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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


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


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


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,


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


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


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


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


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.


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


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


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


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