Network Analysis

What exactly is a project?• PM 1 – I am directing a team of research scientists. We are

running trials on a new analgesic drug on behalf of apharmaceutical company.

• It is my responsibility to design the experiments and make surethat proper scientific and legal procedures are followed, so that ourresults can be subjected to independent statistical analysis.

• A new drug• PM 2- The international aid agency which employs me is sending

me to New Delhi to organize the introduction of multimediaresources at a teachers’ training college.

• My role is quite complex. I have to make sure that appropriateresources are purchased- and in some cases developed within thecollege.

• I also have to encourage the acceptance of these resources bylecturers and students within the college.

A new method of teaching students

Project• A project is a temporary Endeavour involving a connected

sequence of activities and a range of resources,• which is designed to achieve a specific and unique outcome and• which operates within time, cost and quality constraints and• Which is often used to introduce change?

• “A project is a series of activities directed to accomplishment of adesired objective.”

Plan your work first…..then work your plan

Characteristic of a project:-l A unique, one-time operational activity or effortl Requires the completion of a large number of interrelated activitiesl Established to achieve specific objectivel Resources, such as time and/or money, are limitedl Typically has its own management structurel Need leadership

Examples– constructing houses, factories, shopping malls, athletic

stadiums or arenas– developing military weapons systems, aircrafts, new ships– launching satellite systems– constructing oil pipelines– developing and implementing new computer systems– planning concert, football games, or basketball tournaments– Introducing new products into market.–

What is project management?• The application of a collection of tools and techniques to direct the

use of diverse resources towards the accomplishment of a unique,complex, one time task within time, cost and quality constraints.

• Its origins lie in World War II, when the military authorities usedthe techniques of operational research to plan the optimum use ofresources.One of these techniques was the use of networks to represent asystem of related activities.

Work break down structure

Project can be splitted into small tasks with sequence of theirexecution. This process is known as work break down structure “

A method of breaking down a project into individual elements(Components, subcomponents, activities and tasks) in ahierarchical structure which can be scheduled and cost.

It defines tasks that can be completed independently of other tasks,facilitating resource allocation, assignment of responsibilities andmeasurement and control of the project. It is foundation of projectplanning. It is developed before identification of dependencies andestimation of activity durations. It can be used to identity the tasksin the CPM and PERT

Network Representation

Each activity of the project is represented by an arc pointing in thedirection of progress in the project.

The nodes of the network establish the precedence relationshipsamong the different activities of the project.

Network analysis• Network analysis is the general name given to certain specific

techniques which can be used for the planning, managementand control of projects.

Network is a graphical representation of all the Activities andEvents arranged in a logical and sequential order. • Networkanalysis plays an important role in project management.• A projectis a combination of interrelated activities all of which must beexecuted in a certain order for its completion.

Main objectives are:Complete the project within stipulated period..Optimize resources utilization.Better coordination in interdependent activities.

C.P.M & P.E.R.T are two methodologies to analyze the networkA flow-chart that illustrates;The order in which tasks will be performedDependencies between tasksUse of nodes and arrows

Arrows An arrow leads from tail to head directionallyIndicate ACTIVITY, a time consuming effort that is required toperform a part of the work.Comprise three elementsNodes/ Event A node is represented by a circle

Indicate EVENT, a point in time where one or more activities startand/or finish.Signals the beginning or ending of an activityDesignates a point in timeRepresented by a circle (node)

Span time –the actual calendar time required to complete an activity

NetworkShows the sequential relationships among activities using nodesand arrows.

It is the combination of all activities and events define theproject and the activity precedence relationships.

ActivityA task or a certain amount of work required in the projectRequires time to complete

Represented by an arrow Activity is the actualperformance of the job. This consumes resources (Time, humanresources, money, and material)

• PERT and CPM are the two most popular network analysistechnique used to assist managers in planning and controlling largescale projects.• PERT- (Programme Evaluation Review Technique)• CPM - (Critical Path Method)

Applications: -Construction of a Residential complex,Commercial complex,Petro-chemical complexShip buildingSatellite mission developmentInstallation of a pipe line project etc...

Predecessor activity: An activity that must occur before anotheractivity.Successor activity: An activity that must occur after anotheractivity.

