The Critical Path Method (CPM) - Construction Project Scheduling and Control - page 79

at event 70, the late time, T L , is 27. Since all dummies have zero duration,
event 60 has T L = 27. For event 50, we must pick the earlier of the following:
T L of event 60 − Duration of G ( 27 − 5 = 22 ) and T L of event 70 − Duration
of H ( 27 − 8 = 19 ) .So, T L for event 50 = 19. For event 40 , T L = 19 − 4 = 15.

For event 30 T L = 19 − 9 = 10. For event 20, pick the earlier of ( 19 − 8 = 11 )

and ( 10 − 0 = 10 ) . Hence, T L = 10 − 0 = 10. For event 10, pick the earliest
of ( 10 − 10 = 0 ) , ( 10 − 5 = 5 ) , and ( 15 − 7 = 8 ) . Clearly, T L = 0.
Event float We easily find that events 40 and 60 have floats of 8 and
3 days, respectively. All other events are critical.

,

Effect of the Imposed Finish Date on the Schedule

So far, all calculations have been based on the duration estimate for each activity, along
with the logic between these activities. The result is a calculated finish date . In many
cases, the calculated finish date is different from that stipulated by the owner. As a
result, the contractor may have to adjust the schedule to meet the owner's imposed fin-
ish date. This possibly means accelerating the schedule, a subject covered in Chapter 8.
In this section, we just study the effect that such an imposed date may have on the
schedule.
The concept is simple. Do the CPM forward pass as usual: find the project's calcu-
lated finish date, based on the assumptions of durations and logic. Then, on the back-
ward pass, start with the imposed finish date and use this date for your backward-pass
calculations. The imposed finish date may be earlier or later than the calculated finish
date:

• If the imposed finish date is earlier than the calculated finish date, the activities
on the critical path will have a negative float equal to the difference between
the imposed finish date and the calculated finish date. Other activities may
also develop a negative float but greater (or less, in absolute value) than the
total float of the critical path. The contractor must accelerate the project (i.e.,
reduce its duration) by an amount of time equal to the negative float of the
critical path. This acceleration, say 8 days, may be taken from several activities
(e.g., 1 day from one activity, 2 days from another, and so on), with a total
reduction in duration that is equal to 8 days.
• If the imposed finish date is later than the calculated finish date, the contractor
is in good shape (at this point). The difference between the two dates may be
regarded as a time contingency , and the contractor may keep the calculated
finish date as a target date. In such a situation, inserting the imposed finish date
into the computer programwill result in the “disappearance” of the critical path.
This occurs because we gave each activity a “bonus float” equal to the difference
between the imposed finish date and the calculated finish date. Since, by default,
most computer programs define critical activities as those with zero or less float,
no critical activities will be found. For this reason, the scheduler should not enter
the imposed finish date until the calculated finish date is determined.