Project Management

PROJECT MANAGEMENT PROJECT MANAGEMENT PERT/CPMPERT/CPM

MANAGEMENT SCIENCEMANAGEMENT SCIENCEByBy

K. Venkaiah BabuK. Venkaiah Babu MBA., (Ph D)MBA., (Ph D)

Science & Humanities Dept., Science & Humanities Dept.,

Sri SarathiSri Sarathi Institute of Engineering & TechnologyInstitute of Engineering & Technology

LECTURE OUT LINELECTURE OUT LINE Introduction to Project Management To understand the project Life Cycle

1. Project Planning 2. W B S

3. Project Scheduling 4. Project Control To apply tools and technique's

Gantt chart /& Mail stone chart CPM PERT & Probabilistic Activity Times

Project Crashing and Time-Cost Trade-off Describe how CPM / PERT have developed

and merged together to provide a useful technique for managing projects.

What is Project?What is Project?

Definition:Definition: ““Set of inter-related activities”Set of inter-related activities”Unique, one-time operation activity or effortUnique, one-time operation activity or effort to plan, implement, and control the management of

large, one time projects Application:Application:

Used in Construction, Shipbuilding, Weapons, Used in Construction, Shipbuilding, Weapons, Systems Development, etc.Systems Development, etc.

Applies to uncertain technology projectsApplies to uncertain technology projects Applies to variable cost resource allocationApplies to variable cost resource allocation

Project CharacteristicsProject Characteristics Set of ActivitiesSet of Activities

Single unitSingle unit

Money & Time related Money & Time related

General purpose General purpose

High labor skills requiredHigh labor skills required

Project ElementsProject Elements

Objective of Project Management Scope (Limitations / Boundary) Contract requirements Schedules Resources (Physical) Personnel (Psychological) Control Risk and problem analysis

Generic Project Life CycleGeneric Project Life Cycle

EXAMPLES OF EXAMPLES OF PROJECTSPROJECTS

EXAMPLES OF EXAMPLES OF PROJECTSPROJECTS

Examples of ProjectsExamples of ProjectsExamples of ProjectsExamples of Projects

Building constructionBuilding construction


Building constructionBuilding construction New product introductionNew product introduction

9” Nude Sandalfoot9” Nude SandalfootMedium to Tall (B)Medium to Tall (B)

No nonsenseNo nonsense

Sheer to waist pantyhose

New! Improved!

New! Improved!


Building constructionBuilding construction New product introductionNew product introduction Training seminarTraining seminar


Building constructionBuilding construction New product introductionNew product introduction Training seminarTraining seminar Research project Research project

Examples of ProjectsExamples of Projects

Building constructionBuilding construction New product introductionNew product introduction Training seminarTraining seminar Research projectResearch project S/W developmentS/W development Planning concert, football games, or basketball Planning concert, football games, or basketball

tournamentstournaments

Project ScopeProject Scope

Scope statementScope statement A document that provides an understanding, A document that provides an understanding,

justification, and expected result of a projectjustification, and expected result of a project Statement of workStatement of work

written description of objectives of a projectwritten description of objectives of a project Work breakdown structureWork breakdown structure

breaks down a project into components, breaks down a project into components, subcomponents, and activitiessubcomponents, and activities

What is Project Management? (PM)What is Project Management? (PM)

PM is the application of knowledge, skills, PM is the application of knowledge, skills, tools and techniques to project activities in tools and techniques to project activities in order to meet project requirements. order to meet project requirements.

Project Management…Project Management… is an art.is an art. is a science.is a science. has a set of tools and methods.has a set of tools and methods.

