Project Management – Homework 3
VSB 3008
M. J. Liberatore
5.
a.
3
5
5
11
B (2)
0
3
7
9
3
7
A (3)
0
E (6)
9
15
7
13
C (4)
3
F (6)
3
7
3
7
7
15
15
G (2)
13
7
D (4)
3
13
13
18
I (3)
15
15
18
10
H (3)
7
12
15
b. A-C-F-G-I, and A-D-F-G-I.
c. B is not on a critical path and has slack of 4; therefore, do not shorten as it will not
change the project completion time. Shorten C, D, and G one week each. C and D are on
parallel critical paths, reducing them will only reduce project completion time by 1 week.
d. A-C-F-G-I; and A-D-F-G-I. Project completion time is reduced from 18 to 16 weeks.
11.
7
16
10
F (4)
B (3)
8
0
16
11
7
11
A (7)
0
20
20
16
20
D (5)
7
11
7
11
G (5)
16
20
16
C (4)
7
18
E (2)
11
25
18
20
25
a. A-C-D-F-G
b.
Activity
Normal
Time (NT)
Crash Time
(CT)
Normal Cost
(NC)
Crash Cost
(CC)
NT-CT
Cost/day to
expedite
A
7
6
$7,000
$8,000
1
$1,000
B
3
2
5,000
7,000
1
2,000
C
4
3
9,000
10,200
1
1,200
D
5
4
3,000
4,500
1
1,500
E
2
1
2,000
3,000
1
1,000
F
4
2
4,000
7,000
2
1,500
G
5
4
5,000
8,000
1
3,000
Path
CP
A-C-D-F-G:
A-C-D-E-G:
A-B-D-F-G:
A-B-D-E-G:
25
23
24
22
Crash
A
24
22
23
21
Crash
C
23
21
23
21
Crash
D
22
20
22
20
Crash
F
21
20
21
20
A has the lowest crash cost per day of the critical path activities, so crash it by one day at a cost
of $1,000. Next, crash C at a cost of $1,200. Now path A-B-D-F-G is also critical. Now crash
either D or F since they are on both critical paths and have the cheapest crash cost per day of
$1,500. Suppose you pick D and crash it by one day. Then crash F by one day at $1,500.
Alternatively, crash F by one day and then F by another day for the same cost.
Summary of steps to reduce project by four days:
Step
Activity to crash
Cost to crash
Days saved
1
A
$1,000
1
2
C
1,200
1
3
D
1,500
1
4
F
1,500
1
13.
15
21
D (6)
5
15
15
21
B (10)
5
0
15
5
13
A (5)
0
20
21
E (7)
5
5
25
G (4)
14
21
13
17
21
25
13
C (8)
6
14
F (4)
17
21
a. A-B-D-G, 25 weeks, 5+10+6+4.
b.
Activity
Normal
Time (NT)
Normal Cost
(NC)
Crash Time
(CT)
Crash Cost
(CC)
NT-CT
Cost/week
to expedite
A
5
$7,000
3
$13,000
2
$3,000
B
10
12,000
7
18,000
3
2,000
C
8
5,000
7
7,000
1
2,000
D
6
4,000
5
5,000
1
1,000
E
7
3,000
6
6,000
1
3,000
F
4
6,000
3
7,000
1
1,000
G
4
7,000
3
9,000
1
2,000
First, reduce D (lowest cost activity on the critical path) by one week.
After you crash D, two paths are critical of length 24:
A-B-D-G
A-C-E-G
Your options to reduce BOTH paths by one are:
crash G at 2,000 -- on both paths
crash A at 3,000 -- on both paths
crash B to reduce first path at a cost of 2,000 and C or E to crash the second path, so pick
C, it is cheaper at 2,000, for a total cost of 4,000
Therefore, crash G
Now both paths are critical at length 23. Since D and G cannot be crashed further, your
options to reduce both paths by one are:
crash A at 3,000 -- on both paths
crash B to reduce first path at a cost of 2,000 and C or E to crash the second path, so pick
C, it is cheaper at 2,000, for a total cost of 4,000
Therefore, crash A
Summary of activities crashed:
Step
Activity
Cost to crash
Weeks reduced
1
D
$1,000
1
2
G
2,000
1
3
A
3,000
1
Total cost
$6,000