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

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

Learning Curve 0.30 – 0.25 – 0.20 – 0.15 – 0.10 – 0.05 – 0 – | | | | | | 50 100 150 200 250 300 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.

Learning Curve 0.30 – 0.25 – 0.20 – 0.15 – 0.10 – 0.05 – 0 – | | | | | | 50 100 150 200 250 300 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.

Learning Curve 0.30 – 0.25 – 0.20 – 0.15 – 0.10 – 0.05 – 0 – | | | | | | 50 100 150 200 250 300 Learning curve Cumulative units produced Process time per unit (hr) Learning period To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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 | | | | | | 50 100 150 200 250 300 Figure G.1 Cumulative units produced To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

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

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 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

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 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 Cumulative units produced Direct labor hours per locomotive (thousands) k40 = 50,000(0.30488) 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

The 80% Learning Curve Labor hours required for first unit = 50,000 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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 1 1.00000 2 0.90000 3 0.83403 . . 38 0.43634 39 0.43304 40 0.42984 64 0.37382 128 0.24405 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.

The 80% Learning Curve Labor hours required for first unit = 50,000 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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(0.42984) n 1 1.00000 2 0.90000 3 0.83403 . . 38 0.43634 39 0.43304 40 0.42984 64 0.37382 128 0.24405 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.

The 80% Learning Curve Labor hours required for first unit = 50,000 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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 1 1.00000 2 0.90000 3 0.83403 . . 38 0.43634 39 0.43304 40 0.42984 64 0.37382 128 0.24405 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.

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 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

Direct labor hours per locomotive (thousands) The 80% Learning Curve 50 – 40 – 30 – 20 – 10 – 0 – | | | | | | | 40 80 120 160 200 240 280 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.

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

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units n 1 1.00000 2 0.95000 3 0.91540 4 0.88905 5 0.86784 . . 30 0.69090 64 0.62043 128 0.56069 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 n 1 1.00000 2 0.95000 3 0.91540 4 0.88905 5 0.86784 . . 30 0.69090 64 0.62043 128 0.56069 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 n 1 1.00000 2 0.95000 3 0.91540 4 0.88905 5 0.86784 . . 30 0.69090 64 0.62043 128 0.56069 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 20,727 20,727(30) = 621,810 n 1 1.00000 2 0.95000 3 0.91540 4 0.88905 5 0.86784 . . 30 0.69090 64 0.62043 128 0.56069 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 2 30,000(0.86784) = 26,035 3 30,000(0.79945) = 23,983 4 30,000(0.74080) = 22,224 5 30,000(0.69090) = 20,727 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 3 30,000(0.79945) = 23,983 4 30,000(0.74080) = 22,224 5 30,000(0.69090) = 20,727 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 4 30,000(0.74080) = 22,224 5 30,000(0.69090) = 20,727 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.

Estimating Labor Requirements Example G.2 Units per Cumulative Month Month Units 1 2 2 2 3 5 3 5 10 4 8 18 5 12 30 Cumulative Cumulative Average Time Total Hours Month per Unit for All Units 1 30,000(0.95000) = 28,500 28,500(2) = 57,000 2 30,000(0.86784) = 26,035 26,035(5) = 130,175 3 30,000(0.79945) = 23,983 23,983(10) = 239,830 4 30,000(0.74080) = 22,224 22,224(18) = 400,032 5 30,000(0.69090) = 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 To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.