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

The backward-pass 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.