Question

Given the following information, you are to determine the following

• Project network.
• Early, late and slack activity times.
• Project duration.
• Critical path

Task	Predecessor	Duration
A	None	5
B	A	8
C	A	15
D	A	10
E	A	10
F	B	10
G	C, D	12
H	E,	15
I	G, H	7
J	F,G,I	10
K	J	12

Answer 1

Network Diagram -

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

Earliest Finish (EF) = ES + Activity Duration

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

Latest Start (LS) = LF - Activity Duration

Slack = LS-ES = LF-EF

Computing using the above gives us the below -

			Earliest	Earliest	Latest	Latest
Activity	Predecessor	Duration	Start Time	Finish Time	Start Time	Finish Time	Slack
A	-	5	0	5	0	5	0
B	A	8	5	13	21	29	16
C	A	15	5	20	5	20	0
D	A	10	5	15	10	20	5
E	A	10	5	15	7	17	2
F	B	10	13	23	29	39	16
G	C, D	12	20	32	20	32	0
H	E	15	15	30	17	32	2
I	G, H	7	32	39	32	39	0
J	F, G, I	10	39	49	39	49	0
K	J	12	49	61	49	61	0

Possible Network Paths and their Duration are -

ABFJK --> 45
ACGJK --> 54
ACGIJK --> 61
ADGJK --> 49
ADGIJK --> 56
AEHIJK --> 59

Hence, Project duration is the duration of the longest path = 61

Critical path is the path with longest duration = ACGIJK