PERT / CPM:CONCEPT OF NETWORK, RULES FOR CONSTRUCTION OF NETWORK

<< Introduction:USES OF OPERATIONS RESEARCH, Marketing, Personnel

PERT / CPM:DUMMY ACTIVITIES, TO FIND THE CRITICAL PATH >>

Operations Research (MTH601)

Ignizio, J.P., Linear Programming in Single and Multiple Objective System. Prentice-Hall

Segment II: PERT / CPM

Lectures 4 -10

Operations Research (MTH601)

INTRODUCTION

PERT is an acronym for "Programme Evaluation and Review Technique". This was created as a means to

plan and accelerate the development of the Polaris Ballistic Missile. In USA the defence department developed a

nuclear missile to be launched from beneath the ocean's surface by a mobile submarine, which would be an effective

deterrent against aggression by an enemy. This paved way to plan how to design, develop and plan the different

stages in the production of a missile and how quickly this task could be completed. A planning and scheduling

technique named PERT gave the answer to these questions.

In any new venture, uncertainties are bound to creep in. PERT incorporated these uncertainties into a

model, which provides a reasonable answer to these uncertainties. There are certain statistical aspects scheduling

large projects consisting of numerous activities whose completion times are uncertain and are independent of one

another. PERT is an event-oriented technique. By 'event' we mean reaching a certain stage of completion of the

project.

Another technique, Critical Path Method, abbreviated as CPM, has emerged simultaneously. It is also a

network technique but it is concerned with obtaining the trade-off, between cost and completion date for large

projects. In any project consisting of several activities each activity can be completed in a normal duration with

normal cost. If we employ more persons or skilled people or given overtime to the workers, the activity could be

completed in a reduced duration known as crash duration. But this involves an increased cost in the form of

additional resources. With CPM the amount needed to complete the various activities is assumed to be known with

certainty. So, the direct costs for the activities increase and hence the cost of the project also increases. By reducing

the activity duration of some or all possible completed ahead of the schedule. This will naturally reduce the

overhead cost for the entire project. On one hand the direct expenses increase, if we shorten the activity duration,

but, the indirect expenses for the project are reduced. We have to strike a balance or an optimum time schedule, or a

least cost schedule is to be obtained. This is the purpose of the Critical Path Method. Thus CPM is not concerned

with uncertain job times as in PERT. PERT is useful in research and developmental projects, whereas CPM is

mostly used in construction projects, or in situations already handled, so that the details like the normal completion

time, crash duration and cost of crashing are already known.

The following are the suggested applications when PERT or CPM is found useful.

The construction of a building or of a highway.

Planning and launching a new product.

Scheduling maintenance for a project.

The manufacture and assembly of a large machine tool.

To conduct a music or drama festival.

Preparation of budget for a company.

CONCEPT OF NETWORK

The first step in the application of CPM / PERT is to develop a network representation of the project plan.

Operations Research (MTH601)

A 'network' is defined as a graphic representation with a flow of some type in its branches. It represents

nodes and branches. Below in table 1, we represent different systems satisfying the definition of network in the

physical world.

Operations Research (MTH601)

Table 5.1

Physical

Nodes

Branches

Flow

situation

Highway systems

Intersections

Roads

Vehicles

Communication

Switching points

Wires

Messages

systems

Fluid supply

Pumping stations

Pipes

Fluid

systems

Production

Work centres

Handling routes

Jobs

systems

Project

Decision points

Activities

Time

Management

Airway systems

Airports

Airlines

Aircraft

A node is the intersection of the two branch lines. It is denoted by a circle. Each branch represents an

activity. Each node represents an event, which is a specific definable accomplishment recognizable at a particular

instant of time. The arrowheads indicate the sequence in which events must be achieved. Thus an event is the

completion of all the activities leading into that node and this event must precede the initiation of the activity leading

out of the node.

node

Branch

node

Fig. 1

An arrow diagram represents a project graph. An arrow connecting two nodes, representing two events,

represents each activity. The head of the arrow identifies the start of the activity.

Let us take an example and illustrate the construction of arrow diagram for a project.

Example 1: A company is interested in preparing a budget. The details of the activities and the departments

involved are given in the Table 2.

Table 2

The project of preparation of a Production budget.

Job

Alternate

Job

Department

Identification

Description

1-2

Forecasting sales

Sales

2-4

Pricing Sales

Sales

2-3

Preparing production Schedule

Engineering

3-4

Costing the production

Costing

4-5

Preparation of budget

President

Table of Contents: