Question

PERT

Consider the following table:

Activity	Prec. Act	t0	tml	tp	te
A	-	3	4	5	4
B	-	5	8	11	8
C	A	1	2	3	2
D	B	2	5	8	5
E	B	4	6	8	6
F	C,D	1	1	1	1
G	E	3	4	5	4
H	G,F	2	3	4	3

1) Construct a PERT network.

[NOTE: This is the most crucial part of the exercise. Make sure you have the correct network before proceeding to the next sections.]

2) By using ES, EF, LF, LS, find the slack of each activity and the critical path.

3) Find the completion time and the standard deviation (σ) for the project— round off the standard deviation to the nearest hundredth: two decimal places.  

4) What is the completion time at 95% and 99% confidence levels?

5) What is the likelihood of this project being completed earlier than 20 days?

5) Between 21 and 23 days?

Answer 1

Task	O	M	P	Te	Var^0.5	Variance
A	3	4	5	4	0.333333	0.111111
B	5	8	11	8	1	1
C	1	2	3	2	0.333333	0.111111
D	2	5	8	5	1	1
E	4	6	8	6	0.666667	0.444444
F	1	1	1	1	0	0
G	3	4	5	4	0.333333	0.111111
H	2	3	4	3	0.333333	0.111111

Activity	ES	EF	LS	LF	SLACK
A	0	4	11	15	11
B	0	8	0	8	0
C	4	6	15	17	11
D	8	13	12	17	4
E	8	14	8	14	0
F	13	14	17	21	4
G	14	18	14	18	0
H	18	21	18	21	0

Critical path is BEGH with duration 21

Variance of critical path =1.6666

SD of critical path = (1.6666)^0.5 =1.29

Completion time at 95% confidence i given by

z = T-Mean/SD = T- 21/1.29

1.645 = T-21/1.29

T=22.665

Completion time at 99% confidence is given by

2.33 = T-21/1.29

T = 24

Note: As per policies, I can answer first 4 parts of a question. Inconvenience is regretted.