Question

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

Activity	Activity Time (days)	Immediate Predecessor(s)
A	2	—
B	4	A
C	5	A
D	2	B
E	1	B
F	8	B, C
G	3	D, E
H	5	F
I	4	F
J	7	G, H, I

1. Draw the network diagram.
2. Calculate the critical path for this project.
3. How much slack is in each of the activities G, H, and I?

Answer 1

(a)

(b)

The critical path of a project is composed of activities with zero total slack. The critical path(s) is/ are the longest path(s) in a project network. The slacks for each activity can be computed by carrying out forward pass and backward pass in the project network.

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

Total slack (or, float) = LF - EF for each activity.

Activity	Durations	ES	EF	LS	LF	Slack
A	2	0	2	0	2	0
B	4	2	6	3	7	1
C	5	2	7	2	7	0
D	2	6	8	15	17	9
E	1	6	7	16	17	10
F	8	7	15	7	15	0
G	3	8	11	17	20	9
H	5	15	20	15	20	0
I	4	15	19	16	20	1
J	7	20	27	20	27	0

So, the critical path is A-C-F-H-J.with a duration of 27 days.

(c)

As we have already computed in part (b), the slack of G, H, and I are 9, 0, and 1 day respectively.