Free Slack:
Free Slack is defined as the amount of time an activity can be delayed without affecting the early start time
of any other job. In other words, the free slack of any activity is the difference between its early finish time and the
earliest of the early start times of all its immediate successors. In the example above, if we take the activity b, its
early finish time is day 3 and its immediate successor c starts at the earliest on day 10. 'c' can start as late as on day
17, but there is not compulsion on c to start exactly on day 10. If he chooses to start on day 10 (earliest start time)
ten b will b\have only 7 days as free slack (difference between early start of c and early finish of b). Similarly for the
job c also we have free slack as the difference between the early finish of c and early start of its immediate successor
'f' i.e. 21-14 = 7 days. Free slack can never exceed total slack. The total slack and free slack for all activities are
given in the following table.
Activity
Total Slack
Free Slack
a
0
0
b
14
7
g
7
0
c
0
7
d
0
0
e
0
0
f
7
0
Independent slack:
It is that portion of the total float within which an activity can be delayed for start without affecting slacks
of the preceding activities. It is computed by subtracting the tail event slack from the free float. If the result is
negative it is taken as zero.
Example The following table gives the activities of a construction project and duration.
Activity
1-2
1-3
2-3
2-4
3-4
4-5
Duration (days)
20
25
10
12
6
10
(i) Draw the network for the project.
(ii) Find the critical path.
(iii) Find the total, free and independent floats each activity.
Solution: The first step is to draw the network and fix early start and early finish schedule and then late
start-late finish schedule as in figure 18 and figure 19.
2 (20, 32)
(0, 20) 20 12
10 (20, 30) 4 10 5
1 25 (36, 46)
6 (30, 36)
(0, 25) 3
Early-Start Early-Finish Schedule
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