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NETWORK SCHEDULING TECHNIQUES
BROAD CONTENTS
Estimating Activity Time
Estimating Total Program Time
Total PERT/CPM Planning
Crash Times
PERT/CPM Problem Areas
Alternative PERT/CPM Model
30.1 Estimating Activity Time:
In order to determine the elapsed time between events requires
that responsible functional
managers evaluate the situation and submit their best estimates.
The calculations for critical
paths and slack times in the previous sections were based on
these best estimates.
Thus, in this ideal situation, the functional manager would have
at his disposal a large volume
of historical data from which to make his estimates. Obviously,
the more historical data
available, the more reliable the estimate would be. Many
programs, however, include events
and activities that are non-repetitive.
In this case, the functional managers must submit their
estimates using three possible
completion assumptions:
Most
optimistic completion time :
This time assumes that everything will go according to plan and
with a minimal amount of
difficulties. This should occur approximately 1 percent of the
time.
Most
pessimistic completion time :
This time assumes that everything will not go according to plan
and that the maximum
potential difficulties will develop. This should also occur
approximately 1 percent of the
time.
Most likely
completion time :
This is the time that, in the mind of the functional manager,
would most often occur should
this effort be reported over and over again.
Two assumptions must be made before these three times can be
combined into a single
expression for expected time. The first assumption is that the
standard deviation, , is one-sixth
of the time requirement range. This assumption stems from
probability theory, where the end
points of a curve are three standard deviations from the mean.
The second assumption requires
that the probability distribution of time required for an
activity be expressible as a beta
distribution.
The expected time between events can be found from the
expression:
In this, te
= expected time,
a
= most optimistic time,
b
= most pessimistic time, and
m
= most
likely time.
Here we take an example. If
a
= 3,
b
= 7, and
m
= 5 weeks, then the expected time,
te,
would be
5 weeks. This value for
te
would then be used as the activity time
between two events in the
construction of a PERT chart. This method for obtaining best
estimates contains a large degree
of uncertainty. If we change the variable times to
a
= 2,
b
= 12, and
m
= 4 weeks, then
te
will
still be 5 weeks. The latter case, however, has a much higher
degree of uncertainty because of
the wider spread between the optimistic and pessimistic times.
Care must be taken in the
evaluation of risks in the expected times.
30.2 Estimating Total Program Time:
It is important to know that in order to calculate the
probability of completing the project on
time, the standard deviations of each activity must be known.
This can be found from the
expression:
Where is the standard deviation of the expected time,
te.
Another useful expression is the
variance, , which is the square of the standard deviation. The
variance is primarily useful for
comparison to the expected values.
Expected Time Analysis for Critical Path Events in Figure 29.1 (Lecture 29)
However, the standard deviation can be used just as easily,
except that we must identify whether
it is a one, two, or three sigma limit deviation. Figure 30.1
above shows the critical path of
Figure 29.1 (lecture 29), together with the corresponding values
from which the expected times
were calculated, as well as the standard deviations. The total
path standard deviation is
calculated by the square root of the sum of the squares of the
activity standard deviations using
the following expression:
30.3 Total PERT/CPM Planning:
It is necessary to discuss the methodology for preparing PERT
schedules, before we continue
further. PERT scheduling is a six-step process.
Steps one and two begin with the project manager laying out a
list of activities to be performed
and then placing these activities in order of precedence, thus
identifying the interrelationships.
These charts drawn by the project manager are called logic
charts, arrow diagrams, work flow,
215
or simply networks. The arrow diagrams will look like Figure
29.1 (lecture 29) with two
exceptions: The activity time is not identified, and neither is
the critical path.
The next step that is step three is reviewing the arrow diagrams
with the line managers (that is,
the true experts) in order to obtain their assurance that
neither too many nor too few activities
are identified, and that the interrelationships are correct.
In step four, the functional manager converts the arrow diagram
to a PERT chart by identifying
the time duration for each activity. It should be noted here
that the time estimates that the line
managers provide are based on the
assumption of unlimited resources
because the calendar
dates have not yet been defined.
Fifth step is the first iteration on the critical path. It is
here that the project manager looks at the
critical calendar dates in the definition of the project's
requirements. If the critical path does not
satisfy the calendar requirements, then the project manager must
try to shorten the critical path
using methods explained earlier or by asking the line managers
to take the ''fat" out of their
estimates.
Step six is often the most overlooked step. Here the project
manager places calendar dates on
each event in the PERT chart, thus, converting from planning
under unlimited resources to
planning with
limited resources. Even
though the line manager has given you a time estimate,
there is no guarantee that the correct resources will be
available when needed. That is why this
step is crucial. If the line manager cannot commit to the
calendar dates, then replanning will be
necessary. Most companies that survive on competitive bidding
lay out proposal schedules
based on unlimited resources. After contract award, the
schedules are analyzed again because
the company now has limited resources.
