Program Evaluation Review Program Evaluation Review Technique (PERT)Technique (PERT)

Report by:Report by:

Raymund N. SanchezRaymund N. Sanchez

Content of the Content of the PresentationPresentation

DefinitionDefinition Differences between PERT & CPMDifferences between PERT & CPM PurposePurpose Historical PerspectiveHistorical Perspective TerminologiesTerminologies Creating a PERT/CPM diagramCreating a PERT/CPM diagram Schedule Duration CrashSchedule Duration Crash Probabilistic Time EstimatesProbabilistic Time Estimates

– uncertainty of activities and pathsuncertainty of activities and paths– path probabilitiespath probabilities

Problem ExercisesProblem Exercises

DefinitionDefinition

A method to analyze the tasks involved in completing a given project.

Focus is paid to the time needed to complete each task, and identifying the minimum time needed to complete the total project.

PurposePurpose

To simplify the planning and scheduling of large and complex projects.

To incorporate uncertainty in the sense that it was possible to schedule a project not knowing precisely the details and duration's of 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.

PERT & CPM SimilaritiesPERT & CPM Similarities

Both follow the same steps and use network diagrams

Both are used to plan the scheduling of individual activities that make up a project

They can be used to determine the earliest/latest start and finish times for each activity

PERT & CPM DifferencesPERT & CPM Differences

PERT is probabilistic whereas CPM is deterministic

In CPM, estimates of activity duration are based on historical data

In PERT, estimates are uncertain and we talk of ranges of duration and the probability that an activity duration will fall into that range

CPM concentrates on Time/Cost trade off.

Historical BackgroundHistorical Background PERT was invented by Booz Allen Hamilton, Inc.

under contract to the United States Department of Defense's US Navy Special Projects Office in 1958

A part of the Polaris mobile submarine-launched ballistic missile project. This project was a direct response 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

the 1960’s

TerminologiesTerminologies 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 have been completed.

Predecessor event: an event (or events) that immediately precedes 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 be the consequence of more than one activity.

TerminologiesTerminologies PERT activity: is the actual performance of a task. It consumes

time, 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 is normally expected

Pessimistic time (P): the maximum possible time required to accomplish a task, assuming everything goes wrong (but

excluding major catastrophes).

TerminologiesTerminologies Most likely time (M): the best estimate of the time required

to accomplish 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 (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time).

Critical Path: the longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.

TerminologiesTerminologies

Lead time: the time by which a predecessor event must be completed in order to allow sufficient time for the activities that must elapse before a specific PERT event is reached to be completed.

Lag time: the earliest time by which a successor event can follow a specific PERT event.

Slack: the slack of an event is a measure of the excess time and resources available in achieving this event. Positive slack would indicate ahead of schedule; negative slack would indicate behind schedule; and

zero slack would indicate on schedule.

TerminologiesTerminologies Early Start (ES): maximum EF of all predecessor activities,

unless the activity in question is the the first activity, wherein ES is 0

Early Finish (EF): ES plus task duration Late Start (LS): LF minus task duration Late Finish (LF): minimum LS on all successor activities,

unless the activity is the last activity, wherein LF equals EF Activity on Arrow (AOA): a type of PERT diagram wherein

the activities are written on the arrows Activity on Node (AON): a type of PERT diagram wherein

the activities are written on the nodes

Creating a PERT DiagramCreating 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

formulaTe=(O+4M+P)/6

Determine whether to use AOA or AON diagrams

Activity Predecessor Optimistic(a)

Normal(m)

Pessimistic(b)

Te(a+4m+b)/ 6

A --- 2 4 6 4.00

B --- 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

Start

F

C

GE

D

B

A

Finish

Creating a PERT DiagramCreating 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 the

current activity– EF of an activity is computed by adding its ES with its

duration– For activities with 2 or more predecessor activities, use

the predecessor with the higher EF as the ES of the current activity

StartES:0EF:0

FD:4.5

ES:10.33EF:14.83

CD:5.17ES:4

EF:9.17

GD:5.17

ES:14.34EF:19.51

ED:5.17ES:9.17

EF:14.34

DD:6.33ES:4

EF:10.33

BD:5.33ES:0

EF:5.33

AD:4ES:0EF:4

FinishD:0

ES:19.51EF:19.51

Creating a PERT DiagramCreating 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 equal to 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 its

duration– For activities with 2 or more successor activities, use the

successor with the lower LS as the LF of the current activity

StartD:0ES:0EF:0LS:0LF:0

FD:4.5ES:10.33EF:14.83LS:15.01LF:19.51

CD:5.17ES:4EF:9.17LS:4LF:9.17

GD:5.17ES:14.34EF:19.51LS:14.34LF:19.51

ED:5.17ES:9.17EF:14.34LS:9.17LF:14.34

DD:6.33ES:4

EF:10.33LS:8.68LF:15.01

BD:5.33ES:0EF:5.33LS:3.84LF:9.17

AD:4ES:0EF:4LS:0LF:4

FinishD:0

ES:19.51EF:19.51LS:19.51LF:19.51

Creating a PERT DiagramCreating 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 activity’s LF & EF

Critical PathCritical Path

Critical Path: A-C-E-GCritical Path: A-C-E-G Path A-D-F Path A-D-F = 14.83 work = 14.83 work

daysdays Path A-C-E-G Path A-C-E-G = 19.51 work = 19.51 work

daysdays Path B-E-G Path B-E-G = 15.67 work = 15.67 work

daysdays

SlackSlackActivity 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

Gantt ChartGantt Chart

Schedule Duration CrashSchedule Duration Crash Crash :Crash : an effort to reduce the overall time an effort to reduce the overall time

duration of a project by employing one or all of duration of a project by employing one or all of the following techniquesthe following techniques– Adding resources (human or otherwise)Adding resources (human or otherwise)– Increasing work hours (overtime or weekends)Increasing work hours (overtime or weekends)– Lessening qualityLessening quality

A trade-off between shorter task duration and higher task costs

If the cost savings on a delay penalty are higher than the incremental cost of reducing the project duration, then the crashing is justified.

Activity UncertaintyActivity Uncertainty Standard Deviation of an activity is estimated as one

sixth of the difference between the pessimistic and optimistic time estimates

Variance is determined by squaring the standard deviation

The size of the variance reflects the degree of uncertainty associated with the activity’s time. The larger the variance, the greater the uncertainty.

Standard Deviation = tp - to

6

Path UncertaintyPath Uncertainty

Standard Deviation of a path can also be computed to know the uncertainty of a particular

path.

SD of Path= variances of activities on a path

Path ProbabilityPath Probability The probability that a given path will be completed in The probability that a given path will be completed in

a specified length of time can be determined using a specified length of time can be determined using the following formula:the following formula:

Z = Specified Time - Path Mean Path Standard Deviation

If the value of Z is 2.50 more, treat the path probability as 100%. If the value of Z is less than 2.50, use the table of values under the standardized normal curve.

Sample ProblemSample ProblemActivity Description Predecessor Duration

A Receive production authorization --- 0B Determine parts requirements A 2C Determine required resources B 4D Determine material availability C 5E Determine labor availability C 3F 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