Chapter 17 – Project Management
The total cost-curve is plotted below:
Total
1,400
16. Given:
We have the following crashing costs for activities:
Activity
Crash Cost
2nd Week
K
$415
L
—
N
$45
M
$350
J
—
Q
$225
P
—
Y
$90
Z
—
The network diagram is shown below:
M
Chapter 17 – Project Management
17–53
Education.
Step 1:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
39
K-L-M-Q-Y
32
K-N-J-Q-P-Z
39
K-N-J-Q-Y
32
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
Z
$90
L
$125
Q
$200
M
$300
K
$410
K-N-J-Q-P-Z
N
$45
J
$50
Z
$90
Q
$200
K
$410
Chapter 17 – Project Management
Step 2:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
38
K-L-M-Q-Y
32
K-N-J-Q-P-Z
38
K-N-J-Q-Y
32
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
L
$125
Q
$200
M
$300
K
$410
K-N-J-Q-P-Z
N
$45
J
$50
Q
$200
K
$410
Activity L should be shortened 1 week because it has the lowest crashing cost ($125) on Path
K-L-M-Q-P-Z, which will decrease Paths K-L-M-Q-P-Z & K-L-M-Q-Y 1 week as shown
below.
Activity N should be shortened 1 week because it has the lowest crashing cost ($45) on Path
K-N-J-Q-P-Z, which will decrease Paths K-N-J-Q-P-Z & K-N-J–Q-Y 1 week as shown
below.
Combined crashing cost = $170. This cost is ≤ $375.
Activities crashed to this point: Step 1: Activity Z (1st week). Step 2: Activity L (1st week) &
Activity N (1st week).
17–55
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill
Education.
Step 3:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
37
K-L-M-Q-Y
31
K-N-J-Q-P-Z
37
K-N-J-Q-Y
31
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
Q
$200
M
$300
K
$410
K-N-J-Q-P-Z
N
$45
J
$50
Q
$200
K
$410
below.
Activities crashed to this point: Step 1: Activity Z (1st week). Step 2: Activity L (1st week) &
Activity N (1st week). Step 3: Activity Q (1st week).
Chapter 17 – Project Management
17–56
Education.
Step 4:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
36
K-L-M-Q-Y
30
K-N-J-Q-P-Z
36
K-N-J-Q-Y
30
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
Q
$225
M
$300
K
$410
K-N-J-Q-P-Z
N
$45
J
$50
Q
$225
K
$410
Chapter 17 – Project Management
17–57
Education.
Step 5:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
35
K-L-M-Q-Y
29
K-N-J-Q-P-Z
35
K-N-J-Q-Y
29
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
M
$300
K
$410
K-N-J-Q-P-Z
N
$45
J
$50
K
$410
Activity M (1st week) & Activity N (2nd week).
Chapter 17 – Project Management
17–58
Education.
Step 6:
The paths and their expected duration are shown below:
Path
Expected Duration
K-L-M-Q-P-Z
34
K-L-M-Q-Y
28
K-N-J-Q-P-Z
34
K-N-J-Q-Y
28
Rank critical activities according to crash costs:
Path
Activity
Cost per Week
to Crash
K-L-M-Q-P-Z
M
$350
K
$410
K-N-J-Q-P-Z
J
$50
K
$410
Activity M could be shortened 1 week because it has the lowest crashing cost ($350) on Path
Chapter 17 – Project Management
17–59
Education.
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
Length
after
crashing 4
weeks
Length
after
crashing 5
weeks
K-L-M-Q-P-Z
K-L-M-Q-Y
K-N-J-Q-P-Z
K-N-J-Q-Y
39
32
39
32
38
32
38
32
37
31
37
31
36
30
36
30
35
29
35
29
34
28
34
28
Step 1
Crashing
Step 2
Crashing
Step 3
Crashing
Step 4
Crashing
Step 5
Crashing
Activity Cost
z $90
Activity Cost
L $125
N $ 45
$170
Activity Cost
Q $200
Activity Cost
Q $225
Activity Cost
M $300
N $ 45
$345
Conclusion: Expected project duration = 34 weeks (shortened by 5 weeks).
Total crashing cost = $90 + $170 + $200 + $225 + $345 = $1,030.
Mr. T’s yacht will be 2 weeks late.
Total penalty cost = 2 x $375 = $750.
Total Cost = Crashing Cost + Penalty Cost = $1,030 + $750 = $1,780.