The question arises that after all, how can a company bid on
three contracts simultaneously and
put a detailed schedule into each proposal if it is not sure how
many contracts, if any, it will
win? For this reason customers require that formal project plans
and schedules be provided
thirty to ninety days after contract award.
Finally, PERT re-planning should be an ongoing function during
project execution. The best
project managers are those individuals who continually try to
assess what can go wrong and
perform perturbation analysis on the schedule. (This should be
obvious because the constraints
and objectives of the project can change during execution.)
Primary objectives on a schedule
- are:
- Best time
- Least cost
- Least risk
In addition to this, the secondary objectives include:
- Studying
alternatives
- Optimum
schedules
- Effective use
of resources
- Communications
- Refinement of
the estimating process
- Ease of project
control
- Ease of time or
cost revisions
It is quite obvious that these objectives are limited by such
constraints as:
- Calendar
completion
- Cash or cash
flow restrictions
- Limited
resources
- Management
approvals
30.4 Crash Times:
So far no distinction was made between PERT and CPM. The basic
difference between PERT
and CPM lies in the ability to calculate percent complete. PERT
is used in Research and
Development or just development activities, where a
percent-complete determination is almost
impossible.
Therefore, PERT is event oriented rather than activity oriented.
In PERT, funding is normally
provided for each milestone (i.e., event) achieved because
incremental funding along the
activity line has to be based on percent complete. CPM, on the
other hand, is activity oriented
because, in activities such as construction, percent complete
along the activity line can be
determined. CPM can be used as an arrow diagram network without
PERT. The difference
between the two methods lies in the environments in which each
one evolved and how each one
is applied.
In addition, the CPM (activity-type network) has been widely
used in the process industries, in
construction, and in single-project industrial activities.
Common problems include no place to
store early arrivals of raw materials and project delays for
late arrivals.
Project managers can consider the cost of speeding up, or
crashing, certain phases of a project
using strictly the CPM approach. In order to accomplish this, it
is necessary to calculate a
crashing cost per unit time as well as the normal expected time
for each activity. CPM charts,
which are closely related to PERT charts, allow visual
representation of the effects of crashing.
There are these following requirements:
• For a CPM
chart, the emphasis is on activities, not events. Therefore, the PERT chart
should be redrawn with each circle representing an activity
rather than an event.
• In CPM, both
time and cost of each activity are considered.
• Only those
activities on the critical path are considered, starting with the activities for
which
the crashing cost per unit time is the lowest.
The following Figure 30.2 below shows a CPM network with the
corresponding crash time for
all activities both on and off the critical path. The activities
are represented by circles and
include an activity identification number and the estimated
time. The costs expressed in it are
usually direct costs only.
CPM Network
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As shown in the figure 30.2, in order to determine crashing
costs we begin with the lowest
weekly crashing cost, activity A, at $2,000 per week. Although
activity C has a lower crashing
cost, it is not on the critical path. Only critical path
activities are considered for crashing.
Activity A will be the first to be crashed for a maximum of two
weeks at $2,000 per week. The
next activity to be considered would be F at $3,000 per week for
a maximum of three weeks.
These crashing costs are additional expenses above the normal
estimates.
It is important to remember a word of caution concerning the
selection and order of the
activities that are to crash: There is a good possibility that
as each activity is crashed, a new
critical path will be developed. This new path may or may not
include those elements that were
bypassed because they were not on the original critical path.
In the same Figure 30.2 (and assuming that no new critical paths
are developed), activities A, F,
E, and B would be crashed in that order. The crashing cost would
then be an increase of
$37,500 from the base of $120,000 to $157,500. The corresponding
time would then be reduced
from twenty-three weeks to fifteen weeks. This is shown in
Figure 30.3 below to illustrate how
a trade-off between time and cost can be obtained. Also shown in
it is the increased cost of
crashing elements not on the critical path.
CPM Crashing Costs
Crashing these elements would result in a cost increase of
$7,500 without reducing the total
project time. There is also the possibility that this figure
will represent unrealistic conditions
because sufficient resources are not or cannot be made available
for the crashing period.
Importantly, the purpose behind balancing time and cost is to
avoid the useless waste of
resources. If the direct and indirect costs can be accurately
obtained, then a region of feasible
budgets can be found, bounded by the early-start (crash) and
late-start (or normal) activities.
This is shown in Figure 30.4 below.
Region of Feasible Budgets
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Since the direct and indirect costs are not necessarily
expressible as linear functions, time–cost
trade-off relationships are made by searching for the lowest
possible total cost (that is, direct
and indirect) that likewise satisfies the region of feasible
budgets.
Determining Project Duration
Note that like PERT, CPM also contains the concept of slack
time, the maximum amount of
time that a job may be delayed beyond its early start without
delaying the project completion
time. Figure 30.6 below shows a typical representation of slack
time using a CPM chart.
