Network Analysis : Pert & CPM

MADE BY :RUCHIKA TYAGI(LECTURER)CIVIL DEPARTMENTGITAM

Introduction

Network analysis is one of the important tools for projectmanagement. Whether major or minor a project has to be completed in a definitetime & at a definite cost.

The necessary information of any particular data can berepresented as a project network. These techniques are very useful for planning, scheduling andexecuting large-time bound projects involving careful co-ordinationof variety of complex and interrelated activities

Objectives of network analysis

Helpful in planningInter-relationship of various activitiesCost controlMinimisation of maintenance timeReduction of timeControl on idle resourcesAvoiding delays, interruptions

Applications of networkanalysis

Planning, scheduling, monitoring and control oflarge and complex projects.Construction of factories, highways, building,bridges, cinemas etc.Helpful to army for its missile development.Assembly line schedulingInstallation of computers and high techmachineriesTo make marketing strategies

Methodology Involved in NetworkAnalysis

Describing the Project

Diagramming the network

Estimating the time of completion

Deterministicestimates

Probabilisticestimates

Monitoring the project progress

Key terminology

Activity : All projects may be viewed as composed of activities. It isthe smallest unit of work consuming both time& resources thatproject manager should schedule & control. An activity is represented by an arrow in network diagram

The head of the arrow shows sequence ofactivities.

Classification of activities

Predecessor activity: Activities that must be completedimmediately prior to the start of another activity are calledpredecessor activities. Successor activity : activities that cannot be started until one ormore of other activities are completed but immediately succeedthem are called successor activities.

Concurrent activities: activities that can be accomplished togetherare known as concurrent activities. Dummy activity: An activity which does not consume any resourcebut merely depicts the dependence of one activity on other is calleddummy activity. It is introduced in a network when two or moreparallel activities have the same start and finish nodes.

Event

The beginning & end of an activities are called as events .Events are represented by numbered circles called nodes.

i j

Eventstart

Event finish

Types of Events

Merge event

Burst event

Merge & Burst Event

Path & Network

An unbroken chain of activity arrows connecting the initial event tosome other event is called a path. A network is the graphical representation of logically & sequentiallyconnected arrows & nodes representing activities & events of aproject . It is a diagram depicting precedence relationships betweendifferent activities.

Errors in network logic

Looping : looping is known as cycling error andcreates an impossible situation and it appearsthat none of the activities could ever becompleted. Dangling : sometimes a project network includesan activity which does not fit into the endobjective of the project and is carried out withoutany result related with completion of the project .Such an error in network is called dangling

Guidelines for NetworkConstruction

A complete network diagram should have one stand point & onefinish point.The flow of the diagram should be from left to right.Arrows should not be crossed unless it is completely unavoidable.Arrows should be kept straight & not curved or bent.Angle between arrows should as large as possible.Each activity must have a tail or head event.. No two or moreactivities may have same tail & head events.Once the diagram is complete the nodes should be numbered fromleft to right. It should then be possible to address each activityuniquely by its tail & head event.

Stages for project management

Project planning stages : in order tovisualize the sequencing or precedencerequirements of the activities in a project,it is helpful to draw a network diagram. Scheduling stage : once all work packageshave been identified and given uniquenames or identifiers, scheduling of theproject

Project control stage : project control refers to evaluating

actual progress against the plan. Ifsignificant differences are observed, thenthe scheduling and resources allocationdecisions are changed to update andrevise the uncompleted part of the project

Advantages

Planning & controlling projectsFlexibilityDesignation of responsibilitiesAchievement of objective with least costBetter managerial control

Limitations of PERT /CPM

Network diagrams should have clear starting & ending points ,which are independent of each other which may not be possible inreal life. Another limitation is that it assumes that manager should focus oncritical activities. Resources will be available when needed for completion for an anactivity is again unreal.

Difficulties

Difficulty in securing realistic time estimates.The planning & implementation of networks requires trained staff.Developing clear logical network is troublesome.

Example

Activity

Predecessoractivity

A none

B none

C A

D A

E B

F C

G D & E

1

3

2

5

4

6

A

B

C

D

E

F

G

Draw the network diagram for the following

Activity

Predecessoractivity

A none

B A

C A

D B

E C

F D ,E

1 2

3

4

5 6A

B

C

D

E

F

Critical path

Those activities which contribute directly to the overall duration ofthe project constitute critical activities, the critical activities form achain running through the network which is called critical path. Critical event : the slack of an event is the difference between thelatest & earliest events time. The events with zero slack time arecalled as critical events. Critical activities : The difference between latest start time &earliest start time of an activity will indicate amount of time bywhich the activity can be delayed without affecting the total projectduration. The difference is usually called total float. Activities with 0total float are called as critical activities

Critical path

The critical path is the longest path in the network from the startingevent to ending event & defines the minimum time required tocomplete the project. The critical path is denoted by darker or double lines.