Effective Project ManagersEffective Project Managers

Lead by example Visionaries Technically

competent Decisive/pivotal Good

communicators

Good motivators Stand up to exert

when necessary Support team

members Encourage new

ideas

Qualities of Project Manager:Qualities of Project Manager:Project Manager is the most important member of project team

Process of Project ManagementProcess of Project Management Project Planning Project Scheduling Project ControlProject Team

made up of individuals from various areas and departments within a company

Matrix Organization a team structure with members from functional

areas, depending on skills required

Mechanism of PlanningMechanism of Planning

Define project objective (SMART)Define project objective (SMART) Define work breakdown structure (WBS)Define work breakdown structure (WBS)

Identify tasks and subtasks -- deliverablesIdentify tasks and subtasks -- deliverables Lowest element – stand alone work packageLowest element – stand alone work package

Identify tasks relationshipIdentify tasks relationship Identify possible risksIdentify possible risks Estimate work packages (people, time, etc.)Estimate work packages (people, time, etc.) Create initial scheduleCreate initial schedule Iterate plan (Procedure)Iterate plan (Procedure) DocumentDocument

Benefits of the PlanningBenefits of the Planning

Framework for communicationFramework for communication Clients and coworkersClients and coworkers

Allocate resourcesAllocate resources Personnel, equipment and facilities, budgetPersonnel, equipment and facilities, budget

Benchmark to measure progressBenchmark to measure progress

OBJECTIVES OF OBJECTIVES OF PROJECT MANAGEMENTPROJECT MANAGEMENT

Objectives of Project Objectives of Project ManagementManagement

To complete project within elapsed time To ensure optimum utilization of available

resources without delay To complete a project with a minimum of

capital investment.

PROJECT MANAGEMENT PROJECT MANAGEMENT PROCESSPROCESS

Project Management ProcessProject Management Process

Planning Objectives Resources Work break-

down sched. Organization




Scheduling Project

activities Start &

end times Network




Scheduling Project

activities Start &

end times Network

Controlling Monitor, compare,

revise, action

PROJECT PLANNINGPROJECT PLANNING

Project PlanningProject Planning

Establishing objectivesEstablishing objectives Defining projectDefining project Creating work breakdown Creating work breakdown

structure (WBS) structure (WBS) Determining resourcesDetermining resources Forming organizationForming organization

Work Breakdown StructureWork Breakdown Structure(WBS) (WBS)

First Step in Project Management First Step in Project Management Begins with a Work BreakdownBegins with a Work Breakdown

Lists the “WHAT’ of a Project Begins with Finished Project Consists of Tree Chart, with Each Branch Listing the “WHAT’s” at that

Level Then List Each Task that Must Be Completed to Accomplish the Then List Each Task that Must Be Completed to Accomplish the

“WHAT” “WHAT” Start at top, progressively break work down into work packagesStart at top, progressively break work down into work packages Roll up the packages for bottom up estimatingRoll up the packages for bottom up estimating Packages give clear work assignmentsPackages give clear work assignments

Splits work into manageable, logical packagesSplits work into manageable, logical packages Make sure packages can be tested for completenessMake sure packages can be tested for completeness

Top Down Decomposition, Elemental TasksTop Down Decomposition, Elemental TasksTop Down Decomposition, Elemental TasksTop Down Decomposition, Elemental Tasks

` BUY A HOUSE

LOCATION FINANCINGFIND HOUSE

1 - Criteria 3- Determine affordability

6- Type of House

2- Visit Locations

4- Determine mortgage provider

7- Find Real Estate Agent

5- Lockup mortgage commitment

8- Look for House

9- Make Offer, P&S Agreem't

10 - Closing

Ex: WBS Buy a HouseEx: WBS Buy a House

Project Organization Project Organization

Project Organization Project Organization

Often temporary structure Uses specialists from entire company Headed by project manager

Coordinates activities Monitors schedule

& costs Permanent

structure called ‘matrix organization’

Acct.

Eng. Eng.Mkt.

Mgr.

