The Critical Path Method (CPM) - Construction Project Scheduling and Control - page 66

Free Float

Let us examine the impact that one activity may have on other activities when it con-
sumes its total float or part of it. In example 4.2, if activity B is delayed by only 1 day
and starts on day 3 (which is well within its available float), it will finish on day 9.
( Remember : We always mean the end of the day.) Activity E, then, cannot start on its
early start date (i.e., day 8). The earliest date E can start is day 9. If we delay activity
B by 2 days, activity E cannot start until day 10 and, thus, becomes critical. This 1- or
2-day delay in the start of activity B will not affect the project completion date. How-
ever, if we delay activity B by more than 2 days, it will finish past day 10, which will
affect the start of the critical activity H and, thus, delay the entire project. This discus-
sion illustrates the concept of total float , which was defined previously as the maximum
amount of time an activity can be delayed without delaying the entire project. Note,
though, that this delay—within the total float—may (and did in this case) or may not
delay the early start of the following (succeeding) activities.
Now let us apply the same discussion to activity G. It has 7 days of total float.
Delaying it by as many as 7 days will not impact the succeeding activity, I. The same
argument applies to activity E, only with 2 days of total float.
Next, we discuss yet another case of total float. Consider activity D, which has
13 days of total float. When we delay it by 1 or 2 days, for example, we notice that this
delay does not impact the early start of the following activity, G, since G is waiting for
the completion of activity C as well. However, when the delay of activity D exceeds
6 days, the situation changes. If we consider delaying activity D by 7 days, it finishes on
day 13. Activity G, then, cannot start until day 13. It should finish on day 16, which
will not delay activity I or the entire project. This 7-day delay in activity D delays the
early start of its successor (activity G), yet it does not delay the entire project. We can
increase this delay to 13 days (which is the total float for activity D) without affecting
the completion date of the entire project, but it does impact the succeeding activity, G.
We can divide activity D's 13-day total float into two portions: the first 6 days
will not delay its successor. This is called free float (FF) . The other 7 days will cause a
delay to its successor even though they will not delay the entire project. This is called
interfering float (Int. F) . We can look at the situation this way: activities D and G
share the 7-day interfering float. If the first activity uses it, it will be taken away from
the next activity. Similarly, we can determine that activity B has no free float (total float
is all interfering float). The free float of activity G equals its total float (no interfering
float). To calculate free float for an activity, we need to compare its early finish date with
its successor's early start date. When there is only one successor activity (Figure 4.7a),
the calculation is simple:
Activity G's free float, FF = 22 − 15 = 7 days. When the activity has more than
one successor (Figure 4.7b), you must pick the earliest early start date among the
successors: activity B's free float, FF = min(12 , 8)−8 = 0 days. In general, free float

is calculated by using the following equation:
FF i = min( ES i +1 )− EF (4.6)

where min( ES i +1 ) means the least (i.e., earliest) of the early start dates of succeeding
activities.