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Slack Terminology

Slack Time Calculation

Slack Identification

Network Re-planning

29.1 Slack Terminology:

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

Slack time = TL TE

29.2 Slack Time Calculation:

As shown in Figure 29.1 below, the calculation for slack time is performed for each event in the

network, 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 non-critical

path events. Since event 2 is critical, TL = TE 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.

PERT Network with Slack Time

Therefore, TL (for event 3) = 10 – 5 = 5 weeks. Event 3 can now occur anywhere between

weeks 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.

The same figure 29.1 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.

Comparison Models for a Time- Phase PERT Chart

We must understand that 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.

PERT networks are often not plotted with a time scale, because of these slack times. 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 29.2 above for comparison with total program costs and

manpower planning. Early time requirements for slack variables are utilized in this figure.

Note that 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 29.1

below. 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 this table gives the probability that the earliest time will not be greater than

the original schedule time for this event.

PERT Control Output Information

In the example shown in Figure 29.1, 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

the following 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)

The following Figure 29.3 below shows the earliest and latest times identified on the activity.

In order to calculate the earliest starting times, we must make a forward pass through the

network (that is, 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.

Slack Identification

It is important to note that 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 29.4 below shows the earliest and latest starting and finishing times for a typical


A Typical PERT Chart with Slack Times

29.3 Slack Identification:

Its significance is that 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.

By looking at the earliest and latest start and finish times, we can identify slack. As an example,

look at the two situations below:

According to these, 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.

Here the question arises, what can cause the slack to be negative? Look at Figure 29.5 below.

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 critical path.

Slack Time

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.

Note that 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


  • 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.

29.4 Network Re-planning:

We know that once constructed, the PERT/CPM charts provide the framework from which

detailed planning can be initiated and costs can be controlled and tracked. Much iteration,

however, are normally made during the planning phase before the PERT/CPM chart is finished.

Iteration Process for PERT Schedule Development

This iteration process is shown in the Figure 29.6 above. The slack times form the basis from

which additional iterations, or network replanning, can be performed. Network replanning is

performed either at the conception of the program in order to reduce the length of the critical

path, or during the program, should the unexpected occur. If all were to go according to

schedule, then the original PERT/CPM chart would be unchanged for the duration of the

project. But, how many programs or projects follow an exact schedule from start to finish?

Let us again consider Figure 29.1. Suppose that activities 1–2 and 1–3 in it require manpower

from the same functional unit. Upon inquiry by the project manager, the functional manager

asserts that he can reduce activity 1–2 by one week if he shifts resources from activity 1–3 to

activity 1–2. Should this happen, however, activity 1–3 will increase in length by one week.

Reconstructing the PERT/CPM network as shown in Figure 29.7 below, the length of the

critical path is reduced by one week, and the corresponding slack events are likewise changed.

29.4.1 Network Replanning Techniques:

There are two network replanning techniques based almost entirely upon resources:

resource leveling and resource allocation.

Resource leveling is an attempt to eliminate the manpower peaks and valleys by

smoothing out the period-to-period resource requirements. The ideal situation is to

do this without changing the end date. However, in reality, the end date moves out

and additional costs are incurred.

Resource allocation is an attempt to find the shortest possible critical path based

upon the available or fixed resources. The problem with this approach is that the

employees may not be qualified technically to perform on more than one activity in

a network.

Not all PERT/CPM networks permit such easy rescheduling of resources. Project

managers should make every attempt to reallocate resources so as to reduce the critical

path, provided that the slack was not intentionally planned as a safety valve.

It is important to note here that transferring resources from slack paths to more critical

paths is only one method for reducing expected project time. Several other methods are

available. These are as follows:

  • Elimination of some parts of the project
  • Addition of more resources
  • Substitution of less time-consuming components or activities
  • Parallelization of activities
  • Shortening critical path activities
  • Shortening early activities
  • Shortening longest activities
  • Shortening easiest activities
  • Shortening activities that are least costly to speed up
  • Shortening activities for which you have more resources
  • Increasing the number of work hours per day

In this regard, under the ideal situation, the project start and end dates are fixed, and

performance within this time scale must be completed within the guidelines described

by the statement of work. Should the scope of effort have to be reduced in order to meet

other requirements, the contractor incurs a serious risk in that the project may be

canceled, or performance expectations may no longer be possible.

However, adding resources is not always possible. If the activities requiring these added

resources also call for certain expertise, then the contractor may not have qualified or

experienced employees, and may avoid the risk. The contractor might still reject this

idea, even if time and money were available for training new employees, because on

project termination he might not have any other projects to which to assign these

additional people. However, if the project is the construction of a new facility, then the

labor-union pool may be large enough that additional experienced manpower can be


Another aspect is parallelization of activities. It can be regarded as accepting a risk by

assuming that a certain event can begin in parallel with a second event that would

normally be in sequence with it. This is shown in Figure 29.8 below. One of the biggest

headaches at the beginning of any project is the purchasing of tooling and raw

materials. As shown in Figure below, four weeks can be saved by sending out purchase

orders after contract negotiations are completed, but before the one-month waiting

period necessary to sign the contract. Here the contractor incurs a risk. Should the effort

be canceled or the statement of work change prior to the signing of the contract, the

customer incurs the cost of the termination liability expenses from the vendors. This

risk is normally overcome by the issuance of a long-lead procurement letter

immediately following contract negotiations.

Parallelization of PERT Activities

In addition to this, there are two other types of risk that are common. In the first

situation, engineering has not yet finished the prototype, and manufacturing must order

the tooling in order to keep the end date fixed. In this case, engineering may finally

design the prototype to fit the tooling.

In the second situation, the subcontractor finds it difficult to perform according to the

original blueprints. In order to save time, the customer may allow the contractor to work

without blueprints, and the blueprints are then changed to represent the as-built enditem.

As a result of the complexities of large programs, network re-planning becomes an

almost impossible task when analyzed on total program activities. It is often better to

have each department or division that develops its own PERT/CPM networks, on

approval by the project office, and based on the work breakdown structure. The

individual PERT charts are then integrated into one master chart to identify total

program critical paths, as shown in Figure 29.9 below. It should not be inferred from

this figure that department D does not interact with other departments or that

department D is the only participant for this element of the project.

In addition, segmented PERT charts can also be used when a number of contractors

work on the same program.

Each contractor (or subcontractor) develops his own PERT chart. It then becomes the

responsibility of the prime contractor to integrate all of the subcontractors' PERT charts

to ensure that total program requirements can be met.

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