project management introduces pert/cpm as a tool for planning, scheduling, and controlling projects...
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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
Project Prerequisites
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.
Project Prerequisites
Tasks with alternate execution sequences
Tasks that can be reordered might result inoverall shorter overall execution times andless cost.
Project Prerequisites
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
Project Prerequisites
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 begin- ning node to the net- work’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 )
=+
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
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
B ( 0 )
PREDECESSORTASK
te
B ( 3 )
FOLLOWERTASK
ES
D ( 3 )
=+
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
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
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
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
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
=+
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 = 2C
TASKEXPECTED
TIME
te = 2C
TASKEARLY FINISHTIME
EF = 4C
=+
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
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
=-
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 = 4)B
TASKEXPECTED
TIME
(te = 3)B
TASK LATE STARTTIME
(LS = 1)B
=-
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=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=3 EF=7LS=4 LF=8 S=1
ES= 4 EF= 7LS=10 LF=13 S=6
ES=4 EF=8LS=4 LF=8 S=0
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