Difference between PERT & CPMPERT

A probability model withuncertainty in activityduration . The duration ofeach activity is computedfrom multiple timeestimates with a view totake into account timeuncertainty.

It is applied widely forplanning & schedulingresearch projects.

PERT analysis does notusually consider costs.

CPM

A deterministic model with wellknown activity times based upon thepast experience.

It is used for construction projects &business problems.

CPM deals with cost of projectschedules & minimization.

Float : There are many activities where themaximum time available to finish the activity is morethan the time required to complete the activity. Thedifference between the two times is known as floatavailable for the activity. There are three types of float:

Total float : It is the spare time available when allpreceding activities occur at earliest possible times &all success ding activities occur at latest possibletimes. Total float = Ls – Es or Lf – Ef

Free float : time available when all precedingactivities occur at the earliest possible time &allsucceeding activities also occur at the earliest possibletimes.

Free float = total float - head event slackIndependent Float : it may be defined as theamount of time by which the start of an activity canbe delayed without affecting the earliest start timeof any successor activity , assuming that precedingactivity has finished at its latest finish time.Independent Float = free float – tail event slack

QUESTION :Activity

Predece

ssoractivity

Optimistic (to)

Mostlikely(tm)

Pessimistic (tp)

ABCDEFG

--AABC

D,E

2214431

3326541

1043

141257

CRITICAL PATH : 1-2-5-6 or A-D-G

Activity Expected timeTe = to +4tm+tp 6

A(1-2)B(1-3)C(2-4)D(2-5)E(3-5)F(4-6)G(5-6)

4327642

activity

te Es Ef = Es+te

Lf LS=

Lf -te

Headslack

Tailslack

Total

float

Free

float

Independent

float

1-21-32-42-53-54-65-6

4327642

004436

11

436

119

1013

459

11111313

027459

11

0230000

0000230

0230230

0000230

0000000

PERT

1.

2.

3.

4.

PERT is designed for scheduling complex projects thatinvolve many inter-related tasks. it improves planningprocess because:

It forms planner to define the projects variouscomponents activities.It provides a basis for normal time estimates & yetallows for some measure of optimism or pessimism inestimating the completion dates.It shows the effects of changes to overall plans theycontemplated.It provides built in means for ongoing evaluation of theplan.

ESTIMATING ACTIVITY TIMES

Optimistic time ( t0 ) : is that time estimate of anactivity when everything is assumed to go as per plan.In other words it is the estimate of minimum possibletime which an activity takes in completion under idealconditions. Most likely time ( tm ) : the time which the activity willtake most frequently if repeated number of times. Pessimistic time ( tp) : the unlikely but possibleperformance time if whatever could go wrong , goeswrong in series. In other words it is the longest timethe can take.

EXPECTED TIME The times are combined statically to develop the

expected time te . te = to + 4tm + tp 6 Standard deviation of the time of the time required to

complete the project = tp - to 6

STEPS INVOLVED IN PERT

Develop list of activities.A rough network for PERT is drawn.Events are numbered from left to right.Time estimates for each activity are obtained.Expected time for each activity is calculated : to+4tm+tp /6Using these expected times calculate earliest & latest finish& start times of activities.Estimate the critical path.Using this estimate compute the probability of meeting aspecified completion date by using the standard normalequation

Z = Due date – expected date of completion standard deviation of critical path

QUESTION : The table showsactivities of project. Duration (days)

JOB OPTIMISTIC

MOSTLIKELY

PESSIMISTIC

1-21-32-42-63-43-54-55-6

1531

10252

41034

15455

71537

26658

1.

2.

Draw the network &find expected projectcompletion time.What is the probability that it would becompleted in 41 days.

Variance of critical path

Activity To Tp variance

1-33-44-55-6

51052

152658

2.777.1101Total=10.88

So, standard deviation = 3.30Probability for completing the job in 41 days.Z = DUE DATE – EXPECTED DATE OF COMPLETION S.D. OF CRITICAL PATH = 41 – 36 3.30 = 1.51The tabulated value of corresponding to calculated

value i.e. 1.51 is .4345So probability is .5 + .4345 = .9345 i.e. 93.45% that

project will be completed on 41 day.

QUESTION: Activity predecessor timeestimates (weeks)

activity Preceding activity

to tm tp

ABCDEFG

--AABC

D,E

2214431

3326541

1043

141257

Find the expected duration andvariance of each activity.What is the expected projectlength?Calculate the variance &standarddeviation of the project length.

activity to Tm

tp te variance

ABCDEFG

2214431

3326542

1043

141257

4327642

16/91/91/9

25/916/91/91

Various paths &expected project length A-C-F = 4+2+4 = 10 A-D-G = 4+7+2 = 13 CRITICAL

PATH B-E-G = 3+6+2 = 11Thus critical path is A-D-G with an

expected length of 13 days. Hencethe expected project length is 13days.

Project variance = 16/9 + 25/9 + 1 =