2+2+2+2+2) A construction company has a project proposal, which takes 8 activiti

Question

2+2+2+2+2) A construction company has a project proposal, which takes 8 activities as follows: Activity Duration Time (In DAYS ) Activity Predecessors Optimistic Most Likely Pessimistic Not Available 14 1.7778 12 10 0.4444 Not Available Not Available Not Available 10 Not Available Not Available Not Available Not Available 0.4444 0.4444 4 The Critical Path is: START >A-C>EG END + a) b) c) Supply the missing values on the above table. Based on the critical path, what is the expected duration in days to complete this project? What is the probability that the project will be completed within: 20 days? 25 Days? d) Determine the number of days required to assure at least 97% chance of completing the project.

Explanation / Answer

(a)
We know that, E(d) = (a+4m+b)/6
For activity G,
E(Duration) = (4 + 4*6 + 8)/ 6 = 6

SD(duration) = (b-a)/6
For activity E,
SD(duration) = (11-5)/6 = 1
Var(duration) = 1*1 = 1

(b)
Given the critical path is A, C, E, G
So, the expected duration to complete the project = E(A) + E(C) + E(E) + E(G)
= 8 + 3 + 6 + 6 = 23 days

(c)
Var(duration) = Var(A) + Var(C) + Var(E) + Var(G)
= 1.7778 + 0.1111 + 1 + 0.4444 = 3.3333
SD(duration) = sqrt(3.3333) = 1.8257
(i) For x = 20 days
z = (20 - 23) / 1.8257 = -1.6432

So using z table, probability that project will be completed within 20 days is 0.0502

(ii) For x = 25 days
z = (25 - 23) / 1.8257 = 1.0955

So using z table, probability that project will be completed within 25 days is 0.8633

(d)
Let the probability that project will be completed within x days is 0.97
z value for p=0.97 is 1.8808

So, z = (x - 23) / 1.8257 = 1.8808
x = 23 + 1.8257 * 1.8808 = 26.4338 days

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