PERT (Program Evaluation and Review Technique)
PERT is a variation on Critical Path Analysis that takes a slightly more skeptical view of time estimates made for
each project stage. To use it, estimate the shortest possible
time each activity will take, the most likely length
of time, and the longest time that might be taken if the activity takes longer than expected.
Use the formula below to calculate the time to use for each project stage:
shortest time + 4 x likely time +
This helps to bias time estimates away from the unrealistically short time
scales normally assumed.
Critical Path Analysis is an effective and powerful method of assess
What tasks must be carried out.
Where parallel activity can be performed.
The shortest time in which you can complete a project.
Resources needed to execute a project.
The sequence of activities, scheduling and timings involved.
most efficient way of shortening time on urgent projects.
An effective Critical Path Analysis can make the difference between success and failure on complex projects. It
can be very useful for assessing the importance of problems faced during the implement
ation of the plan.
PERT is a variant of Critical Path Analysis that takes a more skeptical view of the time needed to complete each
Complex projects require a series of activities, some of which must be performed sequentially and others t
can be performed in parallel with other activities. This collection of series and parallel tasks can be modeled as
In 1957 the Critical Path Method (CPM) was developed as a network model for project management. CPM is a
that uses a fixed time estimate for each activity. While CPM is easy to understand and
use, it does not consider the time variations that can have a great impact on the completion time of a complex
Program Evaluation and Review Technique
) is a network model that allows for randomness in
activity completion times. PERT was developed in the late 1950's for the U.S. Navy's Polaris project having
thousands of contractors. It has the potential to reduce both the time and cost required to compl
ete a project.
The Network Diagram
In a project, an activity is a task that must be performed and an event is a milestone marking the completion
of one or more activities. Before an activity can begin, all of its predecessor activities must be completed.
roject network models represent activities and milestones by arcs and nodes. PERT originally was an
network, in which the activities are represented on the lines and milestones on the nodes. Over time,
some people began to use PERT as an
tivity on node
network. For this discussion, we will use the original
form of activity on arc.
The PERT chart may have multiple pages with many sub
tasks. The following is a very simple example of a
The milestones generally are n
umbered so that the ending node of an activity has a higher number than the
beginning node. Incrementing the numbers by 10 allows for new ones to be inserted without modifying the
numbering of the entire diagram. The activities in the above diagram are lab
eled with letters along with the
expected time required to complete the activity.
Steps in the PERT Planning Process
PERT planning involves the following steps:
Identify the specific activities and milestones.
Determine the proper sequence of the
Construct a network diagram.
Estimate the time required for each activity.
Update the PERT chart as the project progresses.
Identify Activities and Milestones
The activities are the tasks required to complete t
he project. The milestones are the events marking the
beginning and end of one or more activities. It is helpful to list the tasks in a table that in later steps can be
expanded to include information on sequence and duration.
Determine Activity Seque
This step may be combined with the activity identification step since the activity sequence is evident for some
tasks. Other tasks may require more analysis to determine the exact order in which they must be performed.
Construct the Network Diagram
Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial
and parallel activities. For the original activity
arc model, the activities are depicted by arrowed lines and
milestones are depicted by circles
If done manually, several drafts may be required to correctly portray the relationships among activities.
Software packages simplify this step by automatically converting tabular activity information into a network
Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used.
A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion times. For each
activity, the model usua
lly includes three time estimates:
generally the shortest time in which the activity can be completed. It is
common practice to specify optimistic times to be three standard deviations from the mean so that
there is approximately a 1% cha
nce that the activity will be completed within the optimistic time.
Most likely time
the completion time having the highest probability. Note that this time is
different from the
the longest time that an activity might r
equire. Three standard deviations
from the mean is commonly used for the pessimistic time.
PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time
for each activity can be approximated using the follo
wing weighted average:
4 x Most likely
Pessimistic ) / 6
This expected time may be displayed on the network diagram.
