Question

ACTIVITY	IMMEDIATE PREDECESSORS	OPTIMISTIC TIME	MOST LIKELY TIME	PRESSMISTIC TIME
A	-	1	2	4
B	-	3	3.5	4
C	-	10	12	12
D	-	4	5	7
E	-	2	4	5
F	A	6	7	8
G	B	2	4	5.5
H	C	5	7.7	9
I	C	9.9	10	12
J	C	2	4	5
K	D	2	4	6
L	E	2	4	6
M	F,G,H	5	6	6.5
N	J,K,L	1	1.1	2
O	I,M	5	7	8
P	N	5	7	9

 

 

Q1.draw an activity network diagram showing es, ef, ls and lm?

Q2.calculate estimated time t and variance for each activity?

Q3 .calculate the project completion time and project variance?

Q4.determine the number of paths associated with the network diagram?

 Q5.find out the critical path?

Q5.you as a manager would like to determine the project completion time, so what is the probability of this project being done in 63 days.?

Q6.what date results in a 99% probability of completion?

 

Answer 1

Step 1:

Completion Time(t) = (a+4m+b)/6

Activity	Immediate Predecessor	Completion Time (t) in Weeks
A		12
B		10
C		5
D	A	8
E	B	3
F	C	4
G	C	4
H	A,E,F	8
I	A,E,F	10
J	D	8
K	G,H,I	6

So Activities on the critical path are- B-E-I-K.

Expected Duration of the project is =10+3+10+6 = 26 weeks

Step 2:

Completion Time(t) = (a+4m+b)/6

Standard Deviation (σ) = (b-a)/6

Variance (σ^2) = (σ)^2

Slack = LS-ES (or) LF-EF

Activity	Immediate Predecessor	Optimistic (a)	Most Likely (m)	Pessimistic (b)	Completion Time (t)	Standard Deviation (σ)	Variance (σ^2)	ES	EF	LS	LF	Slack	CP Variance
A		6	12	18	12	2.00	4.00	0	12	1	13	1
B		5	10	15	10	1.67	2.78	0	10	0	10	0	2.78
C		2	5	8	5	1.00	1.00	0	5	4	9	4
D	A	2	8	14	8	2.00	4.00	12	20	13	21	1
E	B	2	3	4	3	0.33	0.11	10	13	10	13	0	0.11
F	C	3	4	5	4	0.33	0.11	5	9	9	13	4
G	C	2	4	6	4	0.67	0.44	5	9	19	23	14
H	A,E,F	3	8	13	8	1.67	2.78	13	21	15	23	2
I	A,E,F	2	10	18	10	2.67	7.11	13	23	13	23	0	7.11
J	D	2	8	14	8	2.00	4.00	20	28	21	29	1
K	G,H,I	2	6	10	6	1.33	1.78	23	29	23	29	0	1.78
											Summed Variance	11.78
											Project Standard Deviation	3.43