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CPM and PERT are most commonly used methods for project management. There are some similarities and differences between PERT and CPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts to accomplish defined objectives.
CPM AND PERT
PRESENTED BY – Jitendra, Jay, Nidhi, Saloni, Sheetu
FACULTY OF ARCHITECTURE & EKISTICS
JAMIA MILLIA ISLAMIA
NEW DELHI – 110025
“A project is a series of activities directed to accomplishment of a
For example – major event like a wedding or Any construction
What is a Project?
What is a Project Network?
A flow chart that graphically depicts the sequence,
interdependencies, and start and finish times of the project
through the network.
Provides the basis for
scheduling labor and
among project participants
Provides an estimate of
the project’s duration
Provides a basis for
budgeting cash flow
Identifies activities that are
critical and can not be
Benefits of Project Network
Uses nodes to represent the
activity and arrows to represent
It is activity oriented
Uses arrows to represent the
activities and nodes to represent
It is event oriented
Dummy Activity is used to clarify the precedence
relationships between the two activities. It is a
zero time activity and consumes no resources.
• Gantt charts are quite commonly used.
• They provide an easy graphical
representation of when activities (might) take
• Do not clearly indicate details regarding the
progress of activities
• Do not give a clear indication of
interrelationship between the separate
Network Planning Techniques
Program Evaluation & Review
Critical Path Method
step-by-step project management technique
for process planning that defines –
critical and non-critical tasks with the goal of
preventing time-frame problems.
ideally suited to projects consisting of
numerous activities that interact in a complex
Project management technique that shows
the time taken by each component of a
project, and the total time required for its
PERT breaks down the project into events
and activities, and lays down their proper
sequence, relationships, and duration in the
form of a network.
• Critical path is the sequence of activities between a project’s start and finish that
takes the longest time to complete.
• CPM was developed by Du Pont and the emphasis was on the trade-off between the
cost of the project and its overall completion time.
Steps In Determining Critical Path
Provides a graphical view of the project.
Predicts the time required to complete the project.
Shows which activities are critical to maintaining the schedule and which are not.
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 project.
CPM was developed for complex but fairly routine projects with minimum
uncertainty in the project completion times.
For less routine projects there is more uncertainty in the completion times, and
this uncertainty limits its usefulness.
Limitations of CPM
Time Estimation in CPM
Time estimates include:
Total time for completion.
ES- Earliest start time: the earliest time at which the activity can start given that its
precedent activities must be completed first.
EF-Earliest finish time: equals to the earliest start time for the activity plus the time
required to complete the activity. ( EF = ES + time required to complete the activity)
LF- Latest finish time: the latest time in which the activity can be completed without
delaying the project.
LS- Latest start time: equal to the latest finish time minus the time required to
complete the activity. ( LS = LF – time required to complete the activity)
Forward Pass: The early start and early finish times are calculated by moving forward
through the network and considering the predecessor activities.
Backward Pass: The latest start and finish times are calculated by moving backward
through the network.
Slack Time: Slack time for an activity is the difference between its earliest and latest
start time or between the earliest and latest finish time. Critical path is the path of
activities having zero Slack time.
ES Earliest Starting
EF Earliest Finishing
LS Latest Starting
LF Latest Finishing
Slack Difference Time
• In PERT activities are shown as a network of precedence relationships using activity-
on-arrow network construction
• PERT was developed by the US Navy for the planning and control of the Polaris
missile program and the emphasis was on completing the program in the shortest
Steps In PERT
PERT is useful because it provides the following information:
Expected project completion time.
Probability of completion before a specified date.
The critical path activities that directly impact the completion time.
Activities start and end dates.
Limitations of PERT
The activity time estimates are somewhat subjective and depend on judgment,
so there may be biasedness in the estimate.
o Optimistic time (to) – It is the shortest time in which the activity
can be completed.
o Most likely time (tm) – It is the probable time required to perform
o Pessimistic time (tp) – It is the longest estimated time required to
perform an activity.
o Expected time, te = to + 4tm + t
Time Estimation in PERT
Activity Description Precedence Optimistic
A Initial design - 12 16 26 17
A 6 9 18 10
A 8 10 18 11
C 2 3 4 3
E Redesigning B,D 3 4 11 5
E 6 8 10 8
G Set up
F 15 20 25 20
Both CPM and PERT -
PERT and CPM have been used to plan, schedule, and control a wide variety of projects:
R&D of new products and processes
Construction of buildings and highways
Maintenance of large and complex equipment
Design and installation of new systems
PERT/CPM is used to plan the scheduling of individual activities that make up a project.
PERT/CPM can be used to determine the earliest/latest start and finish times for each activity,
the entire project completion time and the slack time for each activity.
PERT and CPM are similar in their basic approach, they do differ in the way activity times are
For each PERT activity three times (optimistic, pessimistic and most likely times) are combined to
determine the expected activity completion time and its variance. Thus, PERT is a probabilistic
technique: it allows us to find the probability of the entire project being completed by any given
CPM, on the other hand, is called a deterministic approach. It uses two time estimate, the normal
time and the crash time, for each activity
1. When will the entire project be completed?
2. What are the critical activities or tasks in the project, that is, the ones that will
delay the entire project if they are late?
3. Which are the noncritical activities, that is, the ones that can run late without
delaying the whole project’s completion time?
4. What is the probability that the project will be completed by a specific date?
5. At any particular date, is the project on schedule, behind schedule, or a head
of the schedule?
6. On any given date, is the money spent equal to, less than, or greater than the
7. Are there enough resources available to finish the project on time?
8. If the project is to be finished in a shorter amount of time, what is the best way
to accomplish this at the least cost? (crash analysis)
Questions answered by PERT & CPM
CPM uses activity oriented network. PERT uses event oriented Network.
