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Unformatted text preview: BUSI 403 Problem Set H Solution Fall 2008 Due: 11/18/08 Problem 1
a. Network diagram
B(8) A(2) G(5) H(4) F(3) C(3) J(2) E(5) I(8) D(4) b. Earliest Start(ES), Earliest Finish(EF), Latest Finish(LF), and Latest Start(LS)
Using the algorithm given in class slides, we can obtain the Earliest Start, Earliest Finish, Latest
Finish, and Latest Start times as shown in the following table. Slack values are also provided in the
table and will be used in parts c) and d).
A B C D E F G H I J Duration 2 8 3 4 5 3 5 4 8 2 Earliest Start 0 2 2 2 6 11 14 19 14 23 Earliest Finish 2 10 5 6 11 14 19 23 22 25 Latest Finish 2 11 6 6 11 14 19 23 23 25 Latest Start 0 3 3 2 6 11 14 19 15 23 Slack 0 1 1 0 0 0 0 0 1 0 c. Critical path(s)
Since a critical path is formed by all activities with 0 slack values, and the slack values for each
activity are calculated in the table from part b), we can see that the critical path is ADEFGHJ.
The finish time for the last activity (activity J) in the critical path is month 25. So the length of the
project is 25 months.
d. Slack for each activity
The slack vales are given from the table in part b).
A
Slack B C D E F G H I J 0 1 1 0 0 0 0 0 1 0 1 BUSI 403 Problem Set H Solution Fall 2008 Due: 11/18/08 Problem 2
a. Crashing the project
The critical path for the initial plan is ACGIJ. On the critical path, activity C has the lowest crashing
cost. So the most economical way to crash the project is to crash activity C by 1 month. The following
is the diagram after crashing activity C by a month. 3
3 H(9) 6
6 B (3) 6
9 6
6 9
12 15
15 E(3)
0
0 3
3 3
3 A (3) ES EF LS LF 10
10 C(7) 3
5 8
10 D (5) 6
8 15
15 12
12 10
12 15
15 18
18 J(3) I (3) F(4)
10
10 12
12 G(2) After crashing activity C by 1 month, the critical paths are ACGIJ and ABHJ, and project duration
becomes 18 months. Since there are 2 critical paths, we can either crash an activity that is common
to both paths or crash 2 activities, one from each path. Note that crashing activity C is the most
economical way to crash the duration of the critical path ACGIJ. However, this is not a viable
alternative since this will not change the duration of ABHJ; the project duration will still be 18
months with ABHJ being the critical path. Here are the possible alternatives to shorten the project
duration by another month (activities H and J cannot be crashed):
Crash A with cost $400
Crash B and C with cost $300+$200=$500
Crash B and G with cost $300+$300=$600
Crash B and I with cost $300+$400=$700
The most economical way to crash by one more month is to crash activity A, which is cheaper than
any other alternative. The following is the diagram after crashing activity A by a month 2 BUSI 403 Problem Set H Solution Fall 2008 Due: 11/18/08 2
2 H(9) 5
5 B (3) 5
8 5
5 8
11 14
14 E(3)
0
0 2
2 2
2 A (2) ES EF LS LF 9
9 5
7 C(7) 2
4 7
9 D (5) 14
14 11
11 9
11 14
14 17
17 J(3) I (3) F(4)
9
9 11
11 G(2) Therefore, to crash the project duration by 2 months, we first crash activity C by 1 month and then
crash activity A by 1 month.
The total cost of crashing:
Activity C crashing by 1 month = $200
Activity A crashing by 1 month = $400
Total crashing cost = $600
b. Critical path after crashing
The new critical paths are: ABHJ and ACGIJ. 3 ...
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 Fall '08
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