Question

2. An automation project has the following activities and related data: Crash Maximum Immed. Time (weeks Activity Prede- Most Pessi. cessors mistic (a) Likely (m) mistic (k) ($1000) Mean Variance Cost week Crashable Weeks 15 C, D, E 2 2a (20 points) Compute the mean and variance of each activity and record them on the table above. 2b. (40 points) Develop the PERT diagram and identify critical

Answer 1

2a. The mean and the variance are given by the formulas as follows: Mean: а+4m+3 Variance (bo Now, calculating the mean and the variance for the following activities as follows: Variance Activity Α Ι A 1+(4x3)+11_ , 1+(4x2)+11_4 Mean 1+(4x3) +11 1+(4x3) +11_ [11-11-2.78|11-11-2 0.11 0.11 1.78 1.78 5.44 0.44 0.11

2b. The PERT diagram for the network can be designed as follows: In a PERT diagram node are represented by numeric digits, and activities are represented on the edges. The PERT diagram for the given network is given as follows: 22 Q3 B(5) Figure 1.

Figure 1 shows that network has multiple critical paths given as follows: • • • 1-2-4-6 = 14 1-3-4-6 = 14 1-3-5-6 = 12 There are two critical paths with maximum duration 14. 2c. The standard deviation of project completion is given as: Standard Deviation=/Variance = 12.55 = 3.543 Therefore, the standard deviation for the given project is 3.543 2d. P(X < 7537) = 0.45 I-37 = 36.55 12.55 712 55 =T = 166.48 Therefore, probability to complete the project before T is 166.48 weeks.