Homework 2
Solutions
IOM580- Project Management
Fall 2008
Hiroshi Ochiumi
1) A project has been defined to contain the following list of activities, along with their
required times for completion:
Activity
A
B
C
D
E
F
G
H
I
Immediate
Predecessors
A
A
A
B
C,D
E,F
D
G,H
Time(days)
1
4
3
7
6
2
7
9
4
a. Draw the network diagram. (5 points)
b. Show the early start and early finish times. (5 points)
5,11
E
1,5
6
B
11,18
G
4
8,10
7
0,1
1,4
A
C
F
I
1
3
2
4
1,8
D
8,17
7
H
18,22
c. Show the critical path. (5 points)
The critical path is A-B-E-G-I.
d. What would happen if Activity F were revised to take four days instead of two? (5
points)
New CP: A-D-F-G-I. Time of completion = 23 days.
2) Following are the precedence requirements, normal and crash activity times, and
normal and crash costs for a construction project
Required Time
(weeks)
Activity
A
B
C
D
E
F
G
H
I
Preceding
Activities
A
A
B
B,C
C
E,F
D,E
H,G
Normal
4
3
2
5
1
3
4
4
6
Crash
2
2
1
3
1
2
2
1
5
Cost ($)
Normal
10,000
6,000
4,000
14,000
9,000
7,000
13,000
11,000
20,000
Crash
11,000
9,000
6,000
18,000
9,000
8,000
25,000
18,000
29,000
a. What are the critical path and the estimated completion time? (5 points)
Critical path A-B-D-H-I.
Normal completion time 22 weeks.
b. To shorten the project by three weeks, which tasks would be shortened and what
would the final total project cost be? (10 points)
Activity
A
B
C
D
E
F
G
H
I
Cost per
week
500
3000
2000
2000
0
1000
6000
2333.333
9000
Possible
decrease
2
1
1
2
0
1
2
3
1
1st week: CP=A-B-D-H-I. Crash A at $500. Critical path stays the same.
2nd week: Crash A again. Critical path stays the same.
3rd week: A is no longer available. It is going to be either B, D, H, or I. We
choose D at $2,000. Total cost for the project shortened three weeks is
97,000.
If you do not compute cost/week correctly, I took 3 points off.
3) For the network and the data shown:
12
D
10
7
B
G
6
10
6
A
E
I
8
9
C
H
14
F
a. Determine the critical path and the early completion time for the project. (5
points)
A-C-F-H-I, 43 weeks, 6+8+14+9+6.
b. Reduce the project completion time by four weeks. Assume a linear cost per day
shortened and show, step by step, how you arrived at your schedule. Also indicate
the critical path in each step. (10 points)
Activity
A
B
C
D
E
F
G
H
I
Normal
Time
(weeks)
6
10
8
12
10
14
7
9
6
Normal
Cost ($)
6,000
10,000
8,000
12,000
10,000
14,000
7,000
9,000
6,000
Crash
Time
(weeks)
4
9
7
10
7
12
5
6
5
Crash
Cost ($)
12,000
11,000
10,000
14,000
12,000
19,000
10,000
15,000
8,000
Activity
Normal
Time (NT)
Normal Cost
(NC)
Crash Time
(CT)
Crash Cost
(CC)
NT-CT
Cost/week
to expedite
A
6
$6,000
4
$12,000
2
$3,000
B
10
10,000
9
11,000
1
1,000
C
8
8,000
7
10,000
1
2,000
D
12
12,000
10
14,000
2
1,000
E
10
10,000
7
12,000
3
667
F
14
14,000
12
19,000
2
2,500
G
7
7,000
5
10,000
2
1,500
H
9
9,000
6
15,000
3
2,000
I
6
6,000
5
8,000
1
2,000
Step
Activity
Cost to crash
Weeks reduced
Critical Path(s)
1
I
$2,000
1
A-C-F-H-I
2
C
2,000
1
A-C-F-H-I
3
H
2,000
1
A-C-F-H-I, and
A-B-D-G-I
4
H and D
3,000
1
A-C-F-H-I, and
A-B-D-G-I
$9,000
4
Total cost
There are other ways to achieve this total cost, too.
If you do not compute cost/week correctly, I took 3 points off.