Transcript Introduction to Operation Research

Unit-II-III
Introduction to
CPM-PERT
Mr. Rahul Mohare
Faculty
Datta Meghe Institute of Management Studies
Atrey Layout, Nagpur
Overview
Project Management
What is CPM?
Procedure
Examples
Analysis
What is PERT?
Procedures
Examples
Analysis
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Project Management
1. A project is a one-off undertaking, with a clear
beginning and end, usually aimed at creating
some useful change or adding value -- typically
to build a new plant or create a new product.
2. Projects bring together resources such as
people, money and material
3. These must be organized and managed to
produce a defined result.
4. The hard part is to bring the project to
completion within a specified time, at no more
than a specified cost.
5. Various tools have been created to help project
managers pull off this invariably challenging
feat.
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Project Management (Contd.)
There are three main points that are most
important to a successful project:
 A Project must meet customer
requirements.
 A Project must be under budget.
 A Project must be completed on time.
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Characteristics of Project
•The duration of a project lasts weeks, months, or even years. During
such a long period, many changes may occur, most of which are difficult
to predict. Such changes may have a significant impact on project costs
technology, and resources. The longer the duration of the project,
uncertain are the execution times and costs.
•A project is complex in nature, involving many interrelated activities and
participants from both within the organization and outside it (e.g.,
suppliers, subcontractors).
•Delays in completion time may be very costly. Penalties for delays may
amount to thousands of dollars per day. Completing projects late may
result in lost opportunities and ill will as well.
•Project activities are sequential. Some activities cannot start until others
are completed.
•Projects are typically a unique undertaking, something that has not been
encountered previously.
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The Project Network Concurrent Activities
Activities can occur at the same time (concurrently).
A dummy activity shows a precedence relationship but
reflects no passage of time.
Two or more activities cannot share the same start and
end nodes.
Expanded Network for Building a House Showing Concurrent Activities
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Introduction- CPM
There are some formal tools to aid project
management. Two of the best known
tools that fill this need are PERT
(Program Evaluation Review Technique)
and CPM (Critical Path Method).
CPM provides the following benefits:
 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.
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Introduction (Contd.)
The essential technique for using CPM is to construct a model of the
project that includes the following:



A list of all activities required to complete the project (typically
categorized within a work breakdown structure
The time (duration) that each activity will take to completion,
The dependencies between the activities
Using these values, CPM calculates the longest path of planned
activities to the end of the project, and the earliest and latest
that each activity can start and finish without making the
project longer. This process determines which activities are
"critical" (i.e., on the longest path) and which have "total float"
(i.e., can be delayed without making the project longer).
In project management, a critical path is the sequence of project
network activities which add up to the longest overall duration.
This determines the shortest time possible to complete the project.
Any delay of an activity on the critical path directly impacts the
planned project completion date (i.e. there is no float on the
critical path).
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Usefulness
CPM/PERT have been useful in planning costs, scheduling
manpower and machine time. CPM/PERT can answer the
following important questions:
•What will be the project duration? What are the risks/
dependencies/ assumptions involved?
•What are the critical activities which could delay the entire
project if they were not completed on time?
•What is the current status of the project i.e. Is the project on
schedule, behind schedule or ahead of schedule?
•If the project has to be finished earlier than planned, what is
the best way to do this at the least cost?
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Terminologies used in CPM/PERT
In order to explain the purpose, structure and operation of PERT and CPM, it is
helpful to define the following terms:
Activity: An activity is an effort that requires resources and takes a certain amount
of time for completion. Examples of activities are: studying for an examination,
designing a part, connecting bridge girders, or training an employee.
Dummy Activity: An activity, which is used to maintain the pre-defined precedence
relationship only during the construction of the project network, is called a dummy
activity. Dummy activity is represented by a dotted arrow and does not consume
any time and resource
Critical activity: A critical activity is an activity that, if even slightly de-layed, will
hold up the scheduled completion date of the entire project.
Path: A path is a series of adjacent activities leading from one event to another.
Critical path: A critical path is the sequence of critical activities that forms a
continuous path between the start of a project and its completion.