PROJECT SCHEDULINGPROJECT SCHEDULING

Project SchedulingProject Scheduling

Sequencing activities Identifying precedence

relationships Determining activity times

& costs Estimating material &

worker requirements Determining critical

activities

JF

MA

MJ

J

Month

Activity

Design

Build

Test

PE

RT

Project Scheduling TechniquesProject Scheduling TechniquesProject Scheduling TechniquesProject Scheduling Techniques

Gantt chartGantt chart Critical Path Method Critical Path Method

(CPM)(CPM) Program Evaluation & Program Evaluation &

Review Technique (PERT)Review Technique (PERT)

More popular Techniques of Network are:More popular Techniques of Network are: CPMCPM Critical Path MethodCritical Path Method PERTPERT Programme Evaluation and Review Method Programme Evaluation and Review Method

LCS LCS Least Cost MethodLeast Cost Method RAMS RAMS Resource Allocation and Multi-project Resource Allocation and Multi-project

SchedulingScheduling MAPMAP Manpower Allocation ProcedureManpower Allocation Procedure RPSMRPSM Resource Planning and Scheduling MethodResource Planning and Scheduling Method GERTGERT Graphical Evaluation and Review Technique Graphical Evaluation and Review Technique

Project Scheduling TechniquesProject Scheduling TechniquesProject Scheduling TechniquesProject Scheduling Techniques

PROJECT CONTROLPROJECT CONTROL

Project ControlProject Control

Time managementTime management Cost managementCost management Quality managementQuality management Performance managementPerformance management

Earned Value AnalysisEarned Value Analysis a standard procedure for numerically a standard procedure for numerically

measuring a project’s progress, forecasting its measuring a project’s progress, forecasting its completion date and cost and measuring completion date and cost and measuring schedule and budget variationschedule and budget variation

CommunicationCommunication Enterprise project managementEnterprise project management

Periodical check list concerned with:Periodical check list concerned with:

GANTT CHARTGANTT CHART

Gantt ChartGantt ChartGantt Chart was developed by…Gantt Chart was developed by…

Henry Laurence Gantt (1861-1919) was a mechanical engineer and management consultant who is most famous for developing the ‘Gantt chart’ in the 1910s. These Gantt charts were employed on major infrastructure projects including the Hoover Dam and Interstate highway system. He refined production control and cost control techniques.

Example of Gantt ChartExample of Gantt Chart| | | | |

Activity

Design house and obtain financing

Lay foundation

Order and receive materials

Build house

Select paint

Select carpet

Finish work

00 22 44 66 88 1010MonthMonth

MonthMonth11 33 55 77 99

Gantt ChartGantt ChartActivities in Buy a HouseActivities in Buy a House

` BUY A HOUSE

LOCATION FINANCINGFIND HOUSE

1 - Criteria 3- Determine affordability

6- Type of House

2- Visit Locations

4- Determine mortgage provider

7- Find Real Estate Agent

5- Lockup mortgage commitment

8- Look for House

9- Make Offer, P&S Agreem't

10 - Closing

TASK PREDECESSOR1-criteria 32-visit loc. 13-affordability4-mortgage co 35-mortg lock 46-type of hse 17-real est agent 2, 68-look for hse 79-offer, P&S 5, 810-closing 9

Gantt Chart Gantt Chart Buy a HouseBuy a House

ID Task Name

1 BUY HOUSE

2 LOCATION

3 Determine location criteria

4 Visit key locations

5 FINANCING

6 Determine affordability

7 Assess Mortagg Provider

8 Secure Mortagg Commitmt

9 FIND HOUSE

10 Type of House

11 Find RealEstate Agent

12 Look for House

13 Make Offer, P&S Agreement

14 Closing

2/5

2/5

2/5

2/14

2/5

2/24

M T W T F S S M T W T F S S M T W T F S S M T W Tek 1 Week 2 Week 3 Week 4

Simple Gantt Chart ViewSimple Gantt Chart ViewSimple Gantt Chart ViewSimple Gantt Chart View

