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7/30/2019 Program Evaluaperttion Review Technique 4707
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Program Evaluation Review Technique
(PERT)
Report by:
Raymund N. Sanchez
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Content of the Presentation
Definition
Differences between PERT & CPM
Purpose Historical Perspective
Terminologies
Creating a PERT/CPM diagram
Schedule Duration Crash Probabilistic Time Estimates
uncertainty of activities and paths
path probabilities
Problem Exercises
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Definition
A method to analyze the tasks involvedin completing a given project.
Focus is paid to the time needed tocomplete each task, and identifying theminimum time needed to complete the
total project.
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Purpose
To simplify the planning and scheduling oflarge and complex projects.
To incorporate uncertainty in the sense that itwas possible to schedule a project notknowing precisely the details and duration'sof all the activities.
Event-oriented technique rather than start-and completion-oriented.
Used more in R&D-type projects where Cost
is not a major factor but Time is.
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PERT & CPM Similarities
Both follow the same steps and use networkdiagrams
Both are used to plan the scheduling ofindividual activities that make up a project
They can be used to determine theearliest/latest start and finish times for eachactivity
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PERT & CPM Differences
PERT is probabilistic whereas CPM isdeterministic
In CPM, estimates of activity duration arebased on historical data
In PERT, estimates are uncertain and we talkof ranges of duration and the probability thatan activity duration will fall into that range
CPM concentrates on Time/Cost trade off.
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Historical Background
PERT was invented by Booz Allen Hamilton, Inc. undercontract to the United States Department of Defense'sUS Navy Special Projects Office in 1958
A part of the Polaris mobile submarine-launchedballistic missile project. This project was a directresponse to the Sputnik crisis
CPM was developed by the dupont company &
Remington-Rand-Univac Used for large construction projects
Each were unaware of the others existence until the1960s
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Terminologies
PERT event: is a point that marks the start or completion of one(or more) tasks. It consumes no time, and uses no resources.It marks the completion of one (or more) tasks. It is not
reached until all of the activities leading to that event havebeen completed.
Predecessor event: an event (or events) that immediatelyprecedes some other event without any other events intervening.
It may be the consequence of more than one activity. Successor event: an event (or events) that immediately follows
some other event without any other events intervening. It may bethe consequence of more than one activity.
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Terminologies
PERT activity: is the actual performance of a task. It consumestime, it requires resources (such as labor, materials, space,machinery), and it can be understood as representing the time,
effort, and resources required to move from one event to another.A PERT activity cannot be completed until the event preceding it
has occurred. Optimistic time (O): the minimum possible time required to
accomplish a task, assuming everything proceeds better than isnormally expected
Pessimistic time (P): the maximum possible time required toaccomplish a task, assuming everything goes wrong (but
excluding major catastrophes).
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Terminologies
Most likely time(M): the best estimate of the time required toaccomplish a task, assuming everything proceeds as normal.
Expected time (TE): the best estimate of the time required to
accomplish a task, assuming everything proceeds as normal (theimplication being that the expected time is the average time thetask would require if the task were repeated on a number ofoccasions over an extended period of time).
Critical Path: the longest possible continuous pathway takenfrom the initial event to the terminal event. It determines the totalcalendar time required for the project; and, therefore, any timedelays along the critical path will delay the reaching of theterminal event by at least the same amount.
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Terminologies
Lead time: the time by which a predecessor event must becompleted in order to allow sufficient time for the activities thatmust elapse before a specific PERT event is reached to be
completed. Lag time: the earliest time by which a successor eventcan follow
a specific PERT event.
Slack: the slackof an event is a measure of the excess time and
resources available in achieving this event. Positive slackwouldindicate ahead of schedule; negative slack would indicate
behind schedule; and zero slackwould indicate on schedule.
