Question

Consider the following data for a project to install a new server at the Northland Pines High​ School

A	4	/
B	3	A
C	6	A
D	4	B
E	1	B
F	6	​B, C
G	3	​D, E
H	3	F
I	5	F
J	7	​G, H, I

How much slack is in each of the activities​ G, H, and​ I?

Answer 1

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

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 = Their EF
LF of all other activities = Min. (LS of their immediate successors)
LS of an activity = Its LF - Its duration

Activity	Duration	Predecessor	ES	EF	LS	LF	Slack = LF - EF
A	4	-	0	4	0	4	0
B	3	A	4	7	7	10	3
C	6	A	4	10	4	10	0
D	4	B	7	11	14	18	7
E	1	B	7	8	17	18	10
F	6	​B, C	10	16	10	16	0
G	3	​D, E	11	14	18	21	7
H	3	F	16	19	18	21	2
I	5	F	16	21	16	21	0
J	7	​G, H, I	21	28	21	28	0

Slack of G, H, and I are 7, 2, and 0 respectively.