Slack Time

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Since there exists only one path through the network that is the longest, the other paths must be either equal in length to or shorter than that path. Therefore, there must exist events and activities that can be completed before the time when they are actually needed. The time differential between the scheduled completion date and the required date to meet critical path is referred to as the slack time. In Figure 12-4, event 4 is not on the crucial path. To go from event 2 to event 5 on the critical path requires seven weeks taking the route 2-3-5. If route 2-4-5 is taken, only four weeks are required. Therefore, event 4, which requires two weeks for completion, should begin anywhere from zero to three weeks after event 2 is complete. During these three weeks, management might find another use for the resources of people, money, equipment, and facilities required to complete event 4.

The critical path is vital for resource scheduling and allocation because the project manager, with coordination from the functional manager, can reschedule those events not on the critical path for accomplishment during other time periods when maximum utilization of resources can be achieved, provided that the critical path time is not extended. This type of rescheduling through the use of slack times provides for a better balance of resources throughout the company, and may possibly reduce project costs by eliminating idle or waiting time.

Slack can be defined as the difference between the latest allowable date and the earliest expected data based on the nomenclature below:

Te = the earliest time (date) on which an event can be expected to take place

Tl = the latest date on which an event can take place without extending the completion date of the project

The calculation for slack time is performed for each event in the network, as shown in Figure 12-6, by identifying the earliest expected date and the latest starting date. For event 1, TL - TE = 0. Event 1 serves as the reference point for the network and could just as easily have been defined as a calendar date. As before, the critical path is represented as a bold line. The events on the critical path have no slack (i.e., TL = TE) and provide the boundaries for the noncritical path events.5 Since event 2 is critical, Tl = TE x 3 + 7 = 10 for event 5. Event 6 terminates the critical path with a completion time of fifteen weeks.

The earliest time for event 3, which is not on the critical path, would be two weeks (TE = 0 + 2 = 2), assuming that it started as early as possible. The latest allowable date is obtained by subtracting the time required to complete the activity from events 3 to 5 from the latest starting date of event 5. Therefore, TL (for event 3) = 10 - 5 = 5 weeks. Event 3 can now occur anywhere between weeks

5 There are special situations where the critical path may include some slacks. These cases are not considered here.

Imagens Explicando Hiv

Figure 12-6. PERT network with slack time.

Figure 12-6. PERT network with slack time.

2 and 5 without interfering with the scheduled completion date of the project. This same procedure can be applied to event 4, in which case TE = 6 and TL = 9.

Figure 12-6 contains a simple PERT network, and therefore the calculation of slack time is not too difficult. For complex networks containing multiple paths, the earliest starting dates must be found by proceeding from start to finish through the network, while the latest allowable starting date must be calculated by working backward from finish to start.

The importance of knowing exactly where the slack exists cannot be overstated. Proper use of slack time permits better technical performance. Donald Marquis has observed that those companies making proper use of slack time were 30 percent more successful than the average in completing technical requirements.6

Because of these slack times, PERT networks are often not plotted with a time scale. Planning requirements, however, can require that PERT charts be reconstructed with time scales, in which case a decision must be made as to whether we wish early or late time requirements for slack variables. This is shown in Figure 12-7 for comparison with total program costs and manpower planning. Early time requirements for slack variables are utilized in this figure.

The earliest times and late times can be combined to determine the probability of successfully meeting the schedule. A sample of the required information is shown in Table 12-2. The earliest and latest times are considered as random variables. The original schedule refers to the schedule for event occurrences that were established at the beginning of the project. The last column in Table 122 gives

6 Donald Marquis, "Ways of Organizing Projects," Innovation, 1969.

Figure 12-7. Comparison models for a time-phase PERT chart.

the probability that the earliest time will not be greater than the original schedule time for this event. The exact method for determining this probability, as well as the variances, is described in Section 12.5.

In the example shown in Figure 12-6, the earliest and latest times were calculated for each event. Some people prefer to calculate the earliest and latest times for each activity instead. Also, the earliest and latest times were identified simply as the time or date when an event can be expected to take place. To make full use of the capabilities of PERT/CPM, we could identify four values:

• The earliest time when an activity can start (ES)

• The earliest time when an activity can finish (EF)

• The latest time when an activity can start (LS)

• The latest time when an activity can finish (LF)


Earliest Time Latest Time


Event Number Expected Variance Expected Variance Slack Sche

Figure 12-8 shows the earliest and latest times identified on the activity.

To calculate the earliest starting times, we must make a forward pass through the network (i.e., left to right). The earliest starting time of a successor activity is the latest of the earliest finish dates of the predecessors. The latest starting time is the total of the earliest starting time and the activity duration.

To calculate the finishing times, we must make a backward pass through the network by calculating the latest finish time. Since the activity time is known, the latest starting time can be calculated by subtracting the activity time from the latest finishing time. The latest finishing time for an activity entering a node is the earliest finishing time of the activities exiting the node. Figure 12-9 shows the earliest and latest starting and finishing times for a typical network.

The identification of slack time can function as an early warning system for the project manager. As an example, if the total slack time available begins to decrease from one reporting period to the next, that could indicate that work is taking longer than anticipated or that more highly skilled labor is needed. A new critical path could be forming.

Looking at the earliest and latest start and finish times can identify slack. As an example, look at the two situations below:

In Situation a, the slack is easily identified as four work units, where the work units can be expressed in hours, days, weeks, or even months. In Situation b, the slack is negative five units of work. This is referred to as negative slack or negative float.

What can cause the slack to be negative? Look at Figure 12-10. When performing a forward pass through a network, we work from left to right beginning at the customer's starting milestone (position 1). The backward pass, however, begins at the customer's end date milestone (position 2), not (as is often taught in the classroom) where the forward pass ends. If the forward pass ends at position 3, which is before the customer's end date, it is possible to have slack on the crit-





Figure 12-8. Slack identification.

Figure 12-9. Atypical PERT chart with slack times.

ical path. This slack is often called reserve time and may be added to other activities or filled with activities such as report writing so that the forward pass will extend to the customer's completion date.

Negative slack usually occurs when the forward pass extends beyond the customer's end date, as shown by position 4 in the figure. However, the backward pass is still measured from the customer's completion date, thus creating negative slack. This is most likely to result when:

Figure 12-10. Slack time.

• The original plan was highly optimistic, but unrealistic

• The customer's end date was unrealistic

• One or more activities slipped during project execution

• The assigned resources did not possess the correct skill levels

• The required resources would not be available until a later date

In any event, negative slack is an early warning indicator that corrective action is needed to maintain the customer's end date.

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