Project Management Introduces Pert/CPM as a tool for planning, scheduling, and controlling projects Applied Management Science for Decision Making, 2e

Project Management

Introduces Pert/CPM as a tool for planning, scheduling, and controlling

projects

Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions Philip A. Vaccaro , PhD

MGMT E-5050

Project Management Overview

• History and Importance

• The Two Pert / CPM Conventions

• Pert / CPM Building Blocks

• ES, EF, LS, LF, and S

Task Times

• Probabilistic PERT

(.wav)

Project Examples

New Product

Development &

Manufacture

New Product

Promotion Campaign

Broadway Shows

Television Programs

Corporate Restructure

Software Conversion

Weapons System

Skyscraper

Bridges & Highways

Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions

Lost revenues and profits

Contract penalties

Loss of clientele

Higher costs due to overruns

Reputation damage

Resource waste

Missed Deadline Consequences

Project Prerequisites

Tasks with clear start/finish points Tasks with alternate execution sequences Tasks with several possible time estimates Tasks that run parallel to each other

THESE PREREQUISITES STRENGTHEN MANAGEMENTACCOUNTABILITY AND PROVIDE FLEXIBILITY IN THE

FACE OF FUNDING CHANGES, STAFFING, & TECHNICALPROBLEMS


Tasks with clear start/finish points

Laying the foundation of a new home starts when the excavation crew and equipment arrive on the site and ends when the foundation has been poured.

Framing starts when the carpenters arrive on site and ends when the frame has been built.


Tasks with alternate execution sequences

Tasks that can be reordered might result inoverall shorter overall execution times andless cost.


Tasks with several possible time estimates

Identifying best case, worst case, and most likelytime estimates for each project task allows us tobetter adopt to changes in funding, deadlines, and unforeseen technical problems.

Flexib

ility


Tasks that run parallel to each other

It is vital that several tasks be scheduled at the same time, so that, if one of them is in danger of falling behind, the others will stand ready to assist with extra funds, personnel, equipment, and other resources.

This will, in turn, save the entire project from fallingbehind schedule!

PERT / CPM History

The Critical Path Method (CPM) was developed in 1957 by J.E. Kelly of Remington Rand and M.R. Walker of DuPont. Originally, CPM was used to assist in building chemical plants, reducing completion time from 7 to 4 years.

CPM requires only one time estimate for each project task

PERT / CPM History

Program Evaluation and Review Technique was developed in 1958 by the United States Navy Special Projects Office.

Originally used to plan and control the Polaris submarine program, reducing completion time from 7 to 4 years !

In 1960, PERT and CPM were combined, hence the term PERT/CPM .

PERT requires 3 time estimates for each project task

U.S. Navy Special Projects Office Grace Murray Hopper

1906 - 1992

Ph.D, Yale University, 1934 Professor, Vassar College, 1931-1941 Developed the COBOL programming language and the compiler Worked on the Mark I & II computers at Harvard University Developed international standards for computer languages Lecturer, consultant, engineer, operations researcher Received 47 honorary degrees Naval reservist First women admiral, U.S. Navy (1984)

FamousStaff

Member

Grace Murray HopperAnecdote

While she was working on the Mark II computer at Harvard University, her associates discovered a moth stuck on a relay, thereby impeding operation. Whereupon she remarked that they were “debugging” the system. The remains of the moth can be found at the Smithsonian Museum of American History in Washington, D.C.

PERT / CPMThe Two Conventions

Activity-on-Node

Activity-on-Arc

TASKS ARE SHOWN ASARROWS ( ARCS )

NODES REPRESENTTASK

START AND FINISH

Activity-on-Node

TASKS ARE SHOWN ASSQUARES ( NODES )

ARROWS REPRESENTTASK PREDECESSOR

RELATIONSHIPS

Activity-on-Node Convention

The network is cleaner and uncluttered

It is natural to view nodes as tasks

It is easier to use than the activity-on-arc convention

U.S. Government switched over to the AON convention in 2001

ADVANTAGES

Activity-on-Node Building Blocks

Nodes represent the tasks/activities

Small nodes represent the start and finish of the project

Arcs/arrows show the predecessor relationships among the tasks

start1st

Task2nd

Task3rd

Taskend

Here, the 2nd task cannot beginuntil the 1st task has been completed.The 3rd task cannot begin until the 2nd

task has been completed.

