Intro to Decision Theory.pdf

DECISION THEORY
(18MTO 01)
Chaitanya Bharathi Institute Of Technology (A)
Chintireddy Sharath Reddy
January 2, 2023

Table of Contents
1 Introduction to Operations Research
2 History/Development of Operations Research
3 Definition of Operations Research
4 Scope of Operations Research
5 Characteristics of Operations Research
6 Limitations of Operations Research
7 Tools/Techniques of Operations Research
Chintireddy Sharath Reddy DECISION THEORY January 2, 2023 2 / 22

Introduction to Operations Research
Operations:
The activities carried out in an organization
Research:
Research is a careful and detailed study into a specific problem, concern,
or issue using the scientific method.
Operational Research is a systematic and analytical approach to
decision making and problem solving.
O.R. is an Branch of applied mathematics that uses techniques and
statistics to arrive at Optimal solutions to solve complex problems.
Operation research is the application of advanced analytical methods
to help make better decisions.
It is typically concerned with determining the maximum profit, sale,
output, crops yield and efficiency And minimum losses, risks, cost, and
time of some objective function.

contd...
OR is the application of scientific methods, techniques & tools to the prob-
lems involving the operations of a system so as to provide those in control
of the system with optimum solution to the problem.

History/Development of Operations Research
The roots of OR can be traced back many decades, when early
attempts were made to use a scientific approach in the management
of organizations.
In 1885 Ferderick W.Taylor emphasised the application of scientific
analysis to methods of production. He conducted experiments in
connection with a simple shovel.
His aim was to find that wight load of ore moved by shovel which would
result in maximum of ore moved with minimum of fatigue.

contd...
In 1917, A.K.Erlang, a Danish mathematician, published his work on
the problem of congestion of telephone traffic.
During World War II:
The beginning of the activity called operations research has generally
been attributed to the military services early in World War II.
Because of the war effort, there was an urgent need to allocate scarce
resources to the various military operations and to the activities
within each operation in an effective manner.
Therefore, the British and then the U.S. military management called
upon a large number of scientists to apply a scientific approach to
dealing with this and other strategic and tactical problems.
In effect, they were asked to do research on (military) operations. These
teams of scientists were the first OR teams.
By developing effective methods of using the new tool of radar, these
teams were instrumental in winning the Air Battle of Britain.

contd...
Post World War II:
Immediately after the war, the success of military attracted the
attension of Industrial managers who were seekig solutions to their
problems.
Consequently OR soon spread from military to government, industrial,
social and economic planning.
The Operations Research Society of America (ORSA) was formed in
1950.
In 1950, OR was introduced as a subject for academic study in
American universities.

contd...
OPERATIONS RESEARCH IN INDIA:
In India, OR came into existence with the opening of a unit in 1949
at Regional Research Laboratory in Hyderabad (Counsil of Scientific
and Industruial Research, located at Tarnaka ).
The Operational Research Society of India(ORSI) was founded in 1957
to provide a forum for the Operational Research Scientists as well as an
avenue to widen their horizon by exchange of knowledge and application
of techniques from outside the country. The Society is affiliated to the
International Federation of Operational Research Societies (IFORS).
The Society Publishes a quarterly journal OPSEARCH, which brings
out high quality and state of the art papers in Operational Research.

Definition of Operations Research:
Each and every definition may explain one or another characteristic
of Operations Research but none of them explain or give a complete
picture of Operations research. But in the academic interest some of
the important definitions are discussed below:
(a) Operations Research is the art of winning wars without actually
fighting them.
- Aurther Clarke.
(b) Operations Research is the art of giving bad answers to problems
where otherwise worse answers are given.
- Thomas L. Satty.
(c) Operations Research is the application of scientific methods,
techniques and tools to operation of a system with optimum solution
to the problem.
- Churchman, Ackoff and Arnoff.
(d) Operations Research is a scientific approach to problem solving for
excutive management. - H.M.Wagner.

contd...
(e) Operations Research is the application of the methods of science to
complex problems arising in the direction and management of large
systems of men, materials and money in industry, business,
Government and defense.
- Operations Society of Great Britain.
(f) Operations Reserach is the application of scientific method by
interdisciplinary teams to problems involving the man-machine
systems so as to provide solutions which best serve the purpose of the
organization as a whole.
- Ackoff & sasieni.
(g) Operations Reserach is an experimental and applied science devoted
to observing, understanding and predicting the behaviour of
purposeful man-machine systems.
- Operations Research Society of America.

Scope of Operations Research
The scope of OR is not only confined to any specific agency like defence
services but today it is widely used in all industrial organisations. It
can be used to find the best solution to any problem be it simple or
complex. It is useful in every field of human activities.

contd...
Let us now discuss some of the fields where Operations Research techniques
can be applied to understand how the techniques are useful to solve the
problems.
(i) In Defense Operations
Administration
Intelligence
Operations, and
Training and supply.
(ii) In Agriculture
The demand for food products is increasing day by day due to popu-
lation explosion. But the land available for agriculture is limited. We
must find newer ways of increasing agriculture yield.
OR techniques used to find optimum allocation of land and various
crops in accordance with the climatic conditions and to find Optimum
distribution of water from various resources like canal for irrigation
purposes.

contd...
(iii) In Traffic control
Due to population explosion, the increase in the number and verities
of vehicles, road density is continuously increasing. Especially in peak
hours, it will be a headache to control the traffic.
Hence proper timing of traffic signaling is necessary. Depending on the
flow of commuters, proper signaling time is to be worked out. This can
be easily done by the application of queuing theory.
(iv) In Hospitals
Many a time we see very lengthy queues of patient near hospitals and
few of them get treatment and rest of them have to go without
treatment because of time factor.
Some times we have problems non-availability of essential drugs,
shortage of ambulances, shortage of beds etc. These problems can be
conveniently solved by the application of operations research
techniques.

