements
Example G.2
Units per Cumulative
Month Month Units
1 2 2
2 3 5
3 5 10
4 8 18
Cumulative Cumulative
Average Time Total Hours
Month per Unit for All Units
1 30,000( ) = 28,500 28,500(2) = 57,000
2 30,000( ) = 26,035 26,035(5) = 130,175
3 30,000( ) = 23,983 23,983(10) = 239,830
4 30,000( ) = 22,224 22,224(18) = 400,032
5 30,000( ) = 20,727 20,727(30) = 621,810
Month 1: 57,000 – 0 = 57,000 /150 = 380 employees
Month 2: 130,175 – 57,000 = 73,175 /150 = 488 employees
Month 3: 239,830 – 130,175 = 109,655 /150 = 731 employees
Month 4: 400,032 – 239,830 = 160,202 /150 = 1068 employees
Month 5: 621,810 – 400,032 = 221,778 /150 = 1479 employees
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