TASK PREDECESSOR1-criteria 32-visit loc. 13-affordability 4-mortgage co 35-mortg lock 46-type of hse 17-real est agent 2, 68-look for hse 79-offer, P&S 5, 810-closing 9

Limitations of Gantt ChartLimitations of Gantt Chart

CPM & PERTCPM & PERTCPM & PERTCPM & PERT

CPM & PERTCPM & PERTCPM & PERTCPM & PERT• Network techniquesNetwork techniques• Developed in 1950’sDeveloped in 1950’s

• CPM by DuPont for chemical plants In 1957 suitable CPM by DuPont for chemical plants In 1957 suitable for Civil & Mechanical Projectsfor Civil & Mechanical Projects

• PERT by U.S. Navy for Polaris missile in 1958 PERT by U.S. Navy for Polaris missile in 1958 consulting with M/s Booz, Allen & Hamiltonconsulting with M/s Booz, Allen & Hamilton

• Consider precedence relationships & Consider precedence relationships & interdependenciesinterdependencies

• Each uses a different estimate of activity timesEach uses a different estimate of activity times

CPM & PERT StepsCPM & PERT StepsCPM & PERT StepsCPM & PERT Steps

• Identify activitiesIdentify activities• Determine sequenceDetermine sequence• Create networkCreate network• Determine activity timesDetermine activity times• Find critical pathFind critical path

• Earliest & Latest start times Earliest & Latest start times • Earliest & Latest finish times Earliest & Latest finish times • Slack or Float Slack or Float

• Completion date?Completion date?• On schedule? Within budget?On schedule? Within budget?• Probability of completing by ...? Probability of completing by ...? (Duration)(Duration)

• Critical activities?Critical activities?• Enough resources available?Enough resources available?• How can the project be finished early at the How can the project be finished early at the

least cost?least cost?

Questions Answered by Questions Answered by PERT & CPMPERT & CPM

Questions Answered by Questions Answered by PERT & CPMPERT & CPM

Constructing NetworksConstructing NetworksConstructing NetworksConstructing Networks

Graphical Representation of Graphical Representation of Events and ActivitiesEvents and Activities

Flow Charting - Uses Nodes and ArrowsFlow Charting - Uses Nodes and Arrows ArrowsArrows

An arrow leads from tail to head directionallyAn arrow leads from tail to head directionally NodesNodes

A node is represented by a circle or any A node is represented by a circle or any mathematical symbolmathematical symbol

ArrowNode

Activity On Node (AON)Activity On Node (AON)

Task is Represented by Node as the Task is Represented by Node as the Completion of an ActivityCompletion of an Activity

Arrows Represent the Sequential Linkages Arrows Represent the Sequential Linkages Between ActivitiesBetween Activities

For Example, Node 1 is Begin, Node 2 is For Example, Node 1 is Begin, Node 2 is Complete Task 1, Node 3 is Complete Task 2Complete Task 1, Node 3 is Complete Task 2

1 2 3

Activity On Arrow (AOA)Activity On Arrow (AOA)

Task is Represented by an Arrow Bounded Task is Represented by an Arrow Bounded on Either End by a Node (Event)on Either End by a Node (Event)

Each Event is Identified by a NumberEach Event is Identified by a Number The Activity is Designated by the Leading The Activity is Designated by the Leading

Event Number and the Following Event Event Number and the Following Event Number - i.e. Activity 1 - 2Number - i.e. Activity 1 - 2

1 2

Designating Task Designating Task RelationshipsRelationships

Sequential vs. Concurrent ActivitiesSequential vs. Concurrent Activities

1 2 3

1

2

3

4

Sequential Task Relationship

Concurrent Task Relationships

Designating “DUMMY” Designating “DUMMY” ActivitiesActivities

Represented by Dashed ArrowsRepresented by Dashed Arrows Show Sequential Relationships Among Show Sequential Relationships Among

Tasks, but Take No time or ResourcesTasks, but Take No time or Resources

1

2

3

4

Dummy Activity 2-3indicates that bothActivities 1-2 and 2-3 mustbe Completed before beginning Activity 3-4

Network TermsNetwork TermsNetwork TermsNetwork Terms

224 Years

Activity (Arrow)

RegisterReceive degree

Project: Obtain a college degree - B. Tech.

