PRECEDENCE DIAGRAMS

Scheduling involves putting the network on a working timetable. Information relating to each activity is contained within an activity box, as shown in figure 9-19.

Forward and Backward Pass Calculations

To place the network on a timetable, you must make time and duration computations for the entire project. These computations establish the critical path and provide the start and finish dates for each activity.

Each activity in the network can be associated with four time values:

0 Early start (ES)- Earliest time an activity may be started;

Figure 9-19.-Information for a precedence activity.

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 computations provide the latest possible start and 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.-Example of forward- and backward-pass calculations.

Figure 9-22.-PDM network with total and free float calculations.

The free and total float times are the amount of scheduled leeway allowed for a network activity, and are referred to as float or slack. For each activity, it is possible to calculate two float values from the results of the forward and backward passes.

TOTAL FLOAT.- The accumulative time span in which the completion of all activities may occur and not delay the termination date of the project is the total float. If the amount of total float is exceeded for any activity, the project end date extends to equal the exceeded amount of the total float.

Calculating the total float consists of subtracting the earliest finish (EF) date from the latest finish (LF) date, that is:

Total float = LF- EF

FREE FLOAT.- The time span in which the completion of an activity may occur and not delay the finish of the projector the start of a successor activity is the free float. If this value is exceeded, it may not affect the project end date but will affect the start of succeeding, dependent activities.

Figure 9-23.-Independent activity.

Figure 9-24.-Dependent activity.

Calculating the free float consists of subtracting the earliest start (ES) date from the latest start (LS) date, or:

Free float = LS - ES

Figure 9-22 is an example of an activity-on-node precedence diagraming method (PDM) network with total and free float calculations completed.

INDEPENDENT ACTIVITY.- An independent activity is an activity that is not dependent upon another activity to start. Activity 1, diagramed in figure 9-23, is an example of an independent activity.

DEPENDENT ACTIVITY.- A dependent activity is an activity that is dependent upon one or more preceding activities being completed before it can start. The relationship in figure 9-24 states that the start of Activity 2 is dependent upon the finish of Activity 1.

Frequently, an activity cannot start until two or more activities have been completed. This appears in the diagram as a merge or junction. In figure 9-25, Activities 3 and 4 must be completed before the start of Activity 5.

Earlier we mentioned a "burst" of activities. A burst is similar to a merge. A burst exists when two or more activities cannot be started until a third activity is completed. In figure 9-24, when Activity 2 is finished, Activities 3 and 4 may start.

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