Question

Activity	Optimistic Time Estimate (weeks)	Most Likely Time Estimates (weeks)	Pessimistic Time Estimates (weeks)	Immediate Predecessor(s)
A	3	6	9	none
B	3	5	7	A
C	4	7	12	A
D	4	8	10	B
E	5	10	16	C
F	3	4	5	D, E
G	3	6	8	D, E
H	5	6	10	F
I	5	8	11	G
J	3	3	3	H, I

A.)Using the information given, construct a network diagram using AON notation.

B.) Using the information given, calculate the expected time for each of the project activities.

C.) Using the information given, calculate the variance for each of the project activities.

D.) Using your results from Problems B and C, Calculate the completion time for this project.

E.) Identify the activities included on the critical path of this project.

F.) Using your results from Problem D and E, Calculate the probability that the project will be completed in 38 weeks.

G.) Calculate the probability that the project will be completed in 42 weeks.

Answer 1

A.)Using the information given, construct a network diagram using AON notation.

B.) Using the information given, calculate the expected time for each of the project activities.

Expected time =( Optimistic Time + 4 (most likely Time) + the pessimistic time) / 6

EG for A

=(3+4(6)+9)/6 =6

Activity	Optimistic Time Estimate	Most Likely Time Estimates (weeks)	Pessimistic Time Estimates (weeks)	Expected time=(Optimistic Time + 4 (most likely Time) + the pessimistic time) / 6
	(weeks)
A	3	6	9	6.00
B	3	5	7	5.00
C	4	7	12	7.33
D	4	8	10	7.67
E	5	10	16	10.17
F	3	4	5	4.00
G	3	6	8	5.83
H	5	6	10	6.50
I	5	8	11	8.00
J	3	3	3	3.00

C.) Using the information given, calculate the variance for each of the project activities.

Variance for each activity =(( Pessimistic time – optimistic time)/ 6)²

EG for A

=((9-3)/6) ²=1

Activity	Optimistic Time Estimate	Most Likely Time Estimates (weeks)	Pessimistic Time Estimates (weeks)	Variance for each activity=((p-o)/6)^2
	(weeks)
A	3	6	9	1.00
B	3	5	7	0.44
C	4	7	12	1.78
D	4	8	10	1.00
E	5	10	16	3.36
F	3	4	5	0.11
G	3	6	8	0.69
H	5	6	10	0.69
I	5	8	11	1.00
J	3	3	3	0.00

D.) Using your results from Problems B and C, Calculate the completion time for this project.

Expected project completion time is determined by the critical path –

Critical Path = longest connected path in the network

PATHS                                  

ABDFHJ-                6+5+7.67+4+6.5+3 =                           32.17 weeks

ABDGIJ -               6+5+7.67+5.83+8+3=                          35.5 weeks

A CEFHJ-                6+7.33+10.17+4+6.5+5=                      39 weeks

ACEGIJ   -               6+7.33+10.17+5.83+8+3=                    40.33 weeks

Critical Path = longest connected path in the network = ACEGIJ =40.33 weeks

Expected completion time for the project, E(t)= 40.33

E.) Identify the activities included on the critical path of this project.

ACEGIJ

F.) Using your results from Problem D and E, Calculate the probability that the project will be completed in 38 weeks.

D=38 weeks

Expected completion time for the project, E(t)= 40.33

Variance of the project

= sum of the variances of the activities in critical path

=

= 1+1.78+3.36+0.69+1+0

=7.83

Z score

=( specified time – path expected completion) / path standard deviation

= (38-40.33)/ ?(7.83)

=   -0.83

Using a standard distribution , we find that a Z value of   - 0.87 yields a probability of 0.2033, which means that probability of completing the project in 38 weeks is 20.33%

G.) Calculate the probability that the project will be completed in 42 weeks.

D=42 weeks

E(t)= 40.33

Variance of the project

= sum of the variances of the activities in critical path

= 1+1.78+3.36+0.69+1+0

=7.83

Z= (42-40.33)/ ?(7.83) =   0.60

Using a standard distribution, we find that a Z value of 0.60 yields a probability of 0.7257, which means that probability completing the project in 42 weeks 72.57%