Event (Node)

Attend class, study etc.

11

Event (Node)

Activity Activity RelationshipsRelationships

Activity Activity RelationshipsRelationships

Activity RelationshipsActivity RelationshipsActivity RelationshipsActivity Relationships

11


11A

B

A & B can occur concurrently

22

33


11 44

22

33

A

B

C

A must be done before C & D can begin

D


11 44

22

33

A

B E

C

B & C must be done before E can begin

D


11 44

22

33

A

B E

C

A must be done before C & D can begin

A & B can occur concurrently

D

B & C must be done before E can begin

Dummy ActivitiesDummy ActivitiesDummy ActivitiesDummy Activities Activities are defined often by beginning & Activities are defined often by beginning &

ending eventsending events Example: Activity 2-3

Every activity must have unique pair of Every activity must have unique pair of beginning & ending eventsbeginning & ending events

It is an imaginary activityIt is an imaginary activity Consume no Time or ResourcesConsume no Time or Resources Dummy activities maintain precedence or Dummy activities maintain precedence or

logical sequence of activities.logical sequence of activities.

Dummy Activities Dummy Activities ExampleExample

Dummy Activities Dummy Activities ExampleExample

Dummy Activities ExampleDummy Activities ExampleDummy Activities ExampleDummy Activities Example

1111 444433331-2

2-3

Incorrect

22222-3

3-4


Different activities; same designation

1111 444433331-2

2-3Incorrect

22222-3

3-4


Incorrect

1111 44442222

3333

55551-2

2-3

2-4 4-5

3-4: Dummy activity

Correct

1111 444433331-2

2-3

22222-3

3-4

Some more Example of Dummy Some more Example of Dummy ActivitiesActivities

Ex – IEx – IA Printing invitation Cards

B Collection of Address

C Dispatching of Cards

2222

1111

3333 4444BB

A

CC

2-3: Dummy activity

Some more Example of Dummy Some more Example of Dummy ActivitiesActivities

Ex – IIEx – IIIf A & E are concurrent

B is after A & E and

F is after E

EE

A

FF

BB

Labeling the Events by Labeling the Events by Dr. Fulkerson’s Rules:Dr. Fulkerson’s Rules:

Numbering the events by DR. Fulkerson’s rules:Numbering the events by DR. Fulkerson’s rules: There is a single initial event in the net work diagram. This There is a single initial event in the net work diagram. This

initial event will have arrows coming out of it and none initial event will have arrows coming out of it and none entering it. Number this initial event as 1.entering it. Number this initial event as 1.

Neglect all the arrows emerging out of the initial event Neglect all the arrows emerging out of the initial event numbered 1. Doing so, it will apparently provide one or more numbered 1. Doing so, it will apparently provide one or more new initial events. new initial events.

Number these apparently produced new initial events as 2, 3, 4 Number these apparently produced new initial events as 2, 3, 4 … etc.… etc.

Again neglect all emerging arrows from these numbered Again neglect all emerging arrows from these numbered events. This will create few more initial evens.events. This will create few more initial evens.

Follow rule – 3.Follow rule – 3. Continue this operation until the last event, which has no Continue this operation until the last event, which has no

emerging arrows, is numbered.emerging arrows, is numbered.

Numbering the EventsNumbering the Events

AA

mmmm nnnn

oooo

pppp

qqqq

rrrr

ssss ttttBB

CC

AA GG

DD

FF

II

HH

JJ

Network ExampleNetwork ExampleNetwork ExampleNetwork Example

You’re a project manager for Bechtel. You’re a project manager for Bechtel. Construct the network.Construct the network.

