This document provides an overview of project management techniques including network analysis, CPM, and PERT. It defines key terms like activities, events, paths, and networks. Network analysis is used to plan, schedule, and control complex projects by representing relationships between activities. CPM uses deterministic activity times while PERT accounts for uncertainty with probabilistic estimates. The critical path consists of activities that directly determine the project duration. Project management involves planning, scheduling, and controlling a project over its stages.

1. Project ManagementProject Management
: PERT & CPM: PERT & CPM
BY:BY:
RANDHIR KUMARRANDHIR KUMAR
Roll No – 1503050Roll No – 1503050
Department of Civil EngineeringDepartment of Civil Engineering
National Institute Of Technology PatnaNational Institute Of Technology Patna
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2. ContentContent
 IntroductionIntroduction
 Network analysis & its applicationNetwork analysis & its application
 Stages of Project ManagementStages of Project Management
 CPMCPM
 PERTPERT
 ConclusionConclusion
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3. IntroductionIntroduction
ProjectProject
•• A project is an interrelated set of activities that has aA project is an interrelated set of activities that has a
definite starting and ending point and that results in adefinite starting and ending point and that results in a
unique product or service.unique product or service.
Project managementProject management
•• Project management is a scientific way of planning,Project management is a scientific way of planning,
implementing, monitoring & controlling the various aspectsimplementing, monitoring & controlling the various aspects
of a project such as time, money, materials, manpower &of a project such as time, money, materials, manpower &
other resources.other resources.
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4. Network AnalysisNetwork Analysis
 Network analysis is one of the important tools for projectNetwork analysis is one of the important tools for project
management.management.
 Whether major or minor a project has to be completed in a definiteWhether major or minor a project has to be completed in a definite
time & at a definite cost.time & at a definite cost.
 The necessary information of any particular data can beThe necessary information of any particular data can be
represented as a project network.represented as a project network.
 These techniques are very useful for planning, scheduling andThese techniques are very useful for planning, scheduling and
executing large-time bound projects involving careful co-ordinationexecuting large-time bound projects involving careful co-ordination
of variety of complex and interrelated activitiesof variety of complex and interrelated activities
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5. Objectives of network analysisObjectives of network analysis
 Helpful in planningHelpful in planning
 Inter-relationship of various activitiesInter-relationship of various activities
 Cost controlCost control
 Minimisation of maintenance timeMinimisation of maintenance time
 Reduction of timeReduction of time
 Control on idle resourcesControl on idle resources
 Avoiding delays, interruptionsAvoiding delays, interruptions
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6. Applications of network analysisApplications of network analysis
 Planning, scheduling, monitoring and control ofPlanning, scheduling, monitoring and control of
large and complex projects.large and complex projects.
 Construction of factories, highways, building,Construction of factories, highways, building,
bridges, cinemas etc.bridges, cinemas etc.
 Helpful to army for its missile development.Helpful to army for its missile development.
 Assembly line schedulingAssembly line scheduling
 Installation of computers and high techInstallation of computers and high tech
machineriesmachineries
 To make marketing strategiesTo make marketing strategies
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7. Methodology Involved in NetworkMethodology Involved in Network
AnalysisAnalysis
Describing the Project
Diagramming the network
Estimating the time of completion
Deterministic
estimates
Probabilistic
estimates
Monitoring the project progress
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8. Key terminologyKey terminology
 Activity : All projects may be viewed as composed of activities.Activity : All projects may be viewed as composed of activities.
It is the smallest unit of work consuming both time& resourcesIt is the smallest unit of work consuming both time& resources
that project manager should schedule & control.that project manager should schedule & control.
 An activity is represented by an arrow in network diagramAn activity is represented by an arrow in network diagram
The head of the arrow shows sequence of
activities.
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9. Classification of activitiesClassification of activities
 Predecessor activityPredecessor activity: Activities that must be completed: Activities that must be completed
immediately prior to the start of another activity are calledimmediately prior to the start of another activity are called
predecessor activities.predecessor activities.
 Successor activitySuccessor activity : activities that cannot be started until one or: activities that cannot be started until one or
more of other activities are completed but immediately succeedmore of other activities are completed but immediately succeed
them are called successor activities.them are called successor activities.
 Concurrent activitiesConcurrent activities: activities that can be accomplished together: activities that can be accomplished together
are known as concurrent activities.are known as concurrent activities.
 Dummy activityDummy activity: An activity which does not consume any resource: An activity which does not consume any resource
but merely depicts the dependence of one activity on other is calledbut merely depicts the dependence of one activity on other is called
dummy activity. It is introduced in a network when two or moredummy activity. It is introduced in a network when two or more
parallel activities have the same start and finish nodes.parallel activities have the same start and finish nodes.
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10. EventEvent
 The beginning & end of an activities are called as events .The beginning & end of an activities are called as events .
 Events are represented by numbered circles called nodes.Events are represented by numbered circles called nodes.
i j
Event
start
Event
finish
1010
Figure 1

