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