CPM Network with Slack
This figure also shows how target activity costs can be
identified. It can be modified to include
normal and crash times as well as normal and crash costs. In
this case, the cost box in the figure
would contain two numbers: The first number would be the normal
cost, and the second would
be the crash cost. These numbers might also appear as running
totals.
30.5 PERT/CPM Problem Areas:
Even the largest organizations with years of experience in using
PERT and CPM have the same
ongoing problems as newer or smaller companies. Thus, PERT/CPM
models are not without
their disadvantages and problems.
Due to its characteristics, many companies have a difficult time
incorporating PERT systems
because PERT is end-item oriented. Many upper-level managers
feel that the adoption of
PERT/CPM remove a good part of their power and ability to make
decisions. This is
particularly evident in companies that have been forced to
accept PERT/CPM as part of
contractual requirements.
In addition to this, there exists a distinct contrast in PERT
systems between the planners and the
doers. This human element must be accounted for in order to
determine where the obligation
actually lies. In most organizations PERT planning is performed
by the program office and
functional management. Yet once the network is constructed, the
planners and managers
become observers and rely on the doers to accomplish the job
within time and cost limitations.
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Management must convince the doers that they have an obligation
toward the successful
completion of the established PERT/CPM plans.
It is important to note that unless the project is repetitive,
there usually exists a lack of historical
information on which to base the cost estimates of most
optimistic, most pessimistic, and most
likely times. Problems can also involve poor predictions for
overhead costs, other indirect costs,
material and labor escalation factors, and crash costs. It is
also possible that each major
functional division of the organization has its own method for
estimating costs. Engineering, for
example, may use historical data, whereas manufacturing
operations may prefer learning curves.
PERT works best if all organizations have the same method for
predicting costs and
performance.
PERT networks are based on the assumption that all activities
start as soon as possible. This
assumes that qualified personnel and equipment are available.
Regardless of how well we plan,
there almost always exist differences in performance times from
what would normally be
acceptable for the model selected. For the selected model, time
and cost should be wellconsidered
estimates, not a spur-of-the-moment decision.
Another problem is that of cost control. It presents a problem
in that the project cost and control
system may not be compatible with company fiscal planning
policies. Project-oriented costs
may be meshed with non-PERT-controlled jobs in order to develop
the annual budget. This
becomes a difficult chore for cost reporting, especially when
each project may have its own
method for analyzing and controlling costs.
Furthermore, many people have come to expect too much of PERT
-type networks. Figure 30.7
below illustrates a PERT/CPM network broken down by work
packages with identification of
the charge numbers for each activity. Large projects may contain
hundreds of charge numbers.
Subdividing work packages (which are supposedly the lowest
element) even further by
identifying all sub activities has the advantage that direct
charge numbers can be easily
identified, but the time and cost for this form of detail may be
prohibitive. PERT/CPM networks
are tools for program control, and managers must be careful that
the original game plan of using
networks to identify prime and supporting objectives is still
met. Additional detail may mask
this all-important purpose. Remember, networks are constructed
as a means for understanding
program reports. Management should not be required to read
reports in order to understand
PERT/CPM networks.
Figure 30.7:
Using PERT for Work Package Control
30.6 Alternative PERT/CPM Models:
Numerous industries have found applications for this form of
network, because of the many
advantages of PERT/time. A partial list of these advantages
includes capabilities for:
- Trade-off
studies for resource control
- Providing
contingency planning in the early stages of the project
- Visually
tracking up-to-date performance
- Demonstrating
integrated planning
- Providing
visibility down through the lowest levels of the work breakdown structure
- Providing a
regimented structure for control purposes to ensure compliance with the work breakdown structure and the statement of work
• Increasing
functional members' ability to relate to the total program, thus, providing
participants with a sense of belonging
Remember that even with these advantages, in many situations
PERT/time has proved
ineffective in controlling resources. Earlier we have defined
three parameters necessary for the
control of resources: time, cost, and performance. With these
factors in mind, companies began
reconstructing PERT/time into PERT/cost and PERT/performance
models.
In addition, PERT/cost is an extension of PERT/time and attempts
to overcome the problems
associated with the use of the most optimistic and most
pessimistic time for estimating
completion. PERT/cost can be regarded as a cost accounting
network model based on the work
breakdown structure and capable of being subdivided down to the
lowest elements, or work
packages. The advantages of PERT/cost are that it:
• Contains all
the features of PERT/time
• Permits cost
control at any Work Breakdown Structure (WBS) level
Note that the primary reason for the development of PERT/cost
was so that project managers
could identify critical schedule slippages and cost overruns in
time for corrective action to be
taken.
In this regard, many attempts have been made to develop
effective PERT/schedule models. In
almost all cases, the charts are constructed from left to right.
An example of such current
attempts is the
Accomplishment/Cost Procedure (ACP).
Summing up our discussion, unfortunately, the development of
PERT/schedule techniques is
still in its infancy. Although their applications have been
identified, many companies feel
locked in with their present method of control, whether it is
PERT, CPM, or some other
technique. |