25 May Question .101 Given the network shown in Figure 13-1 and the follo
Question
.101 Given the network shown in Figure 13-1 and the following information, what is the variance of the critical path?
| Activity | Expected time | Variance |
| A | 3 | 2 |
| B | 5 | 3 |
| C | 6 | 3 |
| D | 4 | 1 |
| E | 4 | 1 |
| F | 4 | 2 |
| G | 6 | 2 |
| H | 7 | 2 |
(a) 16
(b) 7
(c) 9
(d) 8
(e) none of the above
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PROBLEMS
13.102 Given:
| Activity | Optimistic | Most Likely | Pessimistic |
| A | 3 | 4 | 5 |
| B | 6 | 7 | 14 |
| C | 6 | 9 | 12 |
| D | 0.5 | 1 | 1.5 |
| E | 2 | 3 | 10 |
| F | 4 | 5 | 12 |
| G | 1 | 3 | 11 |
 |
Determine:
(a) the critical path.
(b) the probability that the project will be completed in 22 weeks.
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13.103 A small software development project has five major activities. The times are estimated and provided in the table below.
| Activity | Immediate
Predecessor |
a | m | b |
| A | – | 2 | 5 | 8 |
| B | – | 10 | 10 | 10 |
| C | A | 4 | 7 | 10 |
| D | B | 2 | 5 | 14 |
| E | C | 3 | 3 | 3 |
(a) What is the expected completion time for this project?
(b) What variance would be used in finding probabilities of finishing by a certain time?
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13.104 Development of a new deluxe version of a particular software product is being considered. The activities necessary for the completion of this are listed in the table below.
| Activity | Normal Time | Crash Time | Normal Cost | Crash Cost | Immediate
Predecessor |
| A | 4 | 3 | 2000 | 2600 | – |
| B | 2 | 1 | 2200 | 2800 | – |
| C | 3 | 3 | 500 | 500 | – |
| D | 8 | 4 | 2300 | 2600 | A |
| E | 6 | 3 | 900 | 1200 | B |
| F | 3 | 2 | 3000 | 4200 | C |
| G | 4 | 2 | 1400 | 2000 | D,E |
(a) What is the project completion date?
(b) What is the total cost required for completing this project on normal time?
(c) If you wish to reduce the time required to complete this project by one week, which activity should be crashed, and how much will this increase the total cost?
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13.105 Draw the PERT network associated with the following activities.
| Immediate Predecessor | |
| A | – |
| B | A |
| C | A |
| D | B |
| E | B |
| F | C, E |
| G | A, D |
| H | F |
| I | F |
| J | G, H, I |
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