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BA 333 Operations Management. Project Management PERT/CPM Spring, 1998. Lecture Outline. Project Management Introduction Definition & Background Components event activity critical path PERT/CPM. Introduction to Project Management. Definition

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Ba 333 operations management

BA 333Operations Management

Project Management

PERT/CPM

Spring, 1998


Lecture outline
Lecture Outline

  • Project Management Introduction

    • Definition & Background

    • Components

      • event

      • activity

      • critical path

    • PERT/CPM


Introduction to project management
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


Introduction to project scheduling

Introduction to Project Scheduling


Components of project control systems
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 characteristics
Project Characteristics

  • Single unit

  • Many related activities

  • Difficult production planning & inventory control

  • General purpose equipment

  • High labor skills



Examples of projects1
Examples of Projects

  • Building construction



© 1995 Corel Corp.


Examples of projects2
Examples of Projects

  • Building construction

  • New product introduction

New! Improved!

19 · Nude Sandalfoot

Medium to Tall (B)

No nonsense

Sheer to waist pantyhose

© 1995 Corel Corp.


Examples of projects3
Examples of Projects

  • Building construction

  • New product introduction

  • Training seminar

© 1995 Corel Corp.


Examples of projects4
Examples of Projects

  • Building construction

  • New product introduction

  • Training seminar

  • Research project

© 1995 Corel Corp.




Project management activities2
Project Management Activities

  • Planning

    • Objectives

    • Resources

    • Work break-down sched.

    • Organization


Project management activities3
Project Management Activities

  • Planning

    • Objectives

    • Resources

    • Work break-down sched.

    • Organization

  • Scheduling

    • Project activities

    • Start & end times

    • Network


Project management activities4
Project Management Activities

  • Planning

    • Objectives

    • Resources

    • Work break-down sched.

    • Organization

  • Scheduling

    • Project activities

    • Start & end times

    • Network

  • Controlling

    • Monitor, compare, revise, action



Project planning1
Project Planning

  • Establishing objectives

  • Defining project

  • Creating work breakdown structure

  • Determining resources

  • Forming organization

© 1995 Corel Corp.


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’

Eng.

Eng.

Mkt.

Acct.

Mgr.

© 1995 Corel Corp.



Project scheduling1
Project Scheduling

  • Sequencing activities

  • Identifying precedence relationships

  • Determining activity times & costs

  • Estimating material & worker requirements

  • Determining critical activities

PERT

J

Test

J

M

A

Build

M

F

Month

Design

J

Activity

© 1995 Corel Corp.


Project scheduling techniques
Project Scheduling Techniques

  • Gantt chart

  • Critical Path Method (CPM)

  • Program Evaluation & Review Technique (PERT)

© 1984-1994 T/Maker Co.




Pert cpm
PERT & 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


Questions answered by pert cpm
Questions Answered by PERT & CPM

  • 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?


Pert cpm steps
PERT & CPM Steps

  • Identify activities

  • Determine sequence

  • Create network

  • Determine activity times

  • Find critical path

    • Earliest & latest start times

    • Earliest & latest finish times

    • Slack



Graphical representation of events and activities
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

Arrow

Node


Activity on node

1

2

3

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


Activity on arrow

1

2

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


Designating task relationships

1

2

3

2

1

4

3

Designating Task Relationships

  • Sequential vs. Concurrent Activities

Sequential Task Relationship

Concurrent Task Relationships


Designating dummy activities
Designating “DUMMY” Activities

  • Represented by Dashed Arrows

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

2

1

4

Dummy Activity 2-3

indicates that both

Activities 1-2 and 2-3 must

be Completed before

beginning Activity 3-4

3



Network terms1
Network Terms

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


Network terms2
Network Terms

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

Register

1


Network terms3
Network Terms

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

Register

1

Event (Node)


Network terms4
Network Terms

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

Register

Attend class, study etc.

1

4 Years

Event (Node)


Network terms5
Network Terms

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

Register

Attend class, study etc.