An activity can be in any of these conditions:

It may have a successor(s) but no predecessor(s) - starts a networkIt may have a predecessor(s) but no successor(s) - ends a networkIt may have both predecessor(s) and successor(s) - in the middle ofa network

Rules to draw the network

Each event is presented by the nodes.

Each activity is represented by one, and only one (arc) arrow.

Each activity must be identified by two distinct end nodes.

Activity A has two end nodes:

1- start node, 2 – end node

Rules to draw the network

Rule-1 –

An activity (succeeding) cannot start unless all its preceding activities have been

completed. (not applicable on dummy activity)

A must finish before either B or C can start

both A and B must finish before C can start A must finish before B can star

both A and C must finish before D can start.

• Rule-2:- There should be no loops in the project network.

Rule-3:- Each events should have a distinct number. Usually number at thehead of the arrow is greater than that at its tail. (Fulkerson’s Rule)

ie., numbers should not be duplicated.

Fulkerson’s Rule

The starting event (having no predecessor activity is numbered as 1 )other events are numbered in increasing order from 1 to rightwards,if there are more then 1 initial event found in a diagram , anywherethey are to be numbered from top to bottom in increase order. Notwo events can have the same number in any case.

Rule-4 :

Not more than one activity can have the same preceding andsucceeding events. OR No two events can be connected by more thanone activity.

Rule-4- (Concurrent Activities)

Rule-5

• Network diagram cannot have more than one startingnode or end node.

• The activities emerging from event 1 should have nopredecessor activities & event having highest number indiagram should have no successor activity.

Example-1

• Activity Pred Duration in days

• a - 3

• b - 14

• c - 3

• d a 7

• e d 4

• f c, 10

Example-2

• Activity Pred Duration in days

• a - 3

• b - 14

• c - 3

• d a 7

• e d 4

• f c,e 10 \

Example-3

• a - 3

• b - 14

• c a,b 3

• Useof dummy activity:

• To establish correct precedence relationships, dummyactivities are used.

• A dummy activity, which is normally depicted by a dashedarc, consumes no time or resources.

• For example, if two activities that can start concurrentlyand have the same duration can be represented using adummy activity as:

• A dummy activity is an imaginary activity which can beaccomplished in zero time and which does not consumeresources.

• It may also be used to represent a constraint.{ It Indicatesonly precedence relationships . Does not require any timeof effort}

To maintain the correct precedence relationships, thefollowing questions must be answered as each activity isadded to the network:

(a) What activities must immediately precede the currentactivity?

(b) What activities must follow the current activity?

(c) What activities must occur concurrently with the currentactivity?

The answers to these questions may require the use ofdummy activities to ensure correct precedence among theactivities.

Problem 1

1. Construct the project network consisting of activities A to Lwith the following precedence relationships:

(a) A, B and C, the first activities of the project, can beexecuted concurrently.

(b) A and B precede D.

(c) B precedes E, F and H.

(d) F and C precede G.

(e) (e) E and H precede I and J.

(f) (f) C, D, F and J precede K.

(g) (g) K precede L.

(h) (h) I, G and L are the terminal activities of the

(i) project.

Ans:-

• Activity Pred

• a -

• b -

• c -

• d a, b

• e b

• f b

• g f,c

• h b

• i, j e,f

• K c,d,f,j

• L k

Problem 2

Construct the project network consisting of activities A to Iwith the following precedence relationships:

(a) A and B, the first activities of the project startimmediately.

(b) A and B precede C.

(c) B precedes D and E.

(d) A and B precede F.

(e) F and D precede G and H.

(f) C and G precede I.

(f) E, H and I are terminal activities

Ans

• Activity Pred

• a -

• b -

• c a, b

• d b

• e b

• f a, b

• g f,d

• h f,d

i c,g

Problem 3

• a) Activities (1-2) and (1-3) can start simultaneously.

• b) Activity (1-2) proceeds activity (2-4) and (2-6)

• c) Activities (3-4) and (3-5) can start only on completion of activity

• (1-3).

• d) Activity (4-7) can start only after (2-4) and (3-4) have been

• completed.

• e) Activities (5-7) and (5-9) can not start till activities (2-4), (3-4) and

• (3-5) are completed.

