Question
Doug Casey is in charge of planning and coordinating next spring’s sales management training program for his company. Doug listed the following activity information for this project: Draw a project network. Prepare an activity schedule. What are the critical activities and what is the expected project completion time? If Doug wants a 0.99 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project ?
Answer
The network diagram as per the question
(b)
- Activity Schedule
| Activity | Optimistic (O) | Most Probable (M) | Pessimistic (P) | Expected Time (O + 4M + P)/6 | Variance [(P – O)/6]2 |
| A | 1.5 | 2.0 | 2.5 | 2 | 0.03 |
| B | 2.0 | 2.5 | 6.0 | 3 | 0.44 |
| C | 1.0 | 2.0 | 3.0 | 2 | 0.11 |
| D | 1.5 | 2.0 | 2.5 | 2 | 0.03 |
| E | 0.5 | 1.0 | 1.5 | 1 | 0.03 |
| F | 1.0 | 2.0 | 3.0 | 2 | 0.11 |
| G | 3.0 | 3.5 | 7.0 | 4 | 0.44 |
| H | 3.0 | 4.0 | 5.0 | 4 | 0.11 |
| I | 1.5 | 2.0 | 2.5 | 2 | 0.03 |
(c) Critical Activities as per given data
| Activity | Earliest Start | Latest Start | Earliest Finish | Latest Finish | Slack | Critical Activity |
| A | 0 | 0 | 2 | 2 | 0 | Yes |
| B | 2 | 2 | 5 | 5 | 0 | Yes |
| C | 0 | 1 | 2 | 3 | 1 | |
| D | 2 | 3 | 4 | 5 | 1 | |
| E | 5 | 10 | 6 | 11 | 5 | |
| F | 6 | 11 | 8 | 13 | 5 | |
| G | 5 | 5 | 9 | 9 | 0 | Yes |
| H | 9 | 9 | 13 | 13 | 0 | Yes |
| I | 13 | 13 | 15 | 15 | 0 | Yes |
Therefore the critical path will be A-B-G-H-I-Finish
Expected Completion time= 2 + 3 + 4 + 4 + 2 = 15 weeks
(d) Variance of critical path will be the sum of variances of all the critical activities, that is
σ2 = 0.03 + 0.44 + 0.44 + 0.11 + 0.03 = 1.05
In Probability Distribution Table, we find 0.99 probability occurs at the value of
z = +2.33.
Z= T-E(T)/ σ
= (T-15) / (1.05)1/2
= 2.23
Or
T= 15 + 2.23* (1.05)1/2
=17.4 weeks
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