contd...
(v) In Planning For Economic Growth
In India we have five year planning for steady economic growth. Every
state government has to prepare plans for balanced growth of the
state. Various secretaries belonging to different departments has to
co-ordinate and plan for steady economic growth.
For this all departments can use Operations research techniques for
planning purpose. The question like how many engineers, doctors,
software people etc. are required in future and what should be their
quality to face the then problems etc. can be easily solved.
(vi) In Industry
Production Management
Marketing Management
Financial Management
Purchase Department
Manufacturing Department
Research and Development Department
Accounting Department

Characteristics of Operations Research:
The various definitions of operations research bring out the essential
characteristics of operations research. They are
Interdisciplinary Team Approach
Systems Approach
Improvement in the Quality of Decisions
Scientific Approach
Use of Computer
Quantitative Solution
Human Factors

contd...
(i) Interdisciplinary Team Approach
The problems an operations research analyst face is heterogeneous in
nature, involving the number of variables and constraints, which are
beyond the analytical ability of one person. Hence people from various
disciplines are required to understand the operations research problem,
who applies their special knowledge acquired through experience to get
a better view of cause and effects of the events in the problem and
to get a better solution to the problem on hand. This type of team
approach will reduce the risk of making wrong decisions.
OR is interdisciplinary in nature and needs a team approach solving eco-
nomic, physical, psychological, biological, sociological and engineering
aspects of any problem by the assistance of mathematicians statisti-
cians, engineers, economists, management and computer experts, this
team for a given problem tries to analyse the cause and effect relation-
ship between various parameters and evaluates the outcome of various
alternative strategies.

contd...
(ii) Systems Approach
The essence of systems approach is to find all significant and indirect
effects on all parts of a system and to evaluate each action in terms of
the effects for the system as a whole. e.g., a new strategy of marketing
department can affect all the other departments of the organisation
and so in evaluating the strategy, not only its effects on the marketing
department should be considered but also the effects of the proposal
on other departments as well.
A business or a Government organization or a defence organization may
be considered as a system having various sub-systems. The decision
made by any sub-system will have its effect on other sub-systems. When
dealing with Operations Research problems, one has to consider the
entire system, and characteristics or sub- systems, the inter-relationship
between sub-systems and then analyse the problem, search for a suitable
model and get the solution for the problem. Hence we say Operations
Research is a Systems Approach.

contd...
(iii) Improvement in the Quality of Decisions
OR is a powerful tool in increasing the effectiveness of managerial de-
cision. OR techniques help the decision maker to improve his creative
and judicious capabilities, analyse and understand the problem situa-
tion leading to better control, co-ordination, and system finally better
decisions.
Operations Research provides manager mathematical tools, techniques
and various models to analyse the problem on hand and to evaluate the
outcomes of various alternatives and make an optimal choice. This will
definitely help him in making better and quick decisions. A manager,
without the knowledge of these techniques has to make decisions by
thumb rules or by guess work, which may click some times and many
a time put him in trouble. Hence, a manager who uses Operations
Research techniques will have a better creative ability than a manager
who does not use the techniques.

contd...
(iv) Scientific Approach
OR applies scientific methods, techniques, and tools for the purpose of
analysis and solution for complex problems. In this approach there is no
place for guesswork and the person bias of the decision maker. It is a
formulized process of reasoning and consists of the following steps:
(a) Defining: The problem to be analysed clearly and defining the
conditions for observations.
(b) Observing: Observations are made under different conditions to
determine the behaviour of the system.
(c) Formulating: A hypothesis describing how the various factors
involved are believed to interact and the best solution to the problem
is formulated on the basis of above observations.
(d)Testing: Finally the result of experiment is design and executed,
observations are made and measurements are recorded.
(e) Analysing: Finally the result of experiment are analysis and check
weather hypothesis is accepted or not. Of the hypothesis is accepted
it means the solution obtained is optimum.

contd...
(v) Use of Computer
Use of computer has become an integral part of the operations research
approach to decision making. The computer may be required due to the
complexity of the model, volume of data required or the computations to
be made.
(vi) Quantitative Solution
Operation research assists the management with a quantitative basis for
decision making. OR attempts to provide a systematic and scientific rational
approach for quantitative solutions to the various managerial problems.
(viI) Human Factors
In deriving, Quantitative Solutions we do not consider human factors, which
doubtlessly play a great role in the problems. So, study of OR is incomplete
without study of human factors.

Limitations of Operations Research:
Operation Research has certain limitations. However, these limitations are
mostly related to the problems of model building and the time and money
factors involved in its application rather than its practical utility.
OR tries to find out optimal solution taking into account all the fac-
tors. These factors are enormous and expressing them in quantity and
establishing relationships among these require complicate calculations
which can only be handled by machines (computers).
Implementation of any decision is a delicate task. It must take into
account the complexities of human relations and behaviour.
OR being specialist’s job requires a mathematician or statistician, who
might not be aware of the business problems. Similarly, a manager fails
to understand the complex working of OR. Thus there is a gap between
the two.
When basic data are subjected to frequent changes, incorporating them
into the OR models is a costly and the computational time increases.
Mathematical model are applicable to only specific categories of
problems.

Tools/Techniques of Operations Research
Linear Programming
Queuing Theory
Inventory Control
Network Techniques of PERT and CPM
Sequencing
Transportation Problems
Assignment Problems
Decision Theory and Games Theory
Replacement Problems

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