Durations of activity may be estimated with a
fair degree of accuracy.
Estimate of time for activities are not so
accurate and definite.
It is used extensively in construction projects. It is used mostly in research and development
projects, particularly projects of non-repetitive
Deterministic concept is used. Probabilistic model concept is used.
CPM can control both time and cost when
PERT is basically a tool for planning.
In CPM, cost optimization is given prime
The time for the completion of the project
depends upon cost optimization. The cost is
not directly proportioned to time. Thus, cost is
the controlling factor.
In PERT, it is assumed that cost varies directly
Attention is therefore given to minimize the
time so that minimum cost results. Thus in
PERT, time is the controlling factor.
The Reliable Construction Company Project
The RELIABLE CONSTRUCTION COMPANY has just made the winning bid of $5.4 million to construct a
new plant for a major manufacturer. The manufacturer needs the plant to go into operation within a
year. Therefore, the contract incudes the following provisions:
A penalty of $300,000 if Reliable has not completed construction by the deadline 47 weeks from now.
To provide additional incentive for speedy construction, a bonus of $150,000 will be paid to Reliable if
the plant is completed within 40 weeks.
Thus, Manager of construction company will need to arrange for a number of crews to perform the
various construction activities at different times. Table 10.1 shows his list of the various activities. The
third column provides important additional information for coordinating the scheduling of the crews.
Activity list for the Reliable Construction Co. project
The top entries in this column indicate that :-
1. Excavation does not need to wait for any other activities.
2. Excavation must be completed before starting to lay the foundation.
3. The foundation must be completely laid before starting to put up the rough wall, etc.
When a given activity has more than one immediate predecessor, all must be finished before the
The spreadsheet used by MS Project for entering the activity list for the Reliable
Construction Co. project. On the right is a Gantt chart showing the project schedule.
Scheduling A Project With Pert/Cpm
The project manager for the Reliable Construction Co.
project, wants to use PERT/CPM to develop answers
to a series of questions.
questions that will be answered
Question 1: What is the total time required to
complete the project if no delays occur?
Question 2: When do the individual activities need to
start and finish (at the latest) to meet this project
Question 3: When can the individual activities start
and finish (at the earliest) if no delays occur?
Question 4: Which are the critical bottleneck activities
where any delays must be avoided to prevent delaying
Question 5: For the other activities, how much delay
can be tolerated without delaying project completion?
Figure 1 -The project network for the Reliable
Construction Co. project.
The project network in Fig.1 enables answering all these
questions by providing two crucial pieces of information,
namely, the order in which certain activities must be
performed and the (estimated) duration of each activity.
The Critical Path
The (estimated) project duration equals the length of the longest path through the project network.
This longest path is called the critical path. (If more than one path tie for the longest, they all are
Thus, for the Reliable Construction Co. project, we have
Critical path: START ABCEFJLN FINISH
(Estimated) project duration 44 weeks.
The Paths And Path Lengths Through Reliable’s Project Network
The six paths through the project network in Fig.1 are given in Table 2, along with the calculations of
the lengths of these paths. The path lengths range from 31 weeks up to 44 weeks for the longest
path (the fourth one in the table).
Scheduling Individual Activities
Figure 2 - Earliest start time (ES) and earliest finish time (EF) values for the
initial activities in Fig.1 that have only a single immediate predecessor.
The PERT/CPM scheduling procedure begins
When can the individual activities start and
finish (at the earliest) if no delays occur? Having
no delays means that
(1) The actual duration of each activity turns out
to be the same as its estimated duration and
(2) Each activity begins as soon as all its
immediate predecessors are finished.
Figure 3 - Earliest start time (ES) and earliest finish time
(EF) values for all the activities (plus the START
and FINISH nodes) of the project.
Figure 4 - Latest start time (LS) and latest finish time (LF)
for all the activities (plus the START and
FINISH nodes) of the project.
To identify slack, it is convenient to combine the latest times
in Fig.4 and the earliest times in Fig.3 into a single figure.
Figure 5 - The complete project network showing ES and
LS (in parentheses above the node) and EF and LF (in
parentheses below the node) for each activity of the
project. The darker arrows show the critical path through
the project network.
Identifying Slack In The Schedule
Slack for Reliable’s activities
Each activity with zero slack is on a critical path through
the project network such that any delay along this path
will delay project completion.
Thus, the critical path is START ABCEFJLN FINISH
The slack for an activity is the difference between its latest
finish time and its earliest finish time. In symbols.
Slack LF - EF.
Question 1: What is the total time required to complete the project if no delays occur?
This is the earliest finish time at the FINISH node (EF 44 weeks), as given at the bottom of
Fig. 3 and Fig 5
Question 2: When do the individual activities need to start and finish (at the latest) to meet this
project completion time?
These times are the latest start times (LS) and latest finish times (LF) given in Fig 4
and 5. These times provide a “last chance schedule” to complete the project in 44 weeks if
no further delays occur.
Question 3: When can the individual activities start and finish (at the earliest) if no delaysoccur? These
times are the earliest start times (ES) and earliest finish times (EF) given in Fig 3 and 5
These times usually are used to establish the initial schedule for the project. (Subsequent
delays may force later adjustments in the schedule.)
Question 4: Which are the critical bottleneck activities where any delays must be avoided to prevent
delaying project completion? These are the activities on the critical path shown by the
darker arrows in Fig. 5. needs to focus most of his attention on keeping these particular
activities on schedule in striving to keep the overall project on schedule.
Question 5: For the other activities, how much delay can be tolerated without delaying project
completion? These tolerable delays are the positive slacks given in the middle column of