Program Evaluaperttion Review Technique 4707

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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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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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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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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Program Evaluaperttion Review Technique 4707

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