• f) Activities (6-8) and (6-7) can start only on completion of (2-6).

• g) Activity (8-9) follows activity (6-8).

• h) Activities (8-9), (7-9) and (5-9) can be taken up simultaneously for

• completion of the project.

Historical Evolution.( PERT & CPM)

Before 1957 there was no generally accepted procedure to aid the management

of a Project. In 1958 PERT was developed by team of engineers working on a

Polaris Missile programme of the navy. This was a large project involved 250

prime contractors and about 9000 job contractors. It had about 19 million

components. In such projects it is possible that a delay in the delivery of a small

component might hold the progress of entire project. PERT was used successfully

and the total time of completion was reduced from 7 years to 5 years.

In 1958 Du Pont Company used a technique called Critical Path Method (CPM) to

Schedule and control a very large project like overhauling of a chemical plant,

there by reducing the shutdown period from 130hrs to 90 hrs saving the company 1

million dollar.

Both of these techniques are referred to as project scheduling techniques.

Determining the Project Schedule

• Some activities can be done simultaneously so project duration should beless than 25 weeks

• Critical path analysis is used to determine project duration

• The critical path is the longest path through the network

Critical Path Analysis

Need to find the following for each activity:

• Earliest Start Time (EST)

• Earliest Finish Time (EFT)

• Latest start time (LST)

• Latest Finish Time (LFT)

• Activity Slack

• Each event has two important times associated with it :

• Earliest time , Te , which is a calendar time when a event can occur when allthe predecessor events completed at the earliest possible times

• Latest time , TL , which is the latest time the event can occur with outdelaying the subsequent events and completion of project.

• Difference between the latest time and the earliest time of an event is theslack time for that event

• Positive slack : Slack is the amount of time an event can be delayedwithout delaying the project completion.

• Forward Pass

• Identifies earliest times (EST and EFT)

• EST Rule: All immediate predecessors must be done before an activity canbegin

• If only 1 immediate predecessor, then EST = EFT of predecessor

• If >1 immediate predecessors, then EST = Max {all predecessor EFT’s}

• EFT Rule: EFT = EST + activity time

Backward Pass

• Identifies latest times (LST an LFT)

• LFT Rule:

– If activity is the immediate predecessor to only 1 activity, then

LFT = LST of immediate follower

– If activity is the immediate predecessor to multiple activities, then

LFT = Min {LST of all imm. followers}

• LST Rule: LST = LFT – activity time

• Backward Pass: Latest Start and Finish Times

•

•

Slack Time and Critical Path(s)

• Slack is the length of time an activity can be delayed without delaying theproject Slack = LST – EST

• Activities with 0 slack are Critical Activities

• The Critical Path is a continuous path through the network from start tofinish that includes only critical activities.

• Is that the sequence of activities and events where there is no “slack” i.e..Zero slack.

• Longest path through a network

• minimum project completion time

•

• Total Slack Time vs. Free Slack Time

• Total slack time is shared by more than 1 activity

• Example: A 1 week delay in activity B will leave 0 slack for activity D

• Free slack time is associated with only 1 activity

Example: Activity F has 6 week of free slack time

Problem-1. The following table lists the activities of a maintenanceproject .

Activity Duration

1-2 4

1-3 6

2-6 8

3-4 7

3-5 4

4-6 6

5-6 5

5-7 19

6-7 10

Problem

• Solution : The Flaws are

• i) The activity B and E have same initial and ending nodes , which is notcorrect.

• ii) a loop is formed by activities j,k and l , WHICH IS NOT PERMITTED.

• iii) The dummy activity d2 is unnecessary

Problem

•

Solution :

• Activity Pred

• k -

• L -

• M -

• N K

• O M

• P K,L

• Q N,O

• R L,O

• S R

Problem :

Information on the activities required for a project is as follows

• Draw the network and calculate

• The Earliest start (ES), earliest Finish (EF), latest start (LS),

• latest finish(LF) and TF times of each of the activities.

Name ActivitiesNode

Duration(days)

A 1-2 2B 1-3 7C 1-4 8D 2-5 3E 3-5 6F 3-6 10G 3-7 4H 4-6 6I 5-7 2J 6-8 5K 7-8 6