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Chapter 17 - Project Management
17-31
Education.
b. The project manager will receive a bonus of $1,000 if the project is finished within 26 weeks.
P (T ≤ 26):
Path A-D-E-H:
Expected completion time = 4.00 + 8.00 + 9.17 + 3.17 = 24.34
Using Appendix B Table B: Probability of completion ≤ 26 weeks = 0.8907
Path A-F-G:
Expected completion time = 4.00 + 4.50 + 7.00 = 15.50
Variance = 16/36 + 25/36 + 16/36 = 57/36
Path B-I-J-K:
Expected completion time = 2.17 + 3.33 + 4.00 + 5.33 = 14.83
Variance = 1/36 + 16/36 + 4/36 + 16/36 = 37/36
Standard deviation =√
=.
� = −.
. =−.
Using Appendix B Table B: Probability of completion ≤ 26 weeks = 0.4602
Chapter 17 - Project Management
17-32
The project manager will receive a bonus of $500 if the project is finished within 27 weeks.
P (T ≤ 27):
Path A-D-E-H:
� = −.
Path B-I-J-K:
� = −.
. =.
Chapter 17 - Project Management
17-33
Education.
13. Given:
We have the following list of activities for a project and crashing costs:
Path
Activity
Duration (weeks)
First Crash
Second Crash
Top
A
5
$8
$10
B
6
$7
$9
C
3
$14
$15
Middle
D
3
$9
$11
E
7
$8
$9
C
3
$14
$15
Bottom
F
5
$10
$15
G
5
$11
$13
H
5
$12
$14
Determine which activities should be crashed to shorten the project by 3 weeks as cheaply as
possible. Draw the precedence diagram first.
2
1
3
1
5
6
4
7
E
A
B
C
D
F
G
H
Chapter 17 - Project Management
Step 1:
The paths and their expected duration are shown below:
Path
Expected Duration
A-B-C
14
D-E-C
13
F-G-H
15
Chapter 17 - Project Management
Education.
Choose one activity on each path to crash:
Activity B should be shortened 1 week because it has the lowest crashing cost ($7) on
Path A-B-C.
Activity G should be shortened 1 week because it has the lowest crashing cost ($11) on
Path F-G-H.
Path A-B-C now will be 13 weeks as shown below.
Path
Expected Duration
A-B-C
13
D-E-C
13
F-G-H
13
Critical paths are A-B-C, D-E-C, and F-G-H.
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
A-B-C
A
$8
B
$9
C
$14
D-E-C
E
$8
D
$9
C
$14
F-G-H
H
$12
G
$13
F
$15
on Path D-E-C. The combined crashing cost would be $8 + $8 = $16. However, Activity
C is on both paths and could be crashed for $14.
Activity C should be shortened 1 week at a crashing cost of $14.
Activity H should be shortened 1 week because it has the lowest crashing cost ($12) on
Path F-G-H.
Chapter 17 - Project Management
17-36
A summary of the crashing steps is shown below:
Path
Initial time
Length after
crashing 1 week
Length after
crashing 2 weeks
Length after
crashing 3 weeks
A-B-C
D-E-C
F-G-H
14 wk.
13 wk.
15 wk.
14 wk.
13 wk.
14 wk.
13 wk.
13 wk.
13 wk.
12 wk.
12 wk.
12 wk.
Step 1 Crashing
Step 2 Crashing
Step 3 Crashing
Activity Cost
F $10
Activity Cost
B $ 7
G 11
$18
Activity Cost
C $14
H 12
$26
Conclusion: Expected project duration = 12 weeks. Total crashing cost = $10 + $18 + $26 = $54.
17-37
14. Given:
We have the activities and crashing costs shown below:
Activity
Immediate
Predecessor
Normal Time
(weeks)
Crashing Cost ($000)
First Week
Crashing Cost ($000)
Second Week
A
---
12
$15
$20
B
A
14
$10
$10
C
---
10
$5
$5
D
C
17
$20
$21
E
C
18
$16
$18
F
C
12
$12
$15
G
D
15
$24
$24
H
E
8
---
---
I
F
7
$30
---
J
I
12
$25
$25
K
B
9
$10
$10
M
G
3
---
---
N
H
11
$40
---
P
H, J
8
$20
$20
End
K, M, N, P
Construct a network diagram:
P
B
H
I
A
K
J
F
E
Chapter 17 - Project Management
Determine a minimum-cost crashing schedule that will shave five weeks off the project length:
Step 1:
The paths and their expected duration are shown below:
Path
Expected Duration
A-B-K
35
C-D-G-M
45
C-E-H-N
47
C-E-H-P
44
C-F-I-J-P
49
Activity
Cost per Week
to Crash
C
$5
F
$12
P
$20
J
$25
I
$30
Step 2:
The paths and their expected duration are shown below:
Path
Expected Duration
A-B-K
35
C-D-G-M
44
C-E-H-N
46
C-E-H-P
43
C-F-I-J-P
48
Chapter 17 - Project Management
Step 3:
The paths and their expected duration are shown below:
Path
Expected Duration
A-B-K
35
C-D-G-M
43
C-E-H-N
45
C-E-H-P
42
C-F-I-J-P
47
Critical path is C-F-I-J-P.
Rank critical activities according to crash costs:
Activity
Cost per Week
to Crash
F
$12
P
$20
J
$25
I
$30
Activity F should be shortened 1 week because it has the lowest crashing cost ($12).
Path C-F-I-J-P will decrease 1 week as shown below.
Activities crashed to this point: Step 1: C (first week). Step 2: C (second week). Step 3: F (first
week).
Step 4:
Chapter 17 - Project Management
Step 5:
The paths and their expected duration are shown below:
Path
Expected Duration
A-B-K
35
C-D-G-M
43
C-E-H-N
45
C-E-H-P
42
C-F-I-J-P
45