GENERAL FOUNDRY INC.PROJECT TASKS

TASK A – Build Internal Component

TASK B – Modify Roof and Floor

TASK C – Construct Collection Stack

TASK D – Pour Concrete

TASK E – Build Burner

TASK F – Install Control System

TASK G – Install Pollution Device

TASK H – Inspect & Test

EXAMPLE

General Foundry Inc.THE PERT/CPM NETWORK

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

Time can beexpressed indays, weeks,

or months

Task InterpretationEXAMPLE

2

AES = 0 EF = 2

TASK “A”

TASK “A” EXPECTEDDURATIONTIME IS 2WEEKS

EARLIEST TIMETASK “A” CAN

START IS AT THEEND OF WEEK “0”

THAT IS, THE STARTOF WEEK “1”

EARLIEST TIMETASK “A” CAN

FINISH IS AT THE END OF WEEK “2”

THAT IS, THE START OF WEEK “3”

Expected Task or Activity Time

te = [ 1a + 4m + 1b ] 6optimistic

timeestimate

most likelytime

estimate

pessimistictime

estimate

67%

Weights

Sum of the Weights

A WEIGHTED AVERAGE TIME FORMULA

17% 17%

Expected timesare usually usedfor each task in

the project

Expected Task or Activity Time

GIVEN: a = 1 week , b = 3 weeks , m = 2 weeks

[ 1a + 4m + 1b ] [ 1(1) + 4(2) + 1(3) ] 6 6

12 = te = 2 weeks 6

==

OPTIMISTICTIME

PESSIMISTICTIME

MOST LIKELYTIME

EXAMPLE

The BETA Distribution( a skewed distribution)

m tea bOptimistic

timeMost likely

time (mode)

Pessimistictime

Expectedtime

TASK TIME IS NOTASSUMED TO BE

NORMALLYDISTRIBUTED

The probabilitydistribution

commonly usedto describe the

inherent variabilityin task timeestimates

The BETA DISTRIBUTION

Symmetrical, right, or left-skewed based on the nature of a particular task

Unimodal with a high concentration of probability surrounding the most likely time estimate (m)

No strong empirical reason for using the BETA distribution

Attractive however, because the mean (μ) and the variance ( ) can be easily obtained from the three time estimates “a”, “m”, and “b”

CHARACTERISTICS & COMMENTS

𝝈𝟐

The Critical Path ( CP )

The chain of tasks from project start to end that consumes the longest amount of time.

Any delay in one or more of those tasks will delay the entire project.

The critical path is equal to the project’s expected or mean completion time.

start

A BC

end

D E

Critical Path Characteristics

• Several critical paths may exist within the project network at any given time.

• These critical paths may change or disappear entirely

at any given time as the project progresses

• Management must monitor all critical paths closely.

General Foundry Inc.THE NETWORK

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

General Foundry Inc.1st Critical Path Candidate

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2A-C-F-H

Nine (9) Weeks

General Foundry Inc.2nd Critical Path Candidate

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2A-C-E-G-H

Fifteen (15) weeks

General Foundry Inc.3rd Critical Path Candidate

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2B-D-G-H

Fourteen (14) weeks

The Critical Path

A-C-F-H 9 weeks

A-C-E-G-H 15 weeks

B-D-G-H 14 weeks

The expected,

mean,or

averageproject

completiontime

is15 weeks

General Foundry Inc.THE CRITICAL PATH

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2Fifteen (15) Weeks

Expected, Mean, or AverageProject Completion Time

μ Here, 15 Weeks

50% CHANCE OFCOMPLETION BEFORE

μ (15 weeks)

50% CHANCE OFCOMPLETION AFTER

μ (15 weeks)

THE CRITICAL PATH EQUALS MEAN PROJECT COMPLETION TIME

EARLY START TIME ( ES )

The technique is called FORWARD PASS

The earliest time that each task can begin.

Computed from left to right, that is, from the network’s beginning node to the network’s finish node.