ActivityActivity PredecessorsPredecessorsAA ----BB AACC AADD BBEE BBFF CCGG DDHH E, FE, F

Network Example - AONNetwork Example - AONNetwork Example - AONNetwork Example - AON

A

C

E

F

BD

G

H

Z

Network Example - AOANetwork Example - AOANetwork Example - AOANetwork Example - AOA

2

4

51

3 6 8

7 9A

C F

EBD

H

G

ActivityActivity Predecessors PredecessorsAA ----BB AACC AADD BBEE BBFF CCGG DDHH E, FE, F

Rough arrow diagram Rough arrow diagram

2

4

51

3 6

7A

C F

EBD

H

G

Network Example - AOANetwork Example - AOANetwork Example - AOANetwork Example - AOA

Final Arrow Diagram Final Arrow Diagram

C P M Technique - foretaste C P M Technique - foretaste

Activity oriented techniqueActivity oriented technique Single Time estimationSingle Time estimation Designed for repetitive projectsDesigned for repetitive projects Not Statistically analyzed Not Statistically analyzed Demarcates critical activitiesDemarcates critical activities Dummy activities are not necessaryDummy activities are not necessary Employs words like arrow diagram, nodes and Employs words like arrow diagram, nodes and

floats etcfloats etc Suitable for industrial settings, plant Suitable for industrial settings, plant

maintenance, civil construction projects etc.maintenance, civil construction projects etc.

Critical Path Analysis Critical Path Analysis ExampleExample


Event ID

Pred. Description Time (Wks)

A None Prepare Site 1 B A Pour fdn. & frame 6 C B Buy shrubs etc. 3 D B Roof 2 E D Do interior work 3 F C Landscape 4 G F, E Move In 1



Event ID

Acty.. Description Time (Wks)

A 1 - 2 Prepare Site 1 B 2 - 3 Pour fdn. & frame 6 C 3 - 4 Buy shrubs etc. 3 D 3 - 5 Roof 2 E 5 - 6 Do interior work 3 F 4 - 6 Landscape 4 G 6 - 7 Move In 1

2

4

5

1 3 6 7A.1C.3 F.4

E.3

B.6

D.2

G.1



Event ID

Acty..

A 1 - 2

B 2 - 3 C 3 - 4 D 3 - 5 E 5 - 6 F 4 - 6 G 6 - 7

Different paths from network:Different paths from network:1-2-3-4-6-7 - 1-2-3-4-6-7 - 15 15 (Critical Path)(Critical Path)1-2-3-5-6-7 -1-2-3-5-6-7 - 1313

Earliest Start Time & Earliest Start Time & Finish StepsFinish Steps


• Begin at starting event & work forwardBegin at starting event & work forward• EST = 0 for starting activitiesEST = 0 for starting activities

• EST is earliest startEST is earliest start

• EFT = EST + Activity timeEFT = EST + Activity time• EFT is earliest finishEFT is earliest finish

• EST = Maximum EFT of all predecessors for EST = Maximum EFT of all predecessors for non-starting activitiesnon-starting activities

Latest Start Time & Latest Start Time & Finish StepsFinish Steps


• Begin at ending event & work backwardBegin at ending event & work backward• LFT = Maximum EFT for ending activitiesLFT = Maximum EFT for ending activities

• LFT is latest finish; EFT is earliest finishLFT is latest finish; EFT is earliest finish

• LST = LFT - Activity timeLST = LFT - Activity time• LST is latest startLST is latest start

• LFT = Minimum LST of all successors for LFT = Minimum LST of all successors for non-ending activities.non-ending activities.

Compute Earliest, Latest & Compute Earliest, Latest & Slack durations.Slack durations.

Compute Earliest, Latest & Compute Earliest, Latest & Slack durations.Slack durations.

