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Metoda P.E.R.T. (Program Evaluation and Review Technique).

Programul de Evaluare i Examinare Tehnic (PERT) este un model de tip reea care permite randomizarea

n programarea timpului de ndeplinire a sarcinilor unui proiect. Prin PERT se poate reduce att t impul, ct icosturile unui proiect.

Etape n procesul de planificare PERT:1. Identificarea activitilor specifice i a obiectivelor intermediare:

Este de ajutor sa se alcatuiasc o lista de activiti care, n etape ulterioare, s poata fi extins cu ajutorul

informaiilor avute la dispoziie;2. Determinarea etapizrii activitilor:

Aceast etap presupune o analiz a fiecrei activiti n parte pentru a determina relaiile acestora una cu

cealalta i ordinea n care trebuie finalizate;3. Construirea diagramei de reea:

Construirea diagramei se poate face cu ajutorul unui software specializat sau manual. n ambele cazuri, este

bine s se foloseasc simboluri uzuale ca de exemplu: activitile vor fi reprezentate de sgei, n timp ce

obiectivele intermediare sunt simbolizate prin cercuri.4. Estimarea timpului necesar pentru realizarea fiecrei activiti:

Pentru a determina timpul de realizare a unei activiti, n mod normal se determina trei timpi:timpul

optimistic, "timpul cel mai probabil, "timpul pesimistic.Timpul de realizare a unei activiti se

calculeaz apoi astfel:

Tra=(Topt+4*Tprob+Tpes)/6

5. Determinarea cii critice:

Calea critic se determin prin adugarea timpilor activitilor pentru fiecare secven i determinnd cea

mai lung cale a proiectului.6. Updatarea PERT pe msura ce proiectul progreseaz:Pe masura ce proiectul progreseaz, se pot face modificri. Timpii programai pot fi modificai cu ceirealizai. Daca apar ntarzieri, se vor aloca resurse adiionale pentru recuperarea acestuia i diagrama

PERT va fi modificat pentru a reflecta acest lucru.

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Model PERT - etapizare simpla

Avantaje ale metodei PERT:

Diagrama PERT este mai folositoare dect alte metode utilizate n prezent deoarece ne pune la dispoziie

unele informaii precum: Timpul prognozat de realizare a proiectului;

Probabilitatea de realizare naintea datei specificate;

Activitaile ci critice care au impact direct asupra datei de finalizare a proiectului;

Activitaile care au timp suplimentar la dispoziie care poate fi pus la dispozitia activitatilor ci

critice; Data de ncepere i ncheiere a proiectului.

Dezavantaje ale PERT:

Printre limitarile PERT, se pot aminti urmatoarele: Estimrile timpilor activitilor sunt oarecum subiective i depind de judecata uneia sau mai multor

persoane pe baza unor informaii (complete sau incomplete) avute la dispoziie n momentul realizrii

estimrilor; Chiar dac timpii activitilor sunt bine estimai, PERT accept o beta distribuie a acestor

estimri n cadrul ntregului proiect, n timp ce distribuia real poate fi real.

Chiar daca PERT realizeaz o beta-distribuie similar cu cea real, exist posibilitatea apariiei unor

ntrzieri deoarece timpul asociat de catre PERT cii critice va fi ntotdeauna mai mare dect n mod real.

Program Evaluation & Review Technique(PERT)

PERT Activity TimesoThree time estimates are required

Optimistic time (a) if everything goes according toplan

Mostlikely time (m) most realistic estimate Pessimistic time (b) assuming very unfavorable

conditions

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o Follow beta distributiono Expected time: t = (a + 4m + b)/6o Variance of times: v = [(b a)/6]2

Project Timeso Conduct CPM method using expected activity timeso Expected project time (T)

Sum of critical path activity times (t)

o Project Variance

Sum of critical path activity variances (v)

Probability of Project Completiono Project variance is computed by summing the variances of

critical activitieso 2 = Project variance

= (variances of activities on critical path)

o PERT makes two more assumptions:Total project completion times follow a normal

probability distribution

Activity times are statistically independento What is the probability this project can be completed on or

before the 16 week deadline?

Z =(due date expected date of completion)/p

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Where Z is the number of standard deviations the duedate lies from the mean

Variability of Completion Time for Noncritical Pathso Variability of times for activities on noncritical paths must

be considered when finding the probability of finishing in aspecified time

o Variation in noncritical activity may cause change in criticalpath

Critical Path Method (CPM)

Critical Path Method (CPM) Analysis

oA single time estimate for each activity

o Provides activity information Earliest Start (ES) & Earliest Finish (EF)

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Latest Start (LS) & Latest Finish (LF)

Slack(S): Allowable Delay

o Identifies Critical Path Longest path through the network Shortest time in which the project can be completed Any delay in critical path activities delays the project Critical path activities have 0 slack time

Forward Passo Begin at starting event and work forwardo Earliest Start Time Rule:

If an activity has only one immediate predecessor, itsES equals the EF of the predecessor

If an activity has multiple immediate predecessors, itsES is the maximum of all the EF values of itspredecessors

ES = Max (EF of all immediate predecessors)o Earliest Finish Time Rule:

The earliest finish time (EF) of an activity is the sum ofits earliest start time (ES) and its activity time

EF = ES + Activity time

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Backward Passo Begin with the last event and work backwardso Latest Finish Time Rule:

If an activity is an immediate predecessor for just asingle activity, its LF equals the LS of the activity thatimmediately follows it

If an activity is an immediate predecessor to morethan one activity, its LF is the minimum of all LSvalues of all activities that immediately follow it

LF = Min (LS of all immediate following activities)o Latest Start Time Rule:

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The latest start time (LS) of an activity is thedifference of its latest finish time (LF) and its activitytime

LS = LF Activity time

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The CPM Methodo Create a network diagramo Indentify all possible paths from start to finish through the

networko Determine length (or duration) of each path by adding task

times for all tasks on patho

Longestpath is critical path

Critical path corresponds to longest path in thenetwork for a project completion

All activities (or tasks) on critical path are calledcritical activities

Advantages & Limitations of PERT/CPM

Advantages of PERT/CPM1. Especially useful when scheduling and controlling large

projects2. Straightforward concept and not mathematically complex

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3. Graphical networks help to perceive relationships amongproject activities

4. Critical path and slack time analyses help pinpointactivities that need to be closely watched

5. Project documentation and graphics point out who isresponsible for various activities6. Applicable to a wide variety of projects

7. Useful in monitoring not only schedules but costs as well

Limitations of PERT/CPM1. Project activities have to be clearly defined, independent,

and stable in their relationships2. Precedence relationships must be specified and networked

together3. Time estimates tend to be subjective and are subject to

fudging by managers

4. There is an inherent danger of too much emphasis beingplaced on the longest or critical path

Phase 2: Scheduling - relates people,money, & supplies to specific activities &activities to each other

Project activities Start & end times Network

Phase 2: Project Scheduling

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o Identifying precedence relationshipso Sequencing activitieso Determining activity times & costso Estimating material and worker requirementso Determining critical activities