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Terminologies
Early Start (ES): maximum EF of all predecessor activities,unless the activity in question is the the first activity, wherein ESis 0
Early Finish (EF): ES plus task duration
Late Start (LS): LF minus task duration
Late Finish (LF): minimum LS on all successor activities, unlessthe activity is the last activity, wherein LF equals EF
Activity on Arrow (AOA): a type of PERT diagram wherein theactivities are written on the arrows
Activity on Node (AON): a type of PERT diagram wherein theactivities are written on the nodes
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Creating a PERT Diagram
STEPS 1: Determine the tasks that the project requires and the
order in which they must be completed Determine the optimistic, most likely, and pessimistic
time of each task
Compute for the Expected time using the formula
Te=(O+4M+P)/6 Determine whether to use AOA or AON diagrams
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Activity Predecessor Optimistic
(a)
Normal
(m)
Pessimistic
(b)
Te(a+4m+b)/6
A --- 2 4 6 4.00B --- 3 5 9 5.33
C A 4 5 7 5.17
D A 4 6 10 6.33
E B, C 4 5 7 5.17
F D 3 4 8 4.50
G E 3 5 8 5.17f
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Start
F
C
GE
D
B
A
Finish
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Creating a PERT Diagram
STEPS 2: Determine the ES & EF of each activity by:
Start at the beginning moving towards the end ES & EF for the start activity is always 0 since they are
milestones
Use the EF of the predecessor activity as the ES of thecurrent activity
EF of an activity is computed by adding its ES with itsduration
For activities with 2 or more predecessor activities, usethe predecessor with the higher EF as the ES of the
current activity
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Start
ES:0
EF:0
F
D:4.5
ES:10.33
EF:14.83
CD:5.17
ES:4
EF:9.17
G
D:5.17
ES:14.34
EF:19.51
E
D:5.17
ES:9.17
EF:14.34
D
D:6.33
ES:4
EF:10.33
BD:5.33
ES:0
EF:5.33
A
D:4
ES:0
EF:4
Finish
D:0
ES:19.51
EF:19.51
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Creating a PERT Diagram
STEPS 3: Determine the LS & LF of each activity by:
Start at the end and work towards the beginning The LF for the finish activity is equal to EF since it is the
last activity in the project. Since duration is 0, LS is equalto LF
Use the LS of the successor activity as the LF of the
current activity
LS of an activity is computed by subtracting its LF with itsduration
For activities with 2 or more successor activities, use the
successor with the lower LS as the LF of the currentactivity
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Start
D:0
ES:0
EF:0
LS:0
LF:0
F
D:4.5
ES:10.33
EF:14.83
LS:15.01
LF:19.51
C
D:5.17ES:4
EF:9.17
LS:4
LF:9.17
GD:5.17
ES:14.34
EF:19.51
LS:14.34
LF:19.51
ED:5.17
ES:9.17
EF:14.34
LS:9.17
LF:14.34
D
D:6.33
ES:4
EF:10.33
LS:8.68
LF:15.01
B
D:5.33
ES:0
EF:5.33
LS:3.84
LF:9.17
A
D:4
ES:0
EF:4
LS:0
LF:4
Finish
D:0
ES:19.51
EF:19.51
LS:19.51
LF:19.51
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Creating a PERT Diagram
STEPS 4: Compute for the critical path by adding the duration's
of various paths for all activities Determine if any activities have slack by subtracting the
activitys LF & EF
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Critical Path
Critical Path: A-C-E-G
Path A-D-F = 14.83 work days
Path A-C-E-G = 19.51 work days
Path B-E-G = 15.67 work days
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Slack
Activity LF-EF Total
A 4 - 4 0
B 9.17 5.33 3.84
C 9.17 9.17 0
D 15.01 10.33 4.68
E 14.34 14.34 0
F 19.51 14.83 4.68
G 19.51 19.51 0
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Gantt Chart
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Schedule Duration Crash
Crash : an effort to reduce the overall time duration ofa project by employing one or all of the followingtechniques
Adding resources (human or otherwise)
Increasing work hours (overtime or weekends)
Lessening quality
A trade-off between shorter task duration and higher
task costs
If the cost savings on a delay penalty are higher thanthe incremental cost of reducing the project duration,then the crashing is justified.
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Activity Uncertainty
Standard Deviation of an activity is estimated as onesixth of the difference between the pessimistic andoptimistic time estimates
Variance is determined by squaring the standarddeviation
The size of the variance reflects the degree ofuncertainty associated with the activitys time. The
larger the variance, the greater the uncertainty.
Standard Deviation = tp - to
6
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Path Uncertainty
Standard Deviation of a path can also be computed to
know the uncertainty of a particular path.
SD of Path= variances of activities ona path
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Path Probability
The probability that a given path will be completed in aspecified length of time can be determined using thefollowing formula:
Z = Specified Time - Path Mean
Path Standard Deviation
If the value of Z is 2.50 more, treat the path probabilityas 100%. If the value of Z is less than 2.50, use thetable of values under the standardized normal curve.
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Sample ProblemActivity Description Predecessor Duration
A Receive production authorization --- 0
BDetermine parts requirements
A 2C Determine required resources B 4D Determine material availability C 5E Determine labor availability C 3
F Determine equipment availability C 5G Prepare operation schedule D, E, F 8H Prepare & issue shop forms G 7I Manufacture the equipment H 31J Deliver the equipment I 4
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