Question

2. Consider the network described in the table below. Immediate Activity Predecessor(s)Pessimistic Probable Optimistic 15 10 8 K 9 8 7 L 10 6 5 M 3 3 3 N KM 9 5 1 O KM 10 7 4 P LN 10 8 3 Draw the network diagram and answer the following questions. (a) Calculate the expected duration of each activity. (b) Calculate the expected duration and variance of the critical path. (c) Calculate the probability that the project will be completed in more than 28 weeks time units.

Answer 1

ANSWER:

a)

consider:

a - optimistic

b - pessimistic

m - probable

Te - Expected time completion

Activity	a	b	m	Te	(Var)^0.5	Var
J	8	15	10	10.5	1.166666667	1.361111111
K	7	9	8	8	0.333333333	0.111111111
L	5	10	6	6.5	0.833333333	0.694444444
M	3	3	3	3	0	0
N	1	9	5	5	1.333333333	1.777777778
O	4	10	7	7	1	1
P	3	10	8	7.5	1.166666667	1.361111111

Start 0 M End N K

b)

ES - Early start

EF - Early finish

LS - Latest start

LF - Latest finish

Expected time completion:

a + 4m + b 9

variance = standard deviation²

standard deviation:

$\small = \frac{b-a}{6}$

Activity	ES	EF	LS	LF	SLACK
J	0	10.5	0	10.5	0
K	0	8	5.5	13.5	5.5
L	10.5	17	12	18.5	1.5
M	10.5	13.5	10.5	13.5	0
N	13.5	18.5	13.5	18.5	0
O	13.5	20.5	19	26	5.5
P	18.5	26	18.5	26	0

Critical path is JMNP with duration 26

Critical path = J-M-N-P

Expected duration of the critical path = 10.5 + 3 + 5 + 7.5

Expected duration of the critical path = 26 weeks

Variance of the critical path = 1.36 + 0 + 1.78 + 1.36

Variance of the critical path = 4.5

c)

If the project completion time is considered to be normal, the z score for the project to be completed in 28 weeks is found as

$\small Z = \frac{\overline{X}-mean}{standard deviation}$

$\small =\frac{28-26}{2.1213}$

Z = 0.94

From the Z score table, the probability the project will be completed in 28 weeks = 0.8264

The probability of completing the project in more than 28 weeks time = 1 -  0.8264

Probability of completing the project in more than 28 weeks time = 0.174 or ( 17.4%).

If you have any doubts please comment and please don't dislike.

PLEASE GIVE ME A LIKE. ITS VERY IMPORTANT FOR ME.