BA 333 Operations Management Project Management PERT/CPM Spring, 1998.

BA 333Operations Management

Project Management

PERT/CPM

Spring, 1998

Project Management

Spring 1998

Lecture Outline

• Project Management Introduction– Definition & Background– Components

• event

• activity

• critical path

– PERT/CPM

Project Management

Spring 1998

Introduction to Project Management

• Definition– to plan, implement, and control the

management of large, one time projects

• Used in Construction, Shipbuilding, Weapons Systems Development, etc.– Applies to uncertain technology projects– Applies to variable cost resource allocation

• History of PERT/CPM - Navy/Booze Allen Hamilton Consultants

Project Management

Spring 1998

Introduction to Project Scheduling

Introduction to Project Scheduling

Project Management

Spring 1998

Components of Project Control Systems

• Predecessor was Gantt Charts– Horizontal Bar Charts - Time Lines– Tasks– Milestones

• Flow Charts - Relationships Among All Tasks– Activities (tasks that take time and resources)

• sequential vs. concurrent

– Events (an accomplishment occurring at a specific point in time)

Project Management

Spring 1998

Project CharacteristicsProject Characteristics

• Single unit

• Many related activities

• Difficult production planning & inventory control

• General purpose equipment

• High labor skills

Project Management

Spring 1998

Examples of ProjectsExamples of Projects

Project Management

Spring 1998


• Building construction

© 1995 Corel Corp.

Project Management

Spring 1998



• New product introduction

19 · Nude Sandalfoot19 · Nude SandalfootMedium to Tall (B)Medium to Tall (B)

No nonsenseNo nonsense

Sheer to waist pantyhose

New! Improved!

New! Improved!

© 1995 Corel Corp.

Project Management

Spring 1998




• Training seminar

© 1995 Corel Corp.

Project Management

Spring 1998




• Training seminar

• Research project

© 1995 Corel Corp.

Project Management

Spring 1998

Project Management Activities


Project Management

Spring 1998



Planning Objectives Resources Work break-

down sched. Organization

Project Management

Spring 1998





Scheduling Project

activities Start &

end times Network

Project Management

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Scheduling Project

activities Start &

end times Network

Controlling Monitor, compare,

revise, action

Project Management

Spring 1998

Project PlanningProject Planning

Project Management

Spring 1998

Project PlanningProject Planning

• Establishing objectives• Defining project• Creating work breakdown

structure • Determining resources• Forming organization

© 1995 Corel Corp.

Project Management

Spring 1998

Project OrganizationProject Organization

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

– Coordinates activities – Monitors schedule

& costs• Permanent

structure called ‘matrix organization’

© 1995 Corel Corp.

Acct.

Eng. Eng.Mkt.

Mgr.

Project Management

Spring 1998

Project SchedulingProject Scheduling

Project Management

Spring 1998

Project SchedulingProject Scheduling

• Sequencing activities• Identifying precedence

relationships• Determining activity times

& costs• Estimating material &

worker requirements• Determining critical

activities

© 1995 Corel Corp.

JF

MA

MJ

J

MonthActivity

Design

Build

Test

PE

RT

Project Management

Spring 1998

Project Scheduling Techniques

Project Scheduling Techniques

• Gantt chart

• Critical Path Method (CPM)

• Program Evaluation & Review Technique (PERT)

© 1984-1994 T/Maker Co.

Project Management

Spring 1998

Gantt ChartGantt Chart

Project Management

Spring 1998

Gantt ChartGantt Chart

J F M A M J J

Time PeriodActivity

Design

Build

Test

J F M A M J J

Time PeriodActivity

Design

Build

Test

Project Management

Spring 1998

PERT & CPMPERT & CPM

• Network techniques

• Developed in 1950’s– CPM by DuPont for chemical plants– PERT by U.S. Navy for Polaris missile

• Consider precedence relationships & interdependencies

• Each uses a different estimate of activity times

Project Management

Spring 1998

• Completion date?