Activity ES EF LS LF SlackA 1-2 0 1 0 1 0B 2-3 1 7 1 7 0C 3-4 7 10 7 10 0D 3-5 7 9 9 11 2E 5-6 9 11 11 14 3F 4-6 10 14 10 14 0G 6-7 14 15 12 15 0

Earliest Latest Act.Dura.

1632341

PERT PERT & &

Time EstimatesTime Estimates

Event oriented techniqueEvent oriented technique Three time estimationThree time estimation Use of dummy activities are required – Use of dummy activities are required –

representing the proper sequencerepresenting the proper sequence A probabilistic model with uncertainty in A probabilistic model with uncertainty in

activity durationactivity duration Analyzed statistically Analyzed statistically Employs words Network diagram, events and Employs words Network diagram, events and

Slack etcSlack etc

PERT Technique - foretaste PERT Technique - foretaste

Activity Time EstimatesActivity Time Estimates

CPM - One Time Estimate per ActivityCPM - One Time Estimate per Activity PERT - Three Time Estimates per ActivityPERT - Three Time Estimates per Activity

ttoo = Optimistic Time Estimate = Optimistic Time Estimate

ttmm = Most Likely Time Estimate = Most Likely Time Estimate

ttpp = Pessimistic Time Estimate = Pessimistic Time Estimate

Can Calculate Activity Mean Time Can Calculate Activity Mean Time Estimate and VarianceEstimate and Variance

PERT Time EstimatesPERT Time Estimates

Activity Mean Time Estimate = tActivity Mean Time Estimate = tee

Activity Variance Estimate = SigmaActivity Variance Estimate = Sigmaee

• te = (to + 4tm + tp)/6

• Sigmae = (tp - to )/6

Can Use Central Limit Theorem to Estimate Project Time

21

Fid

Ft

t

Ff

E2

L2

E1

L1

Computing the Float value Computing the Float value

Example Network Flow Example Network Flow DiagramDiagram

7

6

5

4

3

2

1

B

A

E

C

D

G

F

H

I

J

Example Activity Example Activity CharacteristicsCharacteristics

AA 1-21-2 1010 1212 1414 1212 2/32/3 BB 1-31-3 99 1111 1313 1111 2/32/3 CC 2-42-4 11 33 1111 44 5/35/3 DD 2-52-5 11 88 99 77 4/34/3 EE 3-43-4 11 77 1313 77 6/36/3 FF 3-63-6 55 1010 1515 1010 5/35/3 GG 4-54-5 88 1313 1818 1313 5/35/3 HH 4-64-6 11 77 1919 88 9/39/3 II 5-65-6 66 1010 2020 1111 7/37/3 JJ 6-76-7 66 1010 1414 1010 4/34/3

Activity a m b te Sigmae


7

6

5

4

3

2

1

te =11

te =12

te =7

te =7

te =13

te =10

te =8

te =11

te =10

te =4



• Begin at starting event & work forwardBegin at starting event & work forward• EST = 0 for starting activitiesEST = 0 for starting activities

• EST is earliest startEST is earliest start

• EFT = EST + Activity timeEFT = EST + Activity time• EFT is earliest finishEFT is earliest finish

• EST = Maximum EFT of all predecessors for EST = Maximum EFT of all predecessors for non-starting activitiesnon-starting activities


7

6

5

4

3

2

1

te =11

te =12

te =7

te =7

te =13

te =10

te =8

te =11

te =10

te =4

ES=12

ES=52

ES=42

ES=31

ES=18

ES=11

ES=0



• Begin at ending event & work backwardBegin at ending event & work backward• LFT = Maximum EFT for ending activitiesLFT = Maximum EFT for ending activities

• LFT is latest finish; EFT is earliest finishLFT is latest finish; EFT is earliest finish

• LST = LFT - Activity timeLST = LFT - Activity time• LST is latest startLST is latest start

• LFT = Minimum LST of all successors for LFT = Minimum LST of all successors for non-ending activities.non-ending activities.