EARLY START TIME FORMULA

PREDECESSORTASK

ES

PREDECESSORTASK

te

FOLLOWERTASK

ES=+

IF THERE ARE SEVERAL CANDIDATES FORTHE FOLLOWER TASK ES , THE LONGEST

ES IS SELECTED

THE VERY FIRST TASK IN A PROJECT HASAN EARLY START TIME OF ZERO

As we progressthrough the project,follower tasks willeventually becomepredecessor tasks

themselves !

General Foundry Inc.EARLY START TIMES

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES = 0

ES = 0

ES = 2

ES = 3

ES = 4

ES = 4

ES = 8

ES = 13

EARLY START TIME SELECTED CALCULATIONS

PREDECESSORTASK

ES

A ( 0 )

PREDECESSORTASK

te

A ( 2 )

FOLLOWERTASK

ES

C ( 2 )

=+


ES IS SELECTED



START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES = 0

ES = 0

ES = 2

ES = 3

ES = 4

ES = 4

ES = 8

ES = 13

EARLY START TIME SELECTED CALCULATIONS

PREDECESSORTASK

ES

B ( 0 )

PREDECESSORTASK

te

B ( 3 )

FOLLOWERTASK

ES

D ( 3 )

=+


ES IS SELECTED



START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES = 0

ES = 0

ES = 2

ES = 3

ES = 4

ES = 4

ES = 8

ES = 13

ES Candidate Selection

4

E

4

D

G

5

ES=4

ES=3

ES=8

COMING IN FROM TASK “E”EARLY START TIME FOR TASK “G”

WOULD BE “8” ( 4 + 4 = 8 )

COMING IN FROM TASK “D”EARLY START TIME FOR TASK “G”

WOULD BE “7” ( 3 + 4 = 7 )

THE HIGHER

EARLY STARTCONTROLS


START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES = 0

ES = 0

ES = 2

ES = 3

ES = 4

ES = 4

ES = 8

ES = 13

ES Candidate Selection

3

F

5

G

H

2

ES=4

ES=8

ES=13

COMING IN FROM TASK “F”EARLY START TIME FOR TASK “H”

WOULD BE “7” ( 4 + 3 = 7 )

COMING IN FROM TASK “G”EARLY START TIME FOR TASK “H”

WOULD BE “13” ( 8 + 5 = 13 )

THE HIGHER

EARLY STARTCONTROLS

EARLY FINISH TIME ( EF )

This technique is also called FORWARD PASS

• The earliest time that each task can finish.

• Computed from left to right, that is, from the network’s beginning node to the network’s finish node.

EARLY FINISH TIME FORMULA

TASK EARLYSTARTTIMEES

TASKEXPECTED

TIMEte

TASKEARLY FINISHTIMEEF

=+

NEEDLESS TO SAY, EARLY FINISH TIMES CANNOT BE COMPUTED UNTIL EARLY START TIMES ARE IDENTIFIED

General Foundry Inc.EARLY FINISH TIMES

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES=0EF=2

ES=0EF=3

ES=2EF=4

ES=3EF=7

ES=4EF=7

ES=4EF=8

ES= 8EF=13

ES=13EF=15

EARLY FINISH TIME SELECTED CALCULATIONS

TASK EARLYSTARTTIME

ES = 0A

TASKEXPECTED

TIME

te = 2A

TASKEARLY FINISHTIME

EF = 2A

=+



START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

ES=0EF=2

ES=0EF=3

ES=2EF=4

ES=3EF=7

ES=4EF=7

ES=4EF=8

ES= 8EF=13

ES=13EF=15

EARLY FINISH TIME SELECTED CALCULATIONS

TASK EARLYSTARTTIME

ES = 2C

TASKEXPECTED

TIME

te = 2C

TASKEARLY FINISHTIME

EF = 4C

=+



START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

EF=2

EF=3

EF=4

EF=7

EF=7

EF=8

EF=13

EF=15

LATE FINISH TIME ( LF )

This technique is called BACKWARD PASS

The latest time thateach task can finishwithout jeopardizingthe project’s expectedcompletion time.

Computed from right to left, that is, from thenetwork’s finish nodeto the network’s startnode.

