Question

3. A project starting this summer has following work breakdown structure Time Estimates (days) Activity Precs Optstic Most Likely Pes Start Pessimistic A, B C, D 56 45 42 31 27 End58 60 39 70 What is the probability that for this project will be completed within 1 60 days? It would be helpful to draw a network first. (12 points)

Answer 1

Please find below the network diagram. Critical path = ACEF.

Start END

Task	Preceding Tasks	Optimistic (a)	Most likely (M)	Pessimistic (b)	PERT Estimate = (a+4*M+b)/6	Deviation = (b-a) / 6	Variance = Square of (b-a) / 6
A	C,D	44	50	56	50.00	2.00	4.000
B	D	45	60	75	60.00	5.00	25.000
C	E	42	45	48	45.00	1.00	1.000
D	F	31	40	49	40.00	3.00	9.000
E	F	27	36	39	35.00	2.00	4.000
F	End	58	70	82	70.00	4.00	16.000

Critical path = ACEF Expected time	50+45+35+70	200.00
Sum of variances on the critical path	4+1+4+16	25.000
Z-score = (Specified time - Expected time)/ sqrt (sum of variance)	(160-200)/sqrt(25)	-8.0

For Z-score beyond -3.5, the probability is almost negligible i.e. there is no chance that project will be completed within 160 days.