Example Activity Example Activity CharacteristicsCharacteristics

1-21-2 1010 1212 1414 1212 2/32/3 00 22 1212 1414 1-31-3 99 1111 1313 1111 2/32/3 00 00 1111 1111 2-42-4 11 33 1111 44 5/35/3 1212 1414 1616 1818 2-52-5 11 88 99 77 4/34/3 1212 2424 1919 3131 3-43-4 11 77 1313 77 6/36/3 1111 1111 1818 1818 3-63-6 55 1010 1515 1010 5/35/3 1111 3232 2121 4242 4-54-5 88 1313 1818 1313 5/35/3 1818 1818 3131 3131 4-64-6 11 77 1919 88 9/39/3 1818 3434 2626 4242 5-65-6 66 1010 2020 1111 7/37/3 3131 3131 4242 4242 6-76-7 66 1010 1414 1010 4/34/3 4242 4242 52 52 5252

to tm tp te Sigmae EST EFT LFTLST

Example Network Flow DiagramExample Network Flow DiagramWith Critical PathWith Critical Path

7

6

5

4

3

2

1

t1-3=110|0|11|11

t1-2=120|2|12|14

t3-4=711|11|18|18

t2-5=712|24|19|31

t4-5=1318|18|31|31

t3-6=1011|32|21|42

t4-6=818|34 |26|42

t5-6=1131|31|42|42

t6-7=1042|42|52|52

t2-4=412|14|16|18

ES|LS|EF|LF

21

Fid

Ft

t

Ff

E2

L2

E1

L1

Computing the Float value Computing the Float value

Distinction between CPM & PERTDistinction between CPM & PERT

Activity oriented technique. It has one time estimate. Designed for repetitive projects. Not statistically analyzed.

It demarcates critical activities. It employs words like arrow diagram,

node, floats etc. Dummy activities are not necessary. Suitable for industrial settings, plant

maintenance, civil construction projects.

A deterministic model with well known activities times based on past experience.

Cost is not directly proportional to time and const is the controlling factor.

Event oriented technique. It has three time estimation. Suitable for non-repetitive projects. Analyzed statistically. It does not demarcated critical and

non-critical activities. It employs words like network

diagram, events Slack etc. Use of dummy activities are required

representing the proper sequence. Suitable for defense projects and R

& D etc. Where activities cannot be predicted.

A probabilistic model with uncertainty in activities duration

Cost varies directly with time and time is the controlling factor.

C P MC P M P E R TP E R T

Benefits & Benefits & Limitations Limitations

of PERT/CPMof PERT/CPM

Benefits & Benefits & Limitations Limitations


Benefits Benefits of PERT/CPMof PERT/CPM

Benefits Benefits of PERT/CPMof PERT/CPM

Useful at many stages of project Useful at many stages of project managementmanagement

Mathematically simpleMathematically simple Use graphical displaysUse graphical displays Give critical path & slack timeGive critical path & slack time Provide project documentationProvide project documentation Useful in monitoring costs and timeUseful in monitoring costs and time

Limitations Limitations of PERT/CPMof PERT/CPMLimitations Limitations


Clearly defined, independent, & stable Clearly defined, independent, & stable activitiesactivities

Specified precedence relationshipsSpecified precedence relationships Activity times (PERT) follow Activity times (PERT) follow

beta distributionbeta distribution Subjective time estimatesSubjective time estimates Over emphasis on critical pathOver emphasis on critical path

ConclusionConclusionConclusionConclusion

Explained what a project isExplained what a project is Summarized the CPM / PERT project Summarized the CPM / PERT project

activities and their time estimatesactivities and their time estimates Drew project networksDrew project networks Compared PERT & CPMCompared PERT & CPM Determined slack & critical pathDetermined slack & critical path Computed project probabilitiesComputed project probabilities

Project ManagementProject Management

PERT/CPMPERT/CPM

THETHE END END

Project Management

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