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
Process time per unit (hr)
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
0.05 –
0–
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50 100 150 200 250 300
Cumulative units produced
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Learning Curve
Process time per unit (hr)
0.30 –
0.25 –
0.20 –
0.15 –
Learning curve
0.10 –
0.05 –
0–
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50 100 150 200 250 300
Cumulative units produced
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Learning Curve
Process time per unit (hr)
0.30 –
0.25 –
0.20 –
0.15 –
Learning curve
0.10 –
Learning
0.05 – period
0–
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50 100 150 200 250 300
Cumulative units produced
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.
Learning Curve
Process time per unit (hr)
0.30 –
0.25 –
0.20 –
0.15 –
0.10 –
Learning
0.05 – period
0–
Figure G.1
Learning curve
Standard time
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50 100 150 200 250 300
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
50 –
40 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
20 –
10 –
0–
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|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 50,000(40)(log 0.8)/(log 2)
20 –
10 –
0–
|
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|
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|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 50,000(40)-0.322
20 –
10 –
0–
|
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|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 50,000(0.30488)
20 –
10 –
0–
|
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|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 15,244 hours
20 –
10 –
0–
|
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|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 15,244 hours
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
k40 = 15,244 hours
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
Cumulative average labor
hours =
10 –
0–
|
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|
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|
40 80 120 160 200 240 280
Cumulative units produced
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
Table H.1
50 Learning
–
80%
Rate
(n = cumulative production)
n40 –
1
230
3
.
.20
.
38
39
10
40
64
128 0
–
–
–
–
Labor hours required for
first unit = 50,000
Learning rate = 80%
1.00000
0.90000
0.83403
.
.
.
0.43634
0.43304
0.42984
0.37382
| 0.24405
|
|
Cumulative average labor
hours =
|
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|
|
40 80 120 160 200 240 280
Cumulative units produced
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
Table H.1
50 Learning
–
80%
Rate
(n = cumulative production)
n40 –
1
230
3
.
.20
.
38
39
10
40
64
128 0
–
–
–
–
Labor hours required for
first unit = 50,000
Learning rate = 80%
1.00000
0.90000
0.83403
.
.
.
0.43634
0.43304
0.42984
0.37382
| 0.24405
|
|
Cumulative average labor
hours = 50,000(0.42984)
|
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|
|
40 80 120 160 200 240 280
Cumulative units produced
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
Table H.1
50 Learning
–
80%
Rate
(n = cumulative production)
n40 –
1
230
3
.
.20
.
38
39
10
40
64
128 0
–
–
–
–
Labor hours required for
first unit = 50,000
Learning rate = 80%
1.00000
0.90000
0.83403
.
.
.
0.43634
0.43304
0.42984
0.37382
| 0.24405
|
|
Cumulative average labor
hours = 21,492 hours
|
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|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
Second unit = 50,000(80%)
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
Second unit = 40,000 hours
20 –
10 –
0–
|
|
|
|
|
|
|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
Fourth unit = 40,000(80%)
20 –
10 –
0–
|
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|
40 80 120 160 200 240 280
Cumulative units produced
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 –
Labor hours required for
first unit = 50,000
Learning rate = 80%
30 –
Fourth unit = 32,000 hours
20 –
10 –
0–
|
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|
|
|
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|
40 80 120 160 200 240 280
Cumulative units produced
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
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
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
Month
1
2
3
4
5
Units per
Month
2
3
5
8
12
Cumulative
Units
2
5
10
18
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
Table H.1
90% Learning Rate
(n = cumulative production)
n
1 Cumulative
1.00000
2Total Hours
0.95000
3for All Units
0.91540
4
0.88905
5
0.86784
.
.
.
.
.
.
30
0.69090
64
0.62043
128
0.56069
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
30,000(0.95000) = 28,500
Table H.1
90% Learning Rate
(n = cumulative production)
n
1 Cumulative
1.00000
2Total Hours
0.95000
3for All Units
0.91540
4
0.88905
5
0.86784
.
