Jeffrey P. Morris
Homework Set 4
ISQS 5343: Operations Management and Management Science
Section 1
4/30/2010
Homework Set 4
April 30, 2010
Table of Contents
Question 1 ..................................................................................................................................................... 3
Question 2 ..................................................................................................................................................... 4
Question 3 ..................................................................................................................................................... 4
Question 4 ..................................................................................................................................................... 5
Question 5 ..................................................................................................................................................... 6
Question 6 ..................................................................................................................................................... 8
Question 7 ..................................................................................................................................................... 8
Page 2
Homework Set 4
April 30, 2010
Question 1
A
B
C
D
E
F
G
H
1
9
Duration
ES
EF
LS
LF
Slack
9
8
12
10
11
6
9
5
1
10
10
18
22
33
33
42
9
17
21
27
32
38
41
46
1
15
10
23
22
36
33
42
9
22
21
32
32
41
41
46
0
5
0
5
0
3
0
0
9
10
8
A
0
9
10
12
21
100
200
300
400
300
200
100
3
6
8
6
9
4
8
17
15
5
22
18
C
0
$
$
$
$
$
$
$
B
1
10
Crash Cost Min Duration
10
D
21
23
22
27
11
5
32
32
E
22
0
32
33
9
41
G
33
6
33
0
41
42
5
46
38
F
Early Start
Duration
Early Finish
36
3
41
Task Name
Late Start
Slack
Late Finish
H
42
0
You find the critical path by looking where there is no slack. Therefore, the critical path is: ACEGH.
Page 3
46
Homework Set 4
April 30, 2010
Question 2
Duration
A
B
C
D
E
F
G
H
Critical Path Duration
Budget
$
9
8
12
10
11
6
9
5
46
1,100
Crash A
6 days
Crash G
1 day
Crash C
1 day
3
8
12
10
11
6
9
5
40
3
8
12
10
11
6
8
5
39
3
8
11
10
11
6
8
5
38
$
500
$
400
$
100
Question 3
You find the critical path by looking where there is no slack. Therefore, the path is: A-C-F-G-H
Standard Deviation: 2.2361
Probability finishes in 20 days: 1.27%
Probability finishes in 25 days: 50.00%
Probability finishes in 30 days: 98.73 %
Page 4
Homework Set 4
April 30, 2010
Question 4
To find the ES, EF, LS and LF for each activity, we used the “Most Likely Time”, which is the middle time
for duration. Below are the results:
Duration
ES
EF
LS
LF
Slack
8
10
5
3
3
6
4
1
1
1
8
10
13
13
19
23
8
10
13
13
16
19
23
24
1
1
8
10
20
13
19
23
8
10
13
13
23
19
23
24
0
0
0
0
7
0
0
0
A
B
C
D
E
F
G
H
1
8
8
13
3
A
1
0
16
Early Start
E
8
20
8
5
Duration
Task Name
7
23
Late Start
Slack
13
23
1
24
C
H
8
0
13
23
19
1
10
10
0
23
F
B
1
6
19
0
23
10
10
3
13
D
19
10
0
4
23
13
G
19
Page 5
Early Finish
0
23
0
24
Late Finish
Homework Set 4
April 30, 2010
Question 5
Page 6
Homework Set 4
April 30, 2010
The total project duration will be 68 days at a cost of $43,120.
It makes sense to include a summary task at the top of your tasks, as it will provide a convenient
way to see a complete summary of the entire project. For example, you can see that the total cost of the
project is listed and the total project duration. Without the summary task, you would need to compute
these figures manually.
Summary tasks have no duration stated in the chart, as the duration is exactly as the name
indicates, a summary of all the tasks under that item. For example, you can see the Design summary task
has six subordinate tasks immediately under the summary task. This way, the total cost and duration can
be calculated for those series of subordinate tasks.
The first subordinate task immediately below a summary task has no predecessor because the
summary task will contain the predecessor for the previous task. That way, all the items in the summary
task will start after the previous task is finished. Once you move on to a summary task, MS Project then
assumes that you will start the first subordinate task to that particular summary task.
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Homework Set 4
April 30, 2010
Question 6
Task
Budget
% Complete
A
B
C
D
E
F
G
BAC
EAC
TAC
ETAC
$
8,000
$
9,600
$
9,000
$
6,000
$
13,500
$
9,000
$
4,800
$ 59,900.00
$ 68,850.57
30
17.14
100%
100%
30%
20%
40%
0%
0%
ACWP
$
$
$
$
$
$
$
$
10,000
9,000
4,000
5,000
3,000
31,000
BCWS
$
$
$
$
$
$
$
$
8,000
2,400
2,000
3,000
15,400
BCWP
$
$
$
$
$
$
$
$
8,000
9,600
2,700
1,200
5,400
26,900
CV
SV
SPI
CPI
7,200
700
(1,800)
5,400
11,500
1.00
4.00
1.35
0.40
1.75
0.80
1.07
0.68
0.24
1.80
0.87
CV
SV
SPI
CPI
$ (2,000)
$
600
$ (1,300)
$ (3,800)
$ 2,400
$
$
$ (4,100)
$
$
$
$
$
$
$
$
The ETAC tells us that the project is ahead of schedule. The EAC tells us that the project is over budget.
Question 7
Task
A
B
C
D
E
F
BAC
EAC
TAC
ETAC
Budget
$
$
$
$
$
$
7,000
10,800
7,000
9,000
13,500
5,000
$ 52,300.00
$ 45,877.19
30
27.78
% Complete
100%
100%
80%
90%
20%
0%
ACWP
BCWS
BCWP
$
$
$
$
$
$
9,000
9,000
4,000
5,000
3,000
-
$
$
$
$
$
$
7,000
10,800
5,000
4,500
4,500
-
$
$
$
$
$
$
7,000
10,800
5,600
8,100
2,700
-
$ (2,000)
$ 1,800
$ 1,600
$ 3,100
$ (300)
$
-
$
$
$
600
$ 3,600
$ (1,800)
$
-
1.00
1.00
1.12
1.80
-
0.78
1.20
1.40
1.62
0.90
-
$
30,000
$
31,800
$
34,200
$ 4,200
$ 2,400
1.08
1.14
The ETAC tells us that the project is ahead of schedule. The EAC tells us that the project is under budget.
Page 8