Question

1. Given the information in the following table:

Activity	Duration	Predecessor
A	4	None
B	6	A
C	4	A
D	2	C
E	4	B
F	5	B, D
G	3	C
H	4	F, G
I	2	E, H

1. Construct the (AON) Activity on Node network diagram
2. Find each activity’s ES, EF, LS and LS
3. Identify all paths. Which path is the critical path?
4. Calculate the slack for each activity.
5. How long will it take to complete the project?

Answer 1

(a) Network Diagram -

(b)

Earliest Start (ES) = the earliest time when the activity can begin

Earliest Finish (EF) = ES + Activity Duration

Latest Finish (LF) = the latest time by when the activity can be finished without changing the project completion duration

Latest Start (LS) = LF - Activity Duration

			Earliest	Earliest	Latest	Latest
Activity	Predecessor	Duration	Start Time	Finish Time	Start Time	Finish Time
A	-	4	0	4	0	4
B	A	6	4	10	4	10
C	A	4	4	8	4	8
D	C	2	8	10	8	10
E	B	4	10	14	15	19
F	B, D	5	10	15	10	15
G	C	3	8	11	12	15
H	F, G	4	15	19	15	19
I	E, H	2	19	21	19	21

(c) Possible Network Paths and their durations are are -

ABEI --> 4+6+4+2 = 16
ABFHI --> 4+6+5+4+2 = 21
ACDFHI --> 4+4+2+5+4+2 = 21
ACGHI --> 4+4+3+4+2 = 17

Hence, critical path is path with longest duration = ABFHI & ACDFHI

(d) Slack = LS-ES = LF-EF

			Earliest	Earliest	Latest	Latest
Activity	Predecessor	Duration	Start Time	Finish Time	Start Time	Finish Time	Slack
A	-	4	0	4	0	4	0
B	A	6	4	10	4	10	0
C	A	4	4	8	4	8	0
D	C	2	8	10	8	10	0
E	B	4	10	14	15	19	5
F	B, D	5	10	15	10	15	0
G	C	3	8	11	12	15	4
H	F, G	4	15	19	15	19	0
I	E, H	2	19	21	19	21	0

(e) Time taken to complete the project = longest duration = 21