• On schedule? Within budget?• Probability of completing by ...?

• Critical activities?

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

least cost?

Questions Answered by PERT & CPM

Questions Answered by PERT & CPM

Project Management

Spring 1998

PERT & CPM StepsPERT & CPM Steps

• Identify activities

• Determine sequence

• Create network

• Determine activity times

• Find critical path– Earliest & latest start times – Earliest & latest finish times – Slack

Project Management

Spring 1998

Constructing NetworksConstructing Networks

Project Management

Spring 1998

Graphical Representation of Events and Activities

• Flow Charting - Uses Nodes and Arrows

• Arrows– An arrow leads from tail to head directionally

• Nodes– A node is represented by a circle

ArrowNode

Project Management

Spring 1998

Activity On Node

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

• Arrows Represent the Sequential Linkages Between Activities

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

1 2 3

Project Management

Spring 1998

Activity On Arrow

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

• Each Event is Identified by a Number

• The Activity is Designated by the Leading Event Number and the Following Event Number - i.e. Activity 1 - 2

1 2

Project Management

Spring 1998

Designating Task Relationships

• Sequential vs. Concurrent Activities

1 2 3

Sequential Task Relationship

1

2

3

4

Concurrent Task Relationships

Project Management

Spring 1998

Designating “DUMMY” Activities

• Represented by Dashed Arrows

• Show Sequential Relationships Among Tasks, but Take No time or Resources

1

2

3

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

Project Management

Spring 1998

Network TermsNetwork Terms

Project Management

Spring 1998


Project: Obtain a college degree (B.S.)

Project Management

Spring 1998


Register


11

Project Management

Spring 1998


Register


11

Event (Node)

Project Management

Spring 1998


4 Years

Register


Event (Node)

Attend class, study etc.

11

Project Management

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4 Years

Activity (Arrow)

Register


Event (Node)


11

Project Management

Spring 1998


224 Years

Activity (Arrow)

RegisterReceive diploma


Event (Node)


11

Event (Node)

Project Management

Spring 1998

Activity RelationshipsActivity Relationships

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11

Project Management

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11A

B

A & B can occur concurrently

22

33

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11 44

22

33

A

B

C

A must be done before C & D can begin

D

Project Management

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11 44

22

33

A

B E

C

B & C must be done before E can begin

D

Project Management

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Dummy ActivitiesDummy Activities

• Activities are defined often by beginning & ending events– Example: Activity 2-3

• Every activity must have unique pair of beginning & ending events– Computer programs get confused

• Dummy activities maintain precedence– Consume no time or resources

Project Management

Spring 1998

Dummy Activities ExampleDummy Activities Example

Project Management

Spring 1998


1111 444433331-2

2-3Incorrect

22222-3

3-4

Project Management

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Different activities; same designation

1111 444433331-2

2-3Incorrect

22222-3

3-4

Project Management

Spring 1998


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

Project Management

Spring 1998

Network Diagramming

• First Step in Project Management

• Begins 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 “WHAT”

Project Management

Spring 1998

Example Work Breakdown

House

Site Prep Masonry Carpentry Finishing

Footings Piers ExteriorWalls

Chimney

MixedConcrete

Forms LaidConcretePoured

FormsRemoved

Project Management

Spring 1998

Listing Of Activities

• Follows the “WHAT” with List of “HOW”

• Each “WHAT” Results in Detailed List of the “Specific” Tasks Necessary to Accomplish the “WHAT”

• Followed by Specification of Sequential and Concurrent Relationships Among Tasks

• Results in Network Flow Diagram Representing the Tasks and Their Relationships

Project Management

Spring 1998

Activity Time Estimates

• CPM - One Time Estimate per Activity

• PERT - Three Time Estimates per Activity– a = Optimistic Time Estimate– m = Most Likely Time Estimate– b = Pessimistic Time Estimate

