Question

	Times (days)
Activity	Optimistic	Most Likely	Pessimistic	Preceding Tasks
1	8	10	13	-
2	5	6	8	-
3	13	15	21	2
4	10	12	14	1,3
5	11	20	30	4
6	4	5	8	5
7	2	3	4	5
8	4	6	10	7
9	2	3	4	8,6

1. Draw the AON Network Diagram
2. Compute the expected activity time
3. Using the expected activity times, compute the early start, early finish, late start, late finish, and total float for each activity.
4. Compute the probability of completing the critical path in 69 days.

Answer 1

(a)

(b)

Activity	Preceding Tasks	a	m	b	te = (a + 4m + b) / 6	Variance = (b - a)2/36
1	-	8	10	13	10.167	0.694
2	-	5	6	8	6.167	0.250
3	2	13	15	21	15.667	1.778
4	1,3	10	12	14	12.000	0.444
5	4	11	20	30	20.167	10.028
6	5	4	5	8	5.333	0.444
7	5	2	3	4	3.000	0.111
8	7	4	6	10	6.333	1.000
9	8,6	2	3	4	3.000	0.111

(c)

Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) time for each activity can be computed using the following rules.

Activity	Preceding Tasks	te = (a + 4m + b) / 6	ES	EF	LS	LF	Total float = LF - EF
1	-	10.167	0.000	10.167	11.667	21.833	11.667
2	-	6.167	0.000	6.167	0.000	6.167	0.000
3	2	15.667	6.167	21.833	6.167	21.833	0.000
4	1,3	12.000	21.833	33.833	21.833	33.833	0.000
5	4	20.167	33.833	54.000	33.833	54.000	0.000
6	5	5.333	54.000	59.333	58.000	63.333	4.000
7	5	3.000	54.000	57.000	54.000	57.000	0.000
8	7	6.333	57.000	63.333	57.000	63.333	0.000
9	8,6	3.000	63.333	66.333	63.333	66.333	0.000

(d)

The critical path consists of activities with zero slack, so the critical path is 2-3-4-5-7-8-9.

Activity	Preceding Tasks	te = (a + 4m + b) / 6	Variance = (b - a)^2/36
2	-	6.167	0.250
3	2	15.667	1.778
4	1,3	12.000	0.444
5	4	20.167	10.028
7	5	3.000	0.111
8	7	6.333	1.000
9	8,6	3.000	0.111
Total		66.333	13.722

So, project mean duration = 66.333
stdev = sqrt(13.722) = 3.704

So,

Prob{duration < 69} = NORM.DIST(69, 66.33, 3.704,1) = 0.764