Creating an Initial Project Network Schedule

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As mentioned, all activities in the network diagram have at least one predecessor and one successor activity, with the exception of the start and end activities. If this convention is followed, the sequence is relatively straightforward to identify. If, however, the convention is not followed, or if date constraints are imposed on some activities, or if the resources follow different calendars, understanding the sequence of activities that result from this initial scheduling exercise can be rather complex.

To establish the project schedule, you need to compute two schedules: the early schedule, which we calculate using the forward pass, and the late schedule, which we calculate using the backward pass.

The early schedule consists of the earliest times at which an activity can start and finish. These are calculated numbers that are derived from the dependencies between all the activities in the project. The late schedule consists of the latest times at which an activity can start and finish without delaying the completion date of the project. These are also calculated numbers that are derived from the dependencies between all of the activities in the project.

The combination of these two schedules gives us two additional pieces of information about the project schedule:

m The window of time within which each activity must be started and finished in order for the project to complete on schedule

■■ The sequence of activities that determine the project completion date

The sequence of activities that determine the project completion date is called the critical path. The critical path can be defined in several ways:

■■ The longest duration path in the network diagram

■■ The sequence of activities whose early schedule and late schedule are the same

■■ The sequence of activities with zero slack or float (we define these terms later in this chapter)

All of these definitions say the same thing: The critical path is the sequence of activities that must be completed on schedule in order for the project to be completed on schedule.

The activities that define the critical path are called critical path activities. Any delay in a critical path activity will delay the completion of the project by the amount of delay in that activity. Critical path activities represent sequences of activities that warrant the project manager's special attention.

The earliest start (ES) time for an activity is the earliest time at which all of its predecessor activities have been completed and the subject activity can begin. The ES time of an activity with no predecessor activities is arbitrarily set to 1, the first day on which the project is open for work. The ES time of activities with one predecessor activity is determined from the earliest finish (EF) time of the predecessor activity. The ES time of activities having two or more predecessor activities is determined from the latest of the EF times of the predecessor activities. The earliest finish (EF) of an activity is calculated as ((ES + Duration) - One time unit). The reason for subtracting the one time unit is to account for the fact that an activity starts at the beginning of a time unit (hour, day, and so forth) and finishes at the end of a time unit. In other words, a one-day activity, starting at the beginning of a day, begins and ends on the same day. For example, take a look at Figure 6.6. Note that activity E has only one predecessor, activity C. The EF for activity C is the end of day 3. Because it is the only predecessor of activity E, the ES of activity E is the beginning of day 4. On the other hand, activity D has two predecessors, activity B and activity C. When there are two or more predecessors, the ES of the successor, activity D in this case, is calculated based on the maximum of the EF dates of the predecessor activities. The EF dates of the predecessors are the end of day 4 and the end of day 3. The maximum of these is 4, and therefore, the ES of activity D is the morning of day 5. The complete calculations of the early schedule are shown in Figure 6.6.

The latest start (LS) and latest finish (LF) times of an activity are the latest times at which the activity can start or finish without causing a delay in the completion of the project. Knowing these times is valuable for the project manager, who must make decisions on resource scheduling that can affect completion dates. The window of time between the ES and LF of an activity is the window within which the resource for the work must be scheduled or the project completion date will be delayed. To calculate these times, you work backward in the network diagram. First set the LF time of the last activity on the network to its calculated EF time. Its LS is calculated as ((LF - Duration) + One time unit). Again, you add the one time unit to adjust for the start and finish of an activity within the same day. The LF time of all immediate predecessor activities is determined by the minimum of the LS, minus one time unit, times of all activities for which it is the predecessor.

Figure 6.6 Forward pass calculations.

For example, let's calculate the late schedule for activity E in Figure 6.7. Its only successor, activity F, has an LS date of day 10. The LF date for its only predecessor, activity E, will therefore be the end of day 9. In other words, activity E must finish no later than the end of day 9 or it will delay the start of activity F and hence delay the completion date of the project. The LS date for activity E will be, using the formula, 9 - 2 + 1, or the beginning of day 7. On the other hand, consider activity C. It has two successor activities, activity D and activity E. The LS dates for them are day 5 and day 7, respectively. The minimum of those dates, day 5, is used to calculate the LF of activity C, namely, the end of day 4. The complete calculations for the late schedule are shown in Figure 6.7.

Critical Path

As mentioned, the critical path is the longest path or sequence of activities (in terms of activity duration) through the network diagram. The critical path drives the completion date of the project. Any delay in the completion of any one of the activities in the sequence will delay the completion of the project. The project manager pays particular attention to critical path activities. The critical path for the example problem we used to calculate the early schedule and the late schedule is shown in Figure 6.8.

Calculating Critical Path

One way to identify the critical path in the network diagram is to identify all possible paths through the network diagram and add up the durations of the activities that lie along those paths. The path with the longest duration time is the critical path. For projects of any size, this method is not feasible, and we have to resort to the second method of finding the critical path—computing the slack time of an activity.

Figure 6.7 Backward pass calculations.

Figure 6.7 Backward pass calculations.

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