LATE FINISH TIME FORMULA

FOLLOWERTASKLATE

FINISHTIME(LF)

FOLLOWERTASK

EXPECTEDTIME(te)

PREDECESSORTASKLATE

FINISHTIME(LF)

=-

IF THERE ARE SEVERAL CANDIDATES

FOR THE PREDECESSOR TASK LF, SELECT THE SHORTEST LF

General Foundry Inc.LATE FINISH TIMES

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

LF = 2

LF = 4

LF = 4

LF = 8

LF = 13

LF = 8

LF = 13

LF = 15

LATE FINISH TIME SELECTED CALCULATIONS

FOLLOWERTASKLATE

FINISHTIME

(LF = 15)H

FOLLOWERTASK

EXPECTEDTIME

(te = 2)H

PREDECESSORTASKLATE

FINISHTIME

(LF = 13)F

=-

IF THERE ARE SEVERAL CANDIDATES

FOR THE PREDECESSOR TASK LF, SELECT THE SHORTEST LF

General Foundry Inc.LATE FINISH TIMES

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

LF = 2

LF = 4

LF = 4

LF = 8

LF = 13

LF = 8

LF = 13

LF = 15

LF Candidate Selection

2

C

4

E

F

3

LF=4

LF=8

LF=13

COMING IN FROM TASK “F”.THE LATE FINISH TIME FOR TASK “C” IS “10” (13-3=10)

COMING IN FROM TASK “E”,THE LATE FINISH TIME FOR

TASK “C” IS “4” (8-4=4)

THE SMALLERLATE FINISH

TIMECONTROLS

LATE START TIME ( LS )

This technique is also calledBACKWARD PASS

The latest possible time that each task can start without jeopardizing the project’s expected completion time.

Computed from right to left, that is, from the network’s finish node to the network’s start node.

LATE START TIME FORMULA

TASKLATE

FINISHTIME(LF)

TASKEXPECTED

TIME(te)

TASK LATE STARTTIME(LS)

=-

NEEDLESS TO SAY, TASK LATE START TIMESCANNOT BE COMPUTED UNTIL TASK LATE

FINISH TIMES ARE IDENTIFIED

General Foundry Inc.LATE START TIMES

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

LS=0LF=2

LS=1LF=4

LS=2LF=4

LS=4LF=8

LS=10LF=13

LS=4LF=8

LS= 8LF=13

LS=13LF=15

LATE START TIME SELECTED CALCULATIONS

TASKLATE

FINISHTIME

(LF = 15)H

TASKEXPECTED

TIME

(te = 2)H

TASK LATE STARTTIME

(LS = 13)H

=-




START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

LS=0LF=2

LS=1LF=4

LS=2LF=4

LS=4LF=8

LS=10LF=13

LS=4LF=8

LS= 8LF=13

LS=13LF=15

LATE START TIME SELECTED CALCULATIONS

TASKLATE

FINISHTIME

(LF = 4)B

TASKEXPECTED

TIME

(te = 3)B

TASK LATE STARTTIME

(LS = 1)B

=-




START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

LS=0

LS=1

LS=2

LS=4

LS=10

LS=4

LS=8

LS=13

SLACK TIME ( S )

The time each task may be postponed without jeopardizing the project’s expected completion time.

The chain of zero slack tasks in the network will also identify the critical path.

ALSO KNOWN AS PRIMARY SLACK

SLACK TIME FORMULAETWO VERSIONS

S = Task LS – Task ES

S = Task LF – Task EF

General Foundry Inc.ALL SLACK TIME CALCULATIONS

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2ES=0 EF=3LS=1 LF=4 S=1

ES=2 EF=4LS=2 LF=4 S=0


ES= 4 EF= 7LS=10 LF=13 S=6


ES=8 EF=13LS=8 LF=13 S=0

ES=13 EF=15LS=13 LF=15 S=0

ES = 0 EF = 2LS = 0 LF = 2 S = 0

General Foundry Inc.PRIMARY SLACK TIMES FOR ALL TASKS

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2TIME in WEEKS

S=0

S=1

S=0

S=1

S=6

S=0

S=0

S=0

General Foundry Inc.CRITICAL PATH VIA ZERO SLACK TIME TASKS

START FINISH

A

B

C

D

E

F

G

H

2

3

2 3

4

4 5

2A-C-E-G-H

S=0

S=1

S=0

S=1

S=6

S=0

S=0

S=0

Probabilistic PERT

1. Critical path time ( CP or μ )

2. CP tasks’ optimistic times ( a )

3. CP tasks’ pessimistic times ( b )

4. CP tasks’ time variances ( )

REQUIRES 4STATISTICS

Generates probabilities for completing a projectbefore and after its expected completion date.

