OPERATIONS RESEARCH

CHAPTER VIII

CPM-PERTInstructor : Lect.Volkan ÇETİNKAYA

PROJECT

“A project is a series of activities directed to accomplishment of a desired

objective.”

Plan your work first…...then work your plan!

INTRODUCTION

PERT: (Project Evaluation and Review

Technique

CPM: (Critical Path Method)

CPM-PERT APPLICATION FIELDS

Building, Airport, Roadway and similar

construction projects.

Loading of new computer systems.

Design of new products.

Ship Constructing

QUESTIONS TO BE REPLIED VIA CPM-PERT When will the project finish?

Which critical activities are there?And not?

What’s the probability of finishing the project in a definite term?

Where is the project?Going on accurately?

Is the project under or below the budget?

Are there adequate resources for the completion of project?

If it is planned to complete the project before planned time,

How can it be done by least cost?

INTRODUCTION CPM: For certain activities , it may be possible to

decrease their completion times by spending more

money.How does this affect the overall completion time

of the project.

PERT: It has probability, It is for a particular activity the

most likely completion time is 4 weeks but it could be

anywhere between 3 weeks and 8 weeks.

DIFFERENCE BTW. PERT and CPM

CPM: In CPM activities are shown as a network of

precedence relationships using activity-on-node network

construction.

Single estimate of activity time

Deterministic activity times

Used in Production management-for the jobs of repetitive in

nature where the activity time estimates can be predicted with

considerable certainty due to existance of past experience

CPM’de faaliyetlerin süreleri kesin olarak

bilinmektedir.

PERT’te faaliyetlerin süre ve maliyetleri kesin

olarak bilinmemekte, bu veriler rassal

değişkenler olarak atanmaktadır. Dolayısıyla

elde edilen kritik yol bir “olasılık kritik yolu”dur.

CPM-PERT FARKI

DIFFERENCE BTW. PERT and CPM

PERT: In PERT activities are shown as a network of

precedence relationships using activity-on-arrow network

construction.

Multiple estimate of activity time

Probabalistic activity times

Used in Project Management-for non-repetitive

jobs(research and development works) where the time

and cost estimates tend to be quite uncertain.

GANNT CHART

Advantages

- Gantt charts are quite commonly

used. They provide an easy

graphical representation of when

activities (might) take place.

Limitations

- Do not clearly indicate details regarding the progress of activities

- Do not give a clear indication of interrelation ship between the separate activities

USE OF NODES AND ARROWS

Arrows: An arrow leads from tail to head directionally.It

indicates ACTIVITY, a time consuming effort that is

required to perform a part of the work.

Nodes: A node is represented by a circle. It indicates

EVENT, a point in time where one or more activities start

and/or finish.

COMMON STEPS for CPM&PERT Describe the project and important activities.

Describe the relationships among facilities.

Draw the project network.

Determine time and cost of all activities.

Compute the longest way(critical path) of the network.

Use the network to plan, to schedule follow and

control the project.

EXAMPLE-1 A new founded company wants to design a product.

Below the activities , priority relationships and

activity durations were given. Draw the project

network. Activity Predecessor Duration

A: Construction of production lines - 8

B:Purchasing - 11

C: Production of semi finished product-1 A 10

D: Production of semi finished product-2 B 7

E: testing of semi finished product-2 D 13

F: Assembly C,E 15

EXAMPLE-2

FINDING CRITICAL PATH

□j = Earliest occurence time of event ‘j’

∆j = Latest occurence time of event ‘j’

Dij = Duration of activity

FINDING CRITICAL PATH Forward Pass: (Earliest Occurence Times) The computations

start at node 1 and advance recursively to end node n .

Backward Pass : (Latest Occurence Times) Following the

completion of the forward pass , the backward pass

computations starts at node n and end at node 1.

FINDING CRITICAL PATH An activity(i,j) will be critical if it satisfies these 3 conditions.

□i = ∆i

□j = ∆j

∆j - ∆i = □j - □i = Dij

EXAMPLE-3

CONSTRUCTION of TIME SCHEDULE Time Schedule for Example 3

EXAMPLE-4 Draw the project network

Compute the critical path according to the data below

Activity Predecessor Duration

A: Construction of production lines - 8

B:Purchasing - 11

C: Production of semi finished product-1 A 10

D: Production of semi finished product-2 B 7

E: testing of semi finished product-2 D 13

F: Assembly C,E 15

PERT PERT: Project Evaluation and Review Technique. Like CPM,

but ist is a probabilistic model.

In PERT, activities fall in to 3 categories:

O : Optimistic

P : Pessimistic

M : Medium

PERT Average Completion Time = (O + 4M + P) /6

Standart Deviation = (P-O)/6

Variance = (

EXAMPLE-5 Let’s look at a project with 8 events and 11 activities.

QUESTIONS: Draw the network of the project. Compute expected time and variance of each activity. Find critical path. Compute the standart deviation of dispersion proving expected time of project. What is the probability of completion of the project in 19 days or less than 19

days?

EXAMPLE-6 Draw the network of the ship construction project.

Compute expected time and variance of each activity.

Find critical path.

Compute the standart deviation of dispersion proving expected time of project.

What is the probability of project completion in 36 weeks?

Activity Name TR Processedor O M PA Permissions İzinler - 2 3 4B Budget Preperation Bütçe Hazırlık - 2 2 2C Draft Draft A,B 2 3 7D Constructing Kaba İnşaat C 5 7 9E Outer Installation Dış Tesisat D 3 4 11F Electrical Works Elektrik İşleri D 3 5 10G Inner Installation İç Tesisat E 5 6 10H Outer Painting Dış Boya G 2 3 4I Inner Painting İç Boya F,H 4 5 6J Other Diğer İşler H 2 3 4K Submittal Teslim I,J 2 3 4