.
.
.
.
.
30
0.69090
64
0.62043
128
0.56069
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
Table H.1
90% Learning Rate
(n = cumulative production)
n
1 Cumulative
1.00000
2Total Hours
0.95000
3for All Units
0.91540
4
0.88905
28,500(2)
=
57,000
5
0.86784
.
.
.
.
.
.
30
0.69090
64
0.62043
128
0.56069
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
Table H.1
90% Learning Rate
(n = cumulative production)
n
1 Cumulative
1.00000
2Total Hours
0.95000
3for All Units
0.91540
4
0.88905
28,500(2)
=
57,000
5
0.86784
.
.
26,035(5)
=
130,175
.
.
.
.
23,983(10) = 239,830
30
0.69090
22,224(18)
=
400,032
64
0.62043
20,727(30)
=
621,810
128
0.56069
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
Cumulative
Total Hours
for All Units
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
Cumulative
Total Hours
for All Units
28,500(2)
=
57,000
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
Cumulative
Total Hours
for All Units
28,500(2)
26,035(5)
= 57,000
= 130,175
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 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
Cumulative
Total Hours
for All Units
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
Month
Month
Units
1
2
2
2
3
5
3
5
10
4
8 Cumulative
18
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
Cumulative
Total Hours
for All Units
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
57,000
0 = 57,000 hours
Month
Month–
Units
1
2
2
2
3
5
3
5
10
4
8 Cumulative
18
Cumulative
5
12 Average Time
30
Total Hours
Month
per Unit
for All Units
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
57,000
0 = 57,000 hours
Month
Month–
Units
Month
1 2: 130,175
2 – 57,000 2= 73,175 hours
2
3
5
3
5
10
4
8 Cumulative
18
Cumulative
5
12 Average Time
30
Total Hours
Month
per Unit
for All Units
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
57,000
0 = 57,000 hours
Month
Month–
Units
Month
1 2: 130,175
2 – 57,000 2= 73,175 hours
Month
2 3: 239,830
3 – 130,175 5= 109,655 hours
Month
3 4: 400,032
5 – 239,83010= 160,202 hours
Month
– 400,03218= 221,778 hoursCumulative
4 5: 621,810
8 Cumulative
5
12 Average Time
30
Total Hours
Month
per Unit
for All Units
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
57,000
0 = 57,000 /150
Month
Month–
Units
Month
1 2: 130,175
2 – 57,000 2= 73,175 /150
Month
2 3: 239,830
3 – 130,175 5= 109,655 /150
Month
3 4: 400,032
5 – 239,83010= 160,202 /150
Month
– 400,03218= 221,778 /150 Cumulative
4 5: 621,810
8 Cumulative
5
12 Average Time
30
Total Hours
Month
per Unit
for All Units
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
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
1:
57,000
0 = 57,000 /150
Month
Month–
Units
Month
1 2: 130,175
2 – 57,000 2= 73,175 /150
Month
2 3: 239,830
3 – 130,175 5= 109,655 /150
Month
3 4: 400,032
5 – 239,83010= 160,202 /150
Month
– 400,03218= 221,778 /150
4 5: 621,810
8 Cumulative
5
12 Average Time
30
Month
per Unit
1
2
3
4
5
30,000(0.95000) = 28,500
30,000(0.86784) = 26,035
30,000(0.79945) = 23,983
30,000(0.74080) = 22,224
30,000(0.69090) = 20,727
= 380 employees
= 488 employees
= 731 employees
= 1068 employees
=Cumulative
1479 employees
Total Hours
for All Units
28,500(2)
26,035(5)
23,983(10)
22,224(18)
20,727(30)
=
=
=
=
=
57,000
130,175
239,830
400,032
621,810
To Accompany Krajewski & Ritzman Operations Management: Strategy and Analysis, Seventh Edition © 2004 Prentice Hall, Inc. All rights reserved.