To calculate the variance for each activity completion time, if three standard deviation times were
the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is
[ ( Pessimistic
Optimistic ) / 6 ]
Determine the Critical Path
The critical path is determined by adding the time
s for the activities in each sequence and determining the
longest path in the project. The critical path determines the total calendar time required for the project. If
activities outside the critical path speed up or slow down (within limits), the total p
roject time does not
change. The amount of time that a non
critical path activity can be delayed without delaying the project is
referred to as
If the critical path is not immediately obvious, it may be helpful to determine the following four q
Earliest Start time
Earliest Finish time
Latest Start time
Latest Finish time
These times are calculated using the expected time for the relevant activities. The earliest start and finish
times of each activ
ity are determined by working forward through the network and determining the earliest
time at which an activity can start and finish considering its predecessor activities. The latest start and finish
times are the latest times that an activity can start
and finish without delaying the project. LS and LF are found
by working backward through the network. The difference in the latest and earliest finish of each activity is
that activity's slack. The critical path then is the path through the network in whic
h none of the activities have
The variance in the project completion time can be calculated by summing the variances in the completion
times of the activities in the critical path. Given this variance, one can calculate the probability that the proj
will be completed by a certain date assuming a normal probability distribution for the critical path. The normal
distribution assumption holds if the number of activities in the path is large enough for the central limit
theorem to be applied.
e critical path determines the completion date of the project, the project can be accelerated by adding
the resources required to decrease the time for the activities in the critical path. Such a shortening of the
project sometimes is referred to as
Update as Project Progresses
Make adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can
be replaced with actual times. In cases where there are delays, additional resources may be needed to
schedule and the PERT chart may be modified to reflect the new situation.
Benefits of PERT
PERT is useful because it provides the following information:
Expected project completion time.
Probability of completion before a specified date.
ical path activities that directly impact the completion time.
The activities that have slack time and that can lend resources to critical path activities.
Activity start and end dates.
The following are some of PERT's weaknesses:
The activity time estimates are somewhat subjective and depend on judgement. In cases where
there is little experience in performing an activity, the numbers may be only a guess. In other cases, if
the person or group performing the activity estimates the
time there may be bias in the estimate.
Even if the activity times are well
estimated, PERT assumes a beta distribution for these time
estimates, but the actual distribution may be different.
Even if the beta distribution assumption holds, PERT assumes tha
t the probability distribution
of the project completion time is the same as the that of the critical path. Because other paths can
become the critical path if their associated activities are delayed, PERT consistently underestimates the
expected project c
The underestimation of the project completion time due to alternate paths becoming critical is perhaps the
most serious of these issues. To overcome this limitation, Monte Carlo simulations can be performed on the
network to eliminate this
optimistic bias in the expected project completion time.
Critical Path Analysis
and PERT Charts
Planning and Scheduling Complex Projects
Related variants: AOA or Activity
Arc or Activity
Critical Path Analysis and PERT are powerf
ul tools that help you to schedule and manage complex projects.
They were developed in the 1950s to control large defense projects, and have been used routinely since then.
As with Gantt Charts, Critical Path Analysis (CPA) or the Critical Path Method (CPM
) helps you to plan all tasks
that must be completed as part of a project. They act as the basis both for preparation of a schedule, and of
resource planning. During management of a project, they allow you to monitor achievement of project goals.
you to see where remedial action needs to be taken to get a project back on course.
Within a project it is likely that you will display your final project plan as a Gantt Chart (using Microsoft Project
or other software for projects of medium complexity o
r an excel spreadsheet for projects of low
complexity).The benefit of using CPA within the planning process is to help you develop and test your plan to
ensure that it is robust. Critical Path Analysis formally identifies tasks which must be completed on t
the whole project to be completed on time. It also identifies which tasks can be delayed if resource needs to
be reallocated to catch up on missed or overrunning tasks. The disadvantage of CPA, if you use it as the
technique by which your project p
lans are communicated and managed against, is that the relation of tasks to
time is not as immediately obvious as with Gantt Charts. This can make them more difficult to understand.
A further benefit of Critical Path Analysis is that it helps you to identi
fy the minimum length of time needed to
complete a project. Where you need to run an accelerated project, it helps you to identify which project steps
you should accelerate to complete the project within the available time.
How to Use the Tool:
Gantt Charts, the essential concept behind Critical Path Analysis is that you cannot start some
activities until others are finished. These activities need to be completed in a sequence, with each stage being
less completed before the next stage ca
n begin. These are 'sequential' activities.
Other activities are not dependent on completion of any other tasks. You can do these at any time before or
after a particular stage is reached. These are non
dependent or 'parallel' tasks.
Drawing a Critical Pa
th Analysis Chart
Use the following steps to draw a CPA Chart:
Step 1. List all activities in the plan
For each activity, show the earliest start date, estimated length of time it will take, and whether it is parallel or
sequential. If tasks are sequentia
l, show which stage they depend on.
