Develop a project network for this problem b Determine the c

Develop a project network for this problem.
b- Determine the critical path for the campaign project and the expected project completion time. (Use the
expected time for the activity completion time).
c- Determine the probability that the project will be completed in less than 34 days.
d- Determine the probability that the project will take more than 29 days

Solution

Let us consider the below network diagram for which completion time is calculated :

Activity

Predecessor

Optimistic Estimates (Days)

Most Likely Estimates (Days)

Pessimistic Estimates (Days)

Expected Duration

(a+4b+c)

6

Variance

((b-a)/6)2

A

None

1

2

4

2.2

0.3

B

A

3

5

8

5.2

0.7

C

B

2

4

5

3.8

0.3

D

B

2

3

6

3.3

0.4

E

B

1

1

1

1.0

0.0

F

C,D

2

4

6

4.0

0.4

G

D,E

2

3

4

3.0

0.1

H

F,G

1

2

5

2.3

0.4

I

G

4

5

9

5.5

0.7

J

H,I

.5

1

3

1.3

0.2

Possible Paths

Path

Total

Path 1

A+B+C+F+H+J

18.8

2.2+5.2+3.8+4.0+2.3+1.3

Path 2

A+B+D+F+H+J

18.3

2.2+5.2+3.3+4.0+2.3+1.3

Path 3

A+B+D+G+H+J

18.6

2.2+5.2+3.3+3.0+2.3+1.3

Path 4

A+B+D+G+I+J

20.5*

2.2+5.2+3.3+3.0+5.5+1.3

Path 5

A+B+E+G+I+J

18.2

2.2+5.2+1.0+3.0+5.5+1.3

Critical Path is 20.3

Project Variance= Sum of variances of activities on the critical path

We know the standard deviation is just the square root of the variance

Project Standard Deviation = sqrt(2.4)=1.55

The project’s expected completion date is 20.5 weeks

Probability of Project Completion:

Z= Due Date - Expected Date of Completion/Standard Deviation

=22-20.5/1.55 =0.967

therefore Z= 83.33%

That means there is a 83.3% probability this project can be completed in 22 weeks or less

* Please Note : It is an assumed example of network analysis since question does not provide network diagram data

Activity	Predecessor	Optimistic Estimates (Days)	Most Likely Estimates (Days)	Pessimistic Estimates (Days)	Expected Duration (a+4b+c) 6	Variance ((b-a)/6)2
A	None	1	2	4	2.2	0.3
B	A	3	5	8	5.2	0.7
C	B	2	4	5	3.8	0.3
D	B	2	3	6	3.3	0.4
E	B	1	1	1	1.0	0.0
F	C,D	2	4	6	4.0	0.4
G	D,E	2	3	4	3.0	0.1
H	F,G	1	2	5	2.3	0.4
I	G	4	5	9	5.5	0.7
J	H,I	.5	1	3	1.3	0.2