Task Time Variance FormulaOF THE BETA DISTRIBUTION

2

where: a = optimistic time b = pessimistic time 6 = constant ( k )

MUCH EASIERFORMULATHAN THE

ONE FOR THENORMAL

PROBABILITYDISTRIBUTION

! = b - a 6 𝝈𝟐

EXAMPLEALL NEW - VARIANCES FABRICATED

Assume the critical

path is 36.33 days

( CP = μ )

Assume the tasks

along the critical

path are:

C,D,E,F,H,K

Assume that the

critical path task

time variances ( σ )

in days are:

C = .11

D = .11

E = .44

F = 1.78

H = 1.00

K = 1.78

2

Requirements

I. What are the chances of finishing the project in 30 days or less?

In other words,

P ( t =< 30 ) = ?

II. What are the chances of finishing the project in 40 days or less?

In other words,

P ( t =< 40 ) = ?

Solution

ProjectVariance = ∑ CP Task Variances ( σ )

.11

.11

.441.781.001.78

5.22 days =

ProjectStd Dev = √5.22 = 2.28 days ( σ )

2

Solution

μ = 36.33 days

σ = 2.28 days

X = 30 days

Project completion time is normally distributed.

Therefore, a normal curve can be drawn with a μ and σ.

Z = X – μ = 30.00 – 36.33 = - 2.78 σ 2.28

The no. of standard deviatesbetween the mean ( μ ) and the

value of interest ( X )

Z .08

2.7 .99728

The percentage of the normalcurve covered to a point that is“2.78” standard deviates to the

left of the mean = 99.728%

-2.78 z

.99728.00272

Solution

Therefore, the probability of finishing the project in 30 days or less is:

1 - .99728 = .00272

P( t =< 30 ) ≈ 0%

Conversely, the probability of finishing the project in more than 30 days is:

.99728

P( t > 30 ) ≈ 100%

Solution

μ = 36.33 days

σ = 2.28 days

X = 40 days

Project completion time is normally distributed.

Therefore, a normal curve can be drawn with a μ and σ.

Z = X – μ = 40.00 – 36.33 = +1.61 σ 2.28

The no. of standard deviatesbetween the mean (μ) and the

value of interest (X)

Z .01

1.6 .94630

The percentage of the normalcurve covered to a point that is“1.61” standard deviates to the

right of the mean = 94.630%

+ 1.61 Z

.94630

.0537

Solution

Therefore, the probability of finishing the project in 40 days or less is:

.94630

P( t=<40 ) ≈ 95%

Conversely, the probability of finishing the project in more than 40 days is:

.0537

P( t>40 ) ≈ 5%

PERT / CPM with QM for WINDOWS

We scroll toPROJECT MANAGEMENT

( PERT / CPM )

Applied Management Science for Decision Making, 2e © 2014 Pearson Learning Solutions

We have only one time estimate for each task

in this project

We select theSINGLE TIME ESTIMATE

program

There are 8 tasksin the project

“Precedence List”is another term forActivity-on-Node

Convention

The tasks are labeledA, B, C, D, etc.

The Data InputTable

“Prec” is an abbreviation for “Predecessor Task”. Here, the program provides for listing as many as 7 predecessor tasks for each task.

Project EstimatedCompletion Time( Critical Path )

Zero Slack Time Tasks Are

Highlighted In Red

The 2nd Solution Is “CHARTS”

Four Different ChartsCan Be Brought Up

By Clicking Their Titles

Early StartEarly Finish

Late StartLate Finish

Critical PathTasks

Here, the program displaysa precedence relationshipdiagram based on what we

entered in the “predecessor” columns

The Critical PathTasks Are Shown

In Red

Templateand

Sample Data

Templateand

Sample Data

Project Management

Documents

Project Management Introduces Pert/CPM as a tool for planning, scheduling, and controlling projects Applied Management Science for Decision Making, 2e