For the project example used here, you will end up with the same task list as explained in the article on Gantt
Charts (we will use the same example as with Gantt Charts to compare the two techniques). The chart is
ated in Figure 1 below:
Figure 1. Task List: Planning a custom
written computer project
A. High level analysis
B. Selection of hardware
D. Detailed analysis of core
E. Detailed analysis of
F. Programming of core
G. Programming of
H. Quality assurance of
I. Quality assurance of
J.Core module training
K. Development and QA of
L. Development and QA of
M. Development of
N. Detailed training
I, J, K, M
Step 2. Plot the activities as a circle and arrow diagram
Critical Path Analyses are presented using circle and arrow diagrams.
In these, circles show events within the project, such as the start and finish of tasks.
The number shown in the
left hand half of the circle allows you to identify each one easily. Circles are sometimes known as nodes.
An arrow running between two event circles shows the activity needed to complete that task. A description of
the task is wri
tten underneath the arrow. The length of the task is shown above it. By convention, all arrows
run left to right. Arrows are also sometimes called arcs.
An example of a very simple diagram is shown below:
This shows the start event (circle 1), and the c
ompletion of the 'High Level Analysis' task (circle 2). The arrow
between them shows the activity of carrying out the High Level Analysis. This activity should take 1 week.
Where one activity cannot start until another has been completed, we start the arr
ow for the dependent
activity at the completion event circle of the previous activity. An example of this is shown below:
Here the activities of 'Select Hardware' and 'Core Module Analysis' cannot be started until 'High Level Analysis'
has been completed
. This diagram also brings out a number of other important points:
Within Critical Path Analysis, we refer to activities by the numbers in the circles at each end. For
example, the task 'Core Module Analysis' would be called activity 2 to 3. 'Select Hardwa
re' would be
activity 2 to 9.
Activities are not drawn to scale. In the diagram above, activities are 1 week long, 2 weeks long,
and 1 day long. Arrows in this case are all the same length.
In the example above, you can see a second number in the top, righ
t hand quadrant of each
circle. This shows the
earliest start time
for the following activity. It is conventional to start at 0. Here
units are whole weeks.
A different case is shown below:
Here activity 6 to 7 cannot start until the other four activitie
s (11 to 6, 5 to 6, 4 to 6, and 8 to 6) have been
Click the link below for the full circle and arrow diagram for the computer project we are using as an example.
Figure 5: Full Critical Path Diagram
This shows all the activities that will take place as part of the project. Notice that each event circle also has a
figure in the bottom, right hand quadrant. This shows the latest finish time that's permissible for the preceding
activity if the project is
to be completed in the minimum time possible. You can calculate this by starting at the
last event and working backwards.The latest finish time of the preceding event and the earliest start time of
the following even will be the same for circles on the cr
You can see that event M can start any time between weeks 6 and 8. The timing of this event is not critical.
Events 1 to 2, 2 to 3, 3 to 4, 4 to 5, 5 to 6 and 6 to 7 must be started and completed on time if the project is to
be completed in 1
0 weeks. This is the 'critical path'
these activities must be very closely managed to ensure
that activities are completed on time. If jobs on the critical path slip, immediate action should be taken to get
the project back on schedule. Otherwise complet
ion of the whole project will slip.
You may find that you need to complete a project earlier than your Critical Path Analysis says is possible. In
this case you need to re
plan your project.
You have a number of options and would need to
assess the impact of each on the project’s cost, quality and
time required to complete it. For example, you could increase resource available for each project activity to
bring down time spent on each but the impact of some of this would be insignificant a
nd a more efficient way
of doing this would be to look only at activities on the critical path.
As an example, it may be necessary to complete the computer project in Figure 5 in 8 weeks rather than 10
weeks. In this case you could look at using two analy
sts in activities 2 to 3 and 3 to 4. This would shorten the
project by two weeks, but may raise the project cost
doubling resources at any stage may only improve
productivity by, say, 50% as additional time may need to be spent getting the team members u
p to speed on
what is required, coordinating tasks split between them, integrating their contributions etc.
In some situations, shortening the original critical path of a project can lead to a different series of activities
becoming the critical path. Fo
r example, if activity 4 to 5 were reduced to 1 week, activities 4 to 8 and 8 to 6
would come onto the critical path.
As with Gantt Charts, in practice project managers use software tools like Microsoft Project to create CPA
Charts. Not only do these ease
make them easier to draw, they also make modification of plans easier and
provide facilities for monitoring progress against plans.