Question

The following table lists the activities needed to complete a project. The first column lists the activities and the “follows” column shows which other activity or activities, (if any), must be completed before these activities can start. The remaining columns give three estimates of the activity duration; the mean duration calculated from these estimates and standard deviation assuming a beta distribution of activity duration.

Activity

Follows

Estimates of durations (days) Optimistic Most likely Pessimistic

A	--	3	6	15
B	A	8	14	26
C	A	1	2	9
D	B	2	5	14
E	C	5	7	21
F	D	2	4	12
G	B, E	6	9	18
H	F	1	3	5
I	D, G	2	3	10
J	G	5	7	15

a) Calculate mean duration and standard deviation for all activities using the beta distribution. (4 points)
  
b) Construct a network diagram for this problem using the mean durations calculated in part (a), calculate the ES (Prec.), LS(Foll.) and the total float for all the activities, and hence identify the critical path . What is the mean completion time for the project? What is the standard deviation of the critical path? (3 0 points)
  
c) What is the 99% confidence interval for the length of the critical path? (4 points)
  
d) Assuming that the probability distribution of the length of the critical path can be approximated by a normal distribution with the mean and standard deviation calculated in part (b), calculate the probability of completing the project within 34 days . (4 points)
  
e) What is the probability that the project will be completed between 38 and 45 days? Show your workings! (4 points)
  
f) Answer the project manager’s question:
“I want to tell the client a project length which I am 89.97% sure that we can meet _- What figure should I give them?" (4 points)

Answer 1