Question

The following information pertains to a project that is about to commence. Determine the duration of the Project, slacks, ES,EF,LS,LF & Critical path. Activity Precedes Estimated Duration (days) A B 15 B C, D 12 C E 6 D End 5 E End 3 F G, H 8 G I 8 H J 9 I End 7 J K 14 K End 6 ________________________________________

Answer 1

Note the following rules to find Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF), and Slack.

Forward pass

ES of the starting activities = 0
ES of all other activities = Max. (EF of their immediate predecessors)
EF of an activity = Its ES + Its duration

Backward pass

LF of ending activities = Max. (All EF's)
LF of all other activities = Min. (LS of their immediate successors)
LS of an activity = Its LF - Its duration

Slack = LF - EF

Activity	Precedes	Estimated Duration (days)	ES	EF	LS	LF	Slack
A	B	15	0	15	1	16	1
B	C, D	12	15	27	16	28	1
C	E	6	27	33	28	34	1
D	End	5	27	32	32	37	5
E	End	3	33	36	34	37	1
F	G, H	8	0	8	0	8	0
G	I	8	8	16	22	30	14
H	J	9	8	17	8	17	0
I	End	7	16	23	30	37	14
J	K	14	17	31	17	31	0
K	End	6	31	37	31	37	0

The critical path is constituted of activities with Slack = 0.

So, the critical path is F-H-J-K and the estimated duration of the project is 37 days.