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NETWORK SCHEDULING TECHNIQUES
BROAD CONTENTS
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
network.
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
when:
- 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
hired.
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. |