• Can Calculate Activity Mean Time Estimate and Variance

Project Management

Spring 1998

PERT Time Estimates

• Activity Mean Time Estimate = te

• Activity Variance Estimate = Sigmae

•te = (a + 4m + b)/6

•Sigmae = (b - a)/6

Can Use Central Limit Theorem to Estimate Project Time

Project Management

Spring 1998

Example Network Flow Diagram

7

6

5

4

3

2

1

B

A

E

C

D

G

F

H

I

J

Project Management

Spring 1998

Example Activity Characteristics

• A 1-2 10 12 14 12 2/3

• B 1-3 9 11 13 11 2/3

• C 2-4 1 3 11 4 5/3

• D 2-5 1 8 9 7 4/3

• E 3-4 1 7 13 7 6/3

• F 3-6 5 10 15 10 5/3

• G 4-5 8 13 18 13 5/3

• H 4-6 1 7 19 8 9/3

• I 5-6 6 10 20 11 7/3

• J 6-7 6 10 14 10 4/3

Activity a m b te Sigmae

Project Management

Spring 1998


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

Project Management

Spring 1998

Early Start & Early Finish

• The Early Start Time for an Activity Emanating from an Event is the Earliest Point in Time that an Activity can Begin– Determined by the Latest Early Finish of All

Activities Terminating in an Event

• The Early Finish for an Activity is the Sum of its Early Start Time and its te

Project Management

Spring 1998


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

Project Management

Spring 1998

Late Start & Late Finish

• The Late Finish Time for an Activity Terminating in an Event is the Point in Time that it can be Completed Without Delaying the Completion of the Project– Determined by Assigning to the LF the Value of the

Earliest LS of all Activities Emanating from the Event

• The Late Start for an Activity is it Late Finish minus its te

Project Management

Spring 1998

Example Activity Characteristics

• 1-2 10 12 14 12 2/3 0 2 12 14

• 1-3 9 11 13 11 2/3 0 0 11 11

• 2-4 1 3 11 4 5/3 12 14 16 18

• 2-5 1 8 9 7 4/3 12 24 19 31

• 3-4 1 7 13 7 6/3 11 11 18 18

• 3-6 5 10 15 10 5/3 11 32 21 42

• 4-5 8 13 18 13 5/3 18 18 31 31

• 4-6 1 7 19 8 9/3 18 34 26 42

• 5-6 6 10 20 11 7/3 31 31 42 42

• 6-7 6 10 14 10 4/3 42 42 52 52

a m b te Sigmae ES EF LFLS

Project Management

Spring 1998

Example Network Flow DiagramWith 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

Project Management

Spring 1998

SLACK

• Total Slack– The Length of Delay in an Activity that Won’t Delay

the Completion of the Project - LF- EF or LS-ES

• Free Slack– The Length of Delay in an Activity that Won’t Delay

the Beginning of Another Activity

• Critical Path – Activities with the Minimum Total Slack - Often

Total Slack on Critical Path Activities = 0

Project Management

Spring 1998

Probabilistic Estimates

• Use of te and Sigmae Allows One to Make Probabilistic Estimates of Completion Dates

• By Summing the te‘s of the Activities on the Critical Path You Can Estimate the Duration of the Entire Project

• By Summing the Variance (Sigmae2) of the Activities

on the Critical Path, You Can estimate the Total Variance of the Critical Path and Make One-Sided Interval Estimates of Project Completion Times

Project Management

Spring 1998

Probabilistic Estimates Example

• 1-3 9 11 13 11 2/3 4/9

• 3-4 1 7 13 7 6/3 36/9

• 4-5 8 13 18 13 5/3 25/9

• 5-6 6 10 20 11 7/3 49/9

• 6-7 6 10 14 10 4/3 16/9

a m b te Sigmae (Sigmae)2

Variance = 130/9 = 14.4Std Dev = 3.8

Probability that the Project Duration is Less than 60 days = Pr(T<60)Same as the Probability that Z < (60-52)/3.8 = 2.1

Therefore: Pr(T<60) = Pr(Z<2.1) = 0.98214 (see App. A, H&R, p. 842)

Project Management

Spring 1998

PERT Probability ExamplePERT Probability Example

You’re a project planner for General Dynamics. A submarine project has an expected completion time of 40 weeks, with a standard deviation of 5 weeks. What is the probability of finishing the sub in 50 weeks or less?