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 Event: An event is a specific accomplishment at a
recognizable point in time; a milestone, a
checkpoint; for example, passing a course at a
university, submission of engineering drafts,
completion of a span on a bridge, or the arrival of a
new machine. Events do not have a time duration
per se. To reach an event, all the activities that
precede it must be completed. An event can be
viewed as a goal attained, while the activities
leading to it can be viewed as the means of
achieving it. Event is indicated by circle in network
diagram
 Network: A network is a logical and chronological
set of activities and events, graphically illustrating
relationships among the various activities and
events of the project.
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Building the Network
AOA Network
AON Network
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A Sample Set of Project Activities
and Precedences
Task
Predecessor
a
--
b
--
c
a
d
b
e
b
f
c, d
g
e
Figure 1 Stage 1 of a Sample
AON Network
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Figure 2 Stage 2 of a Sample
AON Network
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Figure 3 A Completed Sample
AON Network
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Figure 4 Stage 1 of a Sample
AOA Network
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Figure 5 Stage 2 of a Sample
AOA Network
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Figure 6a A Completed Sample
AOA Network
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Figure 6b A Completed Sample AOA
Network Showing the Use of a Dummy
Task
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Situations in network diagram
B
A
A must finish before either B or C can
start
C
A
C
both A and B must finish before C can
start
B
A
C
B
A
D
B
A must finish before B can start
Dummy
C
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both A and C must finish before either of
B or D can start
D
both A and C must finish before D can start
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Example
1. Construct the CPM Network using the details below and
determine the critical path
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Activity
Immediate
Predecessor
Duration
A
-
1
B
A
4
C
A
2
D
A
2
E
D
3
F
D
3
G
E
2
H
F,G
1
I
C,H
3
J
B
2
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CPM NETWORK
A
1
2
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CPM NETWORK
4
D
A
1
2
7
C
B
3
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CPM NETWORK
5
E
4
F
D
6
A
1
2
7
C
B
3
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CPM NETWORK
5
E
G
4
F
D
6
A
1
2
7
C
B
3
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CPM NETWORK
5
E
G
4
F
D
6
H
A
1
2
7
C
B
3
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CPM NETWORK
5
E
G
4
F
D
6
H
I
A
1
2
7
C
8
B
3
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CPM NETWORK
5
E
G
4
F
D
6
H
I
A
1
2
7
C
8
B
J
3
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CPM NETWORK with duration of each activity
5
E(3)
G(2)
4
F(3)
D(2)
6
H(1)
I(3)
A(1)
1
2
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
LFT
EST
5
E(3)
G(2)
4
0
0
1
F(3)
D(2)
A(1)
6
H(1)
I(3)
2
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
LFT
EST
5
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
6
H(1)
I(3)
2
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
5
0
3
E(3)
G(2)
4
0
0
1
A(1)
0
1
LFT
EST
F(3)
D(2)
6
H(1)
I(3)
2
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
0
6
5
0
3
LFT
EST
F(3)
D(2)
6
H(1)
I(3)
2
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
H(1)
I(3)
7
C(2)
8
B(4)
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
H(1)
0
9
7
C(2)
I(3)
8
B(4)
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
0
9
H(1)
7
C(2)
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
H(1)
0
9
7
C(2)
0
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
H(1)
0
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
0
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
0
6
5
0
3
LFT
EST
8
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
6
6
5
0
3
LFT
EST
8
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
0
1
F(3)
D(2)
2
6
6
5
3
3
LFT
EST
8
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
1
1
F(3)
D(2)
2
6
6
5
3
3
LFT
EST
8
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
0
5
J(2)
3
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To find the Critical Path
E(3)
G(2)
4
0
0
1
A(1)
1
1
F(3)
D(2)
2
6
6
5
3
3
LFT
EST
8
8
6
H(1)
9
9
7
C(2)
12
12
I(3)
8
B(4)
10
5
J(2)
3
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Critical Path
5
3
3
E(3)
G(2)
4
0
0
1
A(1)
1
1
F(3)
D(2)
2
6
6
8
8
6
H(1)
9
9
12
12
I(3)
7
C(2)
8
B(4)
10
5
Critical Path 3
J(2)
Critical Path
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PERT
 PERT is a manager’s tool for defining and
coordinating moves for completing a
project’s objectives on time. Its use is not
restricted to the business world.
