Question

1- Consider the table shown below:

Task	Predecessor	Time (weeks)			Expected time	Variance of time
		Optimistic	Most likely	Pessimistic
A	-	1	3	5
B	A	2	6	10
C	B	4	7	10
D	B, C	1	2	9
E	D	2	4	6
F	D,E	4	7	10
G	F	1	3	5

a) Calculate expected time and variance for each task.  

b) Find the critical path and expected project competition time?

c) What is the probability of completing the project on or before 32 weeks?

Answer 1

Answers :

a) Expected time and variance are calculated and tabulated

b) critical path : A-B-C-D-E-F-G

  project completion time = 33 weeks

c) probability of completion in 32 weeks= 64.80%

Explanation :

Task Predecessor Expected Variance time Time (weeks) Optimishi | Palost / Pessimistic likely १ § 2 6 io A - R A 3 6 ng 0.14 1.478 1.000 с B 4 7 10 Rc 9 - ee 3 1.748 A وه 6 4 Oledely DE 4 7 lo 7 1.000 G F " 3 5 3 0.44h Expected time tinne te tez to topth him 6 Variance, to optimistic tinie & Pensimistic time tm Must-likely time. V - to Abetursale diegram! A 3

3841 369 DIAS 01313 Esl Act EE LSI Durif TICI6 197116 Die 120 3199 16 1921 22 3 E30 3014180 kol.3333 237130 1801 Critical path 37 A-B-C-D-E-F-G Project completion time 33 Weeks 2 = 12.694 c) Variance of critical path = 0.144+0.9787 1.0007 1.72 tahhaf 1.000t ahhh O 6.888 26.878 t = 33 weeks, tp = 32 weeks 33-32 10.3811 z 2 2.624 for 2=0.3811 (3/2 0.6480 = = 164.80 % ory 2- 6