A project network is shown below, with three time estimates (Optimistic Time-Mos

Question

A project network is shown below, with three time estimates (Optimistic Time-Most Likely Time- Pessimistic Time (in weeks)) for each activity in the network. 2-3-7 2-5-8 1-3-8 0-0-0 2-4-6 0-0-0 Start End 2-5-11 2-6-13 1-4-10 a. Compute the expected time for each activity in the project network. b. Identify and list all possible paths in the project network. Compute the expected duration for each c. d. e. path in the project network. Identify the critical path. What is the expected project completion time? Compute the variance of each activity on the critical path. Determine the project variance and project standard deviation. Use the PERT analysis results in (c) and (e) to answer questions (f), (g), (h), and (i) below: f. What is the probability that the project can be completed within 20 weeks of its start? h. i. What is the probability that the project can be completed within 11 weeks of its start? Determine the project deadline that gives this project a 59% chance of on-time completion Determine the project deadline that gives this project a 13% chance of on-time completion

Explanation / Answer

Solution :

A :

B : Paths

ADF - 12, BDF - 12.5, BEG - 16 and CEG - 16.5

C : Critical Path : CEG with expected duraiton 16.5

D : Variance of each activity as per table in solution of (A)

E : Project variance : 7.86 and Standard deviation : 2.8

F : Prob (Complete in 20 Weeks), Z = (20-16.5)/2.8 = 1.25. Prob (Complete in 20 Weeks) = 89.40%

G : Prob (Complete in 11 Weeks), Z = (11-16.5)/2.8 = -1.96. Prob (Complete in 11 Weeks) = 2.48%

H : Duration where Probability of completing is 59% Z = 0.2275. 0.2275 = (X-16.5)/2.88 X = 17.13 weeks

I : Duration where Probability of completing is 11% Z = -01.22. -2.22 = (X-16.5)/2.88 X = 13.06 weeks

Activity Immediate Predecessors Optimistic Time (a) Probable Time (m) Pessimistic Time (b) Mean Time (a+4m+b)/6 Variance (b?a)2/36 ES EF LS LF Slack A -- 2 3 7 3.50 0.69 0.00 3.50 4.50 8.00 4.50 B -- 2 4 6 4.00 0.44 0.00 4.00 0.50 4.50 0.50 C -- 1 4 10 4.50 2.25 0.00 4.50 0.00 4.50 0.00 D A, B 2 5 8 5.00 1.00 3.50 8.50 8.00 13.00 4.50 E B, C 2 5 11 5.50 2.25 4.50 10.00 4.50 10.00 0.00 F D 1 3 8 3.50 1.36 8.50 12.00 13.00 16.50 4.50 G E 2 6 13 6.50 3.36 10.00 16.50 10.00 16.50 0.00

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