 It can be applied to any endeavor which
requires planned, controlled, and integrated
work patterns. More often than not,
diversified activities contribute to the
difficulty in completing a project on
schedule.
 Many uncertainties are associated with
these activities. PERT is a technique that
statistically presents knowledge about these
uncertainties.
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 A technique -- that aids the decision-maker,
but does not make decisions for him.
 A technique -- that presents statistical
information regarding the uncertainties
associated with completing the different
activities inherent in the project.
 A method -- for focusing a manager’s
attention on:
– latent problems that require solutions, and
– procedures and adjustments of time, resources,
or performance,
which may improve the probability of meeting
all intended project completion dates.
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Benefits of CPM/PERT






Useful at many stages of project management
Mathematically simple
Give critical path and slack time
Provide project documentation
Useful in monitoring costs
Pert uses probabilistic time estimates to
determine the probability that a project will be
done by a specific time.
 To reduce the length of the project (crashing), we
need to know the critical path of the project and
the cost of reducing individual activity times.
Crashing activities that are not on the critical
path typically do not reduce project completion
time.
 The critical chain approach removes excess
safety time from individual activities and creates
a project buffer atRahul
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The Advantages of PERT and CPM
Detailed planning: The use of PERT and CPM forces management to plan in
detail and to define what must be done to accomplish objectives on time.
Commitments and communications: Management is forced to plan and make
commitments regarding execution times and completion dates. The tools also
provide for better communication among the various departments in an
organization and between suppliers and the client.
Efficient monitoring and control: The number of critical activities in a
network (especially in a large one) is only a small portion of the total activities.
Identification of the critical activities enables the use of an efficient monitoring
system (mainly record-keeping and reports) concentrating only on the critical
activities.
Identifying potential problem areas: The critical activities are also more
likely to become problem areas. Once identified, contingency plans may be
devised.
Proper use of resources: Employing PERT or CPM enables management to
use resources more wisely by examination of the overall plan. Resources can he
transferred to bottleneck or trouble areas from other activities.
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 Rescheduling: The tools enable management to follow up and correct
deviations from schedule as soon as they are detected, thus minimizing
delays.
 Government contracts: Several government agencies require the
submission of a PERT or CPM plan with bids.
 Easily understood: CPM and PERT can be easily understood because they
provide a method for visualizing an entire project. Therefore management
can explain the tools to supervisors and employees in such a way that the
chances of implementation are increased.
 Adaptable to computers: PERT and CPM are easily adaptable to computer
use. Large projects can be planned by computers in seconds is even capable
of diagramming the networks.
 Tools for decision making: PERT and CPM allow management to check
the effectiveness and efficiency of alternative ways of executing projects by
examining possible trade-offs among resources (usually time and cost).
 Assess probability of completion (in PERT only): The probabilities of
successfully meeting deadlines, finishing early, or finishing late can be
assessed by the use of PERT.
 Cost-time trade-offs (in CPM only): CPM enables management to evaluate
trade-offs between the cost of executing a job in a normal way or expediting
activities (called crashing) at a higher cost so as to finish earlier.
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Limitations to CPM/PERT
 Clearly defined, independent and stable
activities
 Specified precedence relationships
 Over emphasis on critical paths
 Deterministic CPM model
 Activity time estimates are subjective and
depend on judgment
 PERT assumes a beta distribution for these
time estimates, but the actual distribution
may be different
 PERT consistently underestimates the
expected project completion time due to
alternate paths becoming critical
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Summary
 A project is a unique, one time event of some
duration that consumes resources and is
designed to achieve an objective in a given time
period.
 Each project goes through a five-phase life
cycle: concept, feasibility study, planning,
execution, and termination.
 Two network planning techniques are PERT and
CPM. Pert uses probabilistic time estimates. CPM
uses deterministic time estimates.
 Pert and CPM determine the critical path of the
project and the estimated completion time. On
large projects, software programs are available
to identify the critical path.
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 Pert uses probabilistic time estimates to
determine the probability that a project will be
done by a specific time.
 To reduce the length of the project (crashing),
we need to know the critical path of the project
and the cost of reducing individual activity
times. Crashing activities that are not on the
critical path typically do not reduce project
completion time.
 The critical chain approach removes excess
safety time from individual activities and
creates a project buffer at the end of the critical
path.
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