© 1995 Corel Corp.

Project Management

Spring 1998

Converting to Standardized Variable


Project Management

Spring 1998



Assume project completion time Assume project completion time follows a normal distribution.follows a normal distribution.

Project Management

Spring 1998



T = 40

= 5

50 XT = 40

= 5

50 X

Normal Normal DistributionDistribution

Assume project completion time Assume project completion time follows a normal distribution.follows a normal distribution.

Project Management

Spring 1998



T = 40

= 5

50 XT = 40

= 5

50 X


z = 0

Z = 1

Z2.0z = 0

Z = 1

Z2.0

Standardized Standardized Normal DistributionNormal Distribution

Project Management

Spring 1998



T = 40

= 5

50 XT = 40

= 5

50 X


ZX T

50 405

2 0.ZX T

50 405

2 0.

z = 0

Z = 1

Z2.0z = 0

Z = 1

Z2.0

Standardized Standardized Normal DistributionNormal Distribution

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Obtaining the ProbabilityObtaining the Probability

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Spring 1998

Z .00 .01 .02

0.0 .50000 .50399 .50798

: : : :

2.0 .97725 .97784 .97831

2.1 .98214 .98257 .98300

Z .00 .01 .02

0.0 .50000 .50399 .50798

: : : :

2.0 .97725 .97784 .97831

2.1 .98214 .98257 .98300


Standardized Normal Standardized Normal Probability Table (Portion)Probability Table (Portion)

Probabilities in bodyProbabilities in body

Project Management

Spring 1998

z = 0

Z = 1

Z2.0z = 0

Z = 1

Z2.0

Z .00 .01 .02

0.0 .50000 .50399 .50798

: : : :

2.0 .97725 .97784 .97831

2.1 .98214 .98257 .98300

Z .00 .01 .02

0.0 .50000 .50399 .50798

: : : :

2.0 .97725 .97784 .97831

2.1 .98214 .98257 .98300


.97725

Standardized Normal Standardized Normal Probability Table (Portion)Probability Table (Portion)

Probabilities in bodyProbabilities in body

Project Management

Spring 1998

Critical Path Method

• Uses Deterministic Time Estimates for Activities

• Also Estimates Cost of Resources Levels for Each Activity

• Generally You Can increase the Resource Commitment and Reduce the Time Estimate for and Activity

• Use CPM to Analyze How To Reduce the Critical Path Most Efficiently

Project Management

Spring 1998

Benefits & Limitations of PERT/CPM

Benefits & Limitations of PERT/CPM

Project Management

Spring 1998

Benefits of PERT/CPM

Benefits of PERT/CPM

• Useful at many stages of project management

• Mathematically simple

• Use graphical displays

• Give critical path & slack time

• Provide project documentation

• Useful in monitoring costs

Project Management

Spring 1998

Limitations of PERT/CPMLimitations

of PERT/CPM

• Clearly defined, independent, & stable activities

• Specified precedence relationships

• Activity times (PERT) follow beta distribution

• Subjective time estimates

• Over emphasis on critical path

Project Management

Spring 1998

ConclusionConclusion

• Explained what a project is

• Summarized the 3 main project management activities

• Drew project networks

• Compared PERT & CPM

• Determined slack & critical path

• Computed project probabilities

BA 333Operations Management

Project Management

PERT/CPM

Spring, 1998

THE END

BA 333 Operations Management Project Management PERT/CPM Spring, 1998.

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