Figure 9-20.Example of forward-pass calculations.
Early finish (EF) Earliest time an activity
may be finished;
Late start (LS) Latest time an activity may
be started and still remain on schedule; and
Late finish (LF) Latest time an activity may
be finished and still remain on schedule.
The main objective of forward-pass computations
is to determine the duration of the network. The
forward pass establishes the early start and finish of
each activity and determines the longest path through
the network (critical path).
The common procedure for calculating the project
duration is to add activity durations successively, as
shown in figure 9-20, along chains of activities until a
merge is found.
At the merge, the largest sum
entering the activity is taken at the start of succeeding
activities. The addition continues to the next point of
merger, and the step is repeated. The formula for
forward-pass calculations is as follows:
ES = EF of preceding activity
EF = ES + activity duration
latest possible start and
computations provide the
finish times that may take
place without altering the network relationships.
These values are obtained by starting the calculations
at the last activity in the network and working
backward, subtracting the succeeding duration of an
activity from the early finish of the activity being
calculated. When a burst of activities emanating
from the same activity is encountered, each path is
calculated. The smallest or multiple value is recorded
as the late finish.
The backward pass is the opposite of the forward
pass. During the forward pass, the early start is added
to the activity duration to become the early finish of
that activity. During the backward pass, the activity
duration is subtracted from the late finish to provide
the late start time of that activity. This late start time
then becomes the late finish of the next activity within
the backward flow of the diagram.
LS = LF activity duration
Figure 9-21 shows a network with forward- and
backward-pass calculations entered.
Figure 9-21.Examp1e of forword- and backward-pass calculations.