11. Types of EventsTypes of Events
 Merge eventMerge event
 Burst eventBurst event
 Merge & Burst EventMerge & Burst Event
1111Figure 2

12. Path & NetworkPath & Network
 An unbroken chain of activity arrows connecting the initial event toAn unbroken chain of activity arrows connecting the initial event to
some other event is called a path.some other event is called a path.
 A network is the graphical representation of logically & sequentiallyA network is the graphical representation of logically & sequentially
connected arrows & nodes representing activities & events of aconnected arrows & nodes representing activities & events of a
project . It is a diagram depicting precedence relationships betweenproject . It is a diagram depicting precedence relationships between
different activities.different activities.
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13. Example
ActivityActivity PredecessorPredecessor
activityactivity
AA nonenone
BB nonenone
CC AA
DD AA
EE BB
FF CC
GG D & ED & E
1
3
2
5
4
6
A
B
C
D
E
F
G
1313Figure 3

14. Draw the network diagram for the following
ActivityActivity PredecessorPredecessor
activityactivity
AA nonenone
BB AA
CC AA
DD BB
EE CC
FF D ,ED ,E
1414

15. 1 2
3
4
5 6
A
B
C
D
E
F
1515
Figure 4

16. Stages for project managementStages for project management
 Project planning stages : in order toProject planning stages : in order to
visualize the sequencing or precedencevisualize the sequencing or precedence
requirements of the activities in a project,requirements of the activities in a project,
it is helpful to draw a network diagram.it is helpful to draw a network diagram.
 Scheduling stage : once all work packagesScheduling stage : once all work packages
have been identified and given uniquehave been identified and given unique
names or identifiers, scheduling of thenames or identifiers, scheduling of the
projectproject
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17.  Project control stage :Project control stage :
project control refers to evaluatingproject control refers to evaluating
actual progress against the plan. Ifactual progress against the plan. If
significant differences are observed, thensignificant differences are observed, then
the scheduling and resources allocationthe scheduling and resources allocation
decisions are changed to update anddecisions are changed to update and
revise the uncompleted part of the projectrevise the uncompleted part of the project
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18. PERT & CPMPERT & CPM
PERT
A probability model with
uncertainty in activity
duration . The duration of
each activity is computed
from multiple time estimates
with a view to take into
account time uncertainty.
It is applied widely for
planning & scheduling
research projects.
PERT analysis does not
usually consider costs.
CPM
A deterministic model with well
known activity times based upon the
past experience.
It is used for construction projects &
business problems.
CPM deals with cost of project
schedules & minimization.
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19. Activity slackActivity slack
Each event has two important times associatedEach event has two important times associated
with it :with it :
-Earliest time-Earliest time ,, TeTe ,, which is a calendar time when awhich is a calendar time when a
event can occur when all the predecessor eventsevent can occur when all the predecessor events
completed at the earliest possible timescompleted at the earliest possible times
-Latest time-Latest time ,, TLTL ,, which is the latest time the event canwhich is the latest time the event can
occur with out delaying the subsequent events andoccur with out delaying the subsequent events and
completion of project.completion of project.
 Difference between the latest time and the earliest timeDifference between the latest time and the earliest time
of an event is theof an event is the slack timeslack time for that eventfor that event
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20. Critical pathCritical path
 Those activities which contribute directly to the overall duration ofThose activities which contribute directly to the overall duration of
the project constitute critical activities, the critical activities form athe project constitute critical activities, the critical activities form a
chain running through the network which is called critical path.chain running through the network which is called critical path.
 Critical eventCritical event : the slack of an event is the difference between the: the slack of an event is the difference between the
latest & earliest events time. The events with zero slack time arelatest & earliest events time. The events with zero slack time are
called as critical events.called as critical events.
 Critical activitiesCritical activities : The difference between latest start time &: The difference between latest start time &
earliest start time of an activity will indicate amount of time by whichearliest start time of an activity will indicate amount of time by which
the activity can be delayed without affecting the total projectthe activity can be delayed without affecting the total project
duration. The difference is usually called total float. Activities with 0duration. The difference is usually called total float. Activities with 0
total float are called as critical activitiestotal float are called as critical activities
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21. Critical pathCritical path
 The critical path is the longest path in the network from the startingThe critical path is the longest path in the network from the starting
event to ending event & defines the minimum time required toevent to ending event & defines the minimum time required to
complete the project.complete the project.
 Is that the sequence of activities and events where there is noIs that the sequence of activities and events where there is no
“slack” i.e..“slack” i.e.. Zero slackZero slack
 The critical path is denoted by darker or double lines.The critical path is denoted by darker or double lines.
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22. We will see below how the network analysis diagram/picture weWe will see below how the network analysis diagram/picture we
construct helps us to answer this question.construct helps us to answer this question.
2222Figure 5