1

4 Years

Activity (Arrow)

Event (Node)


Network terms6
Network Terms

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

Receive diploma

Register

Attend class, study etc.

1

2

4 Years

Activity (Arrow)

Event (Node)

Event (Node)




Activity relationships2
Activity Relationships

2

A

1

3

B

A & B can occur concurrently


Activity relationships3
Activity Relationships

A must be done before C & D can begin

2

D

A

C

1

4

3

B


Activity relationships4
Activity Relationships

2

D

A

C

1

4

3

B

E

B & C must be done before E can begin


Dummy activities
Dummy 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



Dummy activities example1
Dummy Activities Example

2-3

Incorrect

1-2

3-4

1

2

3

4

2-3


Dummy activities example2
Dummy Activities Example

2-3

Incorrect

1-2

3-4

1

2

3

4

2-3

Different activities; same designation


Dummy activities example3
Dummy Activities Example

2-3

Incorrect

1-2

3-4

1

2

3

4

2-3

Correct

1-2

2-4

4-5

4

1

2

5

3

2-3

3-4: Dummy activity


Network diagramming
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”


Example work breakdown
Example Work Breakdown

House

Site Prep

Masonry

Carpentry

Finishing

Exterior

Walls

Footings

Piers

Chimney

Forms

Removed

Concrete

Poured

Mixed

Concrete

Forms Laid


Listing of activities
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


Activity time estimates
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


Pert time estimates
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


Example network flow diagram

2

5

4

7

1

6

3

Example Network Flow Diagram

D

A

G

C

I

H

E

B

J

F


Example activity characteristics

Activity

a

m

b

te

Sigmae

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


Example network flow diagram1

2

5

4

7

1

6

3

Example Network Flow Diagram

te=7

te=12

te=13

te=11

te=4

te=8

te=7

te=10

te=11

te=10


Early start early finish
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


Example network flow diagram2

2

5

4

7

1

6

3

Example Network Flow Diagram

ES=12

ES=31

te=7

te=12

ES=18

ES=52

te=4

te=11

ES=0

te=13

te=8

ES=42

ES=11

te=7

te=10

te=11

te=10


Late start late finish
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


Example activity characteristics1
Example Activity Characteristics

a

m

b

te

Sigmae

ES

LS

EF

LF

  • 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


Example network flow diagram with critical path
Example Network Flow DiagramWith Critical Path

ES|LS|EF|LF

t2-5=7

12|24|19|31

2

5

t1-2=12

0|2|12|14

t5-6=11

31|31|42|42

t4-5=13

18|18|31|31

t2-4=4

12|14|16|18

t4-6=8

18|34 |26|42

4

7

1

t3-4=7

11|11|18|18

t1-3=11

0|0|11|11

t6-7=10

42|42|52|52

6

3

t3-6=10

11|32|21|42


Slack
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


Probabilistic estimates
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


Probabilistic estimates example
Probabilistic Estimates Example

m

a

b

te

Sigmae

(Sigmae)2

  • 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

Variance = 130/9 = 14.4

Std 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)


Pert probability example
PERT 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.



Converting to standardized variable1
Converting to Standardized Variable

Assume project completion time follows a normal distribution.


Converting to standardized variable2
Converting to Standardized Variable

Assume project completion time follows a normal distribution.

Normal Distribution


Converting to standardized variable3
Converting to Standardized Variable

Normal Distribution

Standardized Normal Distribution


Converting to standardized variable4
Converting to Standardized Variable

Normal Distribution

Standardized Normal Distribution



Obtaining the probability1
Obtaining the Probability

Standardized Normal Probability Table (Portion)

Probabilities in body


Obtaining the probability2
Obtaining the Probability

Standardized Normal Probability Table (Portion)

.97725

Probabilities in body


Critical path method
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



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


Limitations of pert cpm
Limitations 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


Conclusion
Conclusion

  • 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 333 operations management1

BA 333Operations Management

Project Management

PERT/CPM

Spring, 1998

THE END


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