04.07.2022 - 05:58

# A small project consisting of eight activities has the following characteristics: (TABLE) a) Draw the PERT network for the project. b) Prepare the activity schedule for the project. c) Determine the critical path. d) If a 30-week deadline is imposed, w

Question:

A small project consisting of eight activities has the following characteristics:

Time – Estimates (in weeks)

Activity Preceding Activity Most optimistic time (a) Most likely time (m) Most pessimistic time (b)
A None 2 4 12
B None 10 12 26
C A 8 9 10
D A 10 15 20
E A 7 7.5 11
F B, C 9 9 9
G D 3 3.5 7
H E, F, G 5 5 5

a) Draw the PERT network for the project.

b) Prepare the activity schedule for the project.

c) Determine the critical path.

d) If a 30-week deadline is imposed, what is the probability that the project will be finished within the time limit?

• April 5, 2023 в 07:34
a) The PERT network for the project is:
     2     4     12
---(A)--------
|              |
|              |
10     12     26
|           /
|          /
|       (B)
|      /   |
|     /    |
|    /     |
|   /      |
| /        |
|/         |
(C)        (D)          3     3.5      7
|        /          /              /
|       /          /              /
|      /           /            (G)
|     /           /              |
|    /           /              |
|    (F)         /               |
|    /         /                |
7.5 /         /                  |
|/         /                    |
(E)      (H)                      5

b) The activity schedule for the project is:
Activity   |  A  |  B  |  C  |  D  |  E  |  F  |  G  |  H  |
-------------------------------------------------------------
Earliest   |  2  | 10  | 10  | 15  |  7  | 19  | 15  | 24  |
Start      |     |     |     |     |     |     |     |     |
-------------------------------------------------------------
Latest     |  2  | 10  | 10  | 15  |  7.5| 19  | 18.5| 24  |
Finish     |     |     |     |     |     |     |     |     |
-------------------------------------------------------------
Slack      |  0  |  0  |  0  |  0  |  0.5|  0  |  3  |  0  |
-------------------------------------------------------------

c) The critical path is A-C-F-H, with a duration of 24 weeks. d) To find the probability that the project will be finished within the 30-week deadline, we need to determine the project variance, which is the sum of the variances of the activities on the critical path. The variance of an activity is (b-a)^2/36, where a is the most optimistic time, b is the most pessimistic time, and 36 is the square of the expected time (m). For activity A, the variance is (12-2)^2/36 = 1.78. For activity C, the variance is (10-8)^2/36 = 0.06. For activity F, the variance is (9-9)^2/36 = 0. For activity H, the variance is (5-5)^2/36 = 0. The project variance is the sum of these variances, which is 1.84. The standard deviation of the project is the square root of the variance, which is 1.36. To find the probability that the project will be finished within 30 weeks, we need to find the z-score for 30 weeks, using the formula z = (30 - 24)/1.36 = 4.41. Using a z-table, we find that the probability of a z-score of 4.41 or higher is very close to 0. Therefore, the probability that the project will be finished within the 30-week deadline is very low.