# h - BUSI 403 Problem Set H Solution Fall 2008 Due Problem 1...

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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 A-D-E-F-G-H-J. 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 A-C-G-I-J. 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 A-C-G-I-J and A-B-H-J, 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 A-C-G-I-J. However, this is not a viable alternative since this will not change the duration of A-B-H-J; the project duration will still be 18 months with A-B-H-J 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: A-B-H-J and A-C-G-I-J. 3 ...
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