The Critical Path Method (CPM) - Construction Project Scheduling and Control - page 69

redundant. The first condition, “without delaying the early start of the succeeding
activities,” is more stringent than “without delaying the entire project.”
We must always realize that FF TF . In fact, free float is the part of total float that

will not affect the early start of the following activities. 7 The other part, interfering
float, may be defined as the maximum amount of time an activity can be delayed
without delaying the entire project but causing delay to the succeeding activities. It
represents the part of the total float that remains after free float is deducted:

≤

TF = FF + Int . ForInt . F = TF-FF

In some scheduling software programs, we may assign a start or a finish constraint
to a certain activity. Total float may then be calculated as the maximum amount of
time we can delay the activity from its early start without delaying the entire project
or the constraint (whichever is more stringent). In example 4.3, let us assign a finish
constraint on activity E: Finish No Later Than (also called Finish on or Before ) day 18.
In this case, TF = 18 − 15 = 3 days. The computer programmay still calculate the free
float on the basis of the early start of the succeeding activities, FF = 7 days, without
regard to the constraint. In such a situation, you may wonder how free float could
be greater than total float. It is not! The software program is calculating the two
variables ( TF and FF ), in this case, using different criteria. Nevertheless, our earlier
rule, FF TF , still stands in all cases.

If we look further into free float, we find that it is calculated so that it does not
affect the succeeding activities, but it may be affected by the preceding activities. For
example, in example 4.3, if activity B is delayed (within its total float), this amount
will be taken away from the total float and the free float of activity E. Let B start on
day 8 and finish on day 15 (using its entire total float). Activity E will then start on
day 15 and finish on day 21. This leaves activity E with only 6 days of total float, one
of which is free float.
This brings us to the definition of independent float (Ind. F) of an activity,
which is not shared or affected by any other activity. We may define it as the maximum
amount of time an activity can be delayed from its early start without delaying the early
start of the succeeding activities and without being affected by the allowable delay of
the preceding activities. Independent float is calculated as follows:

≤

Ind . F i = min( ES i +1 )−max( LF i −1 )− Dur i

F = 22 − 15 − 6 = 1 day. This
equation may result in negative numbers, which should be interpreted as zero
independent float. Independent float is part of

For activity E in the previous example, Ind .

free float, so make sure that

.

Ind TF . Independent float is the only float that can be considered truly an

activity float, that is, not shared with any other activity, predecessor, or successor.

F ≤ FF ≤

7 The author calls free float the “unselfish” portion of the total float.