Question

The following information relates to a project​ (task times are in​ weeks). Use the information to solve for the critical path and then to determine the probability that the project could be completed within 26 weeks.

Task Preceding Task to tm tp

a none 3 5 7

b a   4 7 10

c a 3 5 7

d b 6 9 12

e c 3 7 11

f d,e 3 4 5

The probability that the project is completed within 26 weeks is?

Answer 1

Solution:

Please find the solution below,

TE = (to + 4*tm + tp)/6

And

Hence,

Hence, The critical path is ABDF, as shown below.

And the Variance of Critical path activities is, (it is calculated by the sum of variances of activities A, B, D, and F -- The critical path activities.)

Now, the probability of completing the project within 26 weeks is calculated by the formula given below.

First, calculate the Z value and use the Z value to calculate the required probability.

Given,

--> Critical path.

Hence, the probability is 0.734 of completing the project within 26 weeks.