23. Finding critical pathFinding critical path
2323
Figure 6

24. CRITICAL PATH TAKESCRITICAL PATH TAKES 24 DAYS24 DAYS FOR THEFOR THE
COMPLETION OF THE PROJECTCOMPLETION OF THE PROJECT
2424
Figure 7

25. PERTPERT
PERT is designed for scheduling complex projects thatPERT is designed for scheduling complex projects that
involve many inter-related tasks. it improvesinvolve many inter-related tasks. it improves
planning process because:planning process because:
1.1. It forms planner to define the projects variousIt forms planner to define the projects various
components activities.components activities.
2.2. It provides a basis for normal time estimates & yetIt provides a basis for normal time estimates & yet
allows for some measure of optimism or pessimismallows for some measure of optimism or pessimism
in estimating the completion dates.in estimating the completion dates.
3.3. It shows the effects of changes to overall plans theyIt shows the effects of changes to overall plans they
contemplated.contemplated.
4.4. It provides built in means for ongoing evaluation ofIt provides built in means for ongoing evaluation of
the plan.the plan. 2525

26. ESTIMATING ACTIVITY TIMESESTIMATING ACTIVITY TIMES
 Optimistic time ( tOptimistic time ( t00 )) : is that time estimate of an: is that time estimate of an
activity when everything is assumed to go as per plan.activity when everything is assumed to go as per plan.
In other words it is the estimate of minimum possibleIn other words it is the estimate of minimum possible
time which an activity takes in completion under idealtime which an activity takes in completion under ideal
conditions.conditions.
 Most likely time ( tMost likely time ( tmm )) : the time which the activity will: the time which the activity will
take most frequently if repeated number of times.take most frequently if repeated number of times.
 Pessimistic time ( tp)Pessimistic time ( tp) :: the unlikely but possiblethe unlikely but possible
performance time if whatever could go wrong , goesperformance time if whatever could go wrong , goes
wrong in series. In other words it is the longest timewrong in series. In other words it is the longest time
the can take.the can take.
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27. EXPECTED TIMEEXPECTED TIME
 The times are combined statically to develop theThe times are combined statically to develop the
expected time texpected time tee ..
ttee == to + 4tm + tpto + 4tm + tp
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Standard deviation of the time of the time required toStandard deviation of the time of the time required to
complete the projectcomplete the project
== tp - totp - to
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28. STEPS INVOLVED IN PERTSTEPS INVOLVED IN PERT
 Develop list of activities.Develop list of activities.
 A rough network for PERT is drawn.A rough network for PERT is drawn.
 Events are numbered from left to right.Events are numbered from left to right.
 Time estimates for each activity are obtained.Time estimates for each activity are obtained.
 Expected time for each activity is calculated : to+4tm+tp / 6Expected time for each activity is calculated : to+4tm+tp / 6
 Using these expected times calculate earliest & latest finishUsing these expected times calculate earliest & latest finish
& start times of activities.& start times of activities.
 Estimate the critical path.Estimate the critical path.
 Using this estimate compute the probability of meeting aUsing this estimate compute the probability of meeting a
specified completion date by using the standard normalspecified completion date by using the standard normal
equationequation
Z =Z = Due date – expected date of completionDue date – expected date of completion
standard deviation of critical pathstandard deviation of critical path
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29. AdvantagesAdvantages
 Planning & controlling projectsPlanning & controlling projects
 FlexibilityFlexibility
 Designation of responsibilitiesDesignation of responsibilities
 Achievement of objective with least costAchievement of objective with least cost
 Better managerial controlBetter managerial control
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30. Limitations of PERT /CPMLimitations of PERT /CPM
 Network diagrams should have clear starting & ending points ,Network diagrams should have clear starting & ending points ,
which are independent of each other which may not be possible inwhich are independent of each other which may not be possible in
real life.real life.
 Another limitation is that it assumes that manager should focus onAnother limitation is that it assumes that manager should focus on
critical activities.critical activities.
 Resources will be available when needed for completion for an anResources will be available when needed for completion for an an
activity is again unreal.activity is again unreal.
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31. ConclusionConclusion
With the help of network diagram and byWith the help of network diagram and by
using PERT & CPM techniques we canusing PERT & CPM techniques we can
optimise cost and time of a project as welloptimise cost and time of a project as well
as we can efficiently use the availableas we can efficiently use the available
resources.resources.
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32. ReferencesReferences
 Garton, C. and E. McCulloch. 2005. Fundamentals of Technology
Project Management.
 A Guide to the Project Management Body of Knowledge. 2000.
Project Management Institute.
 www.google.com
 www.linkedin.com
 www.wikipedia.org
 www.researchgate.net
 www.sciencedirect.com
 Bailey, F. A. 1967. A note on PERT/Cost resource allocation.
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