Models of Operations Research is addressed

MODELS IN OPERATIONS
RESEARCH
SUNDAR B. N.

MODELS IN OPERATIONS RESEARCH
A model in Operations Research is a mathematical or
theoretical description of the various variables of a
system representing the basic aspects or the most
important features of a typical problem under
investigation. The objective of the model is to
identify the significant factors and
interrelationships.
It helps in deciding how the changes in one or more
variables of a model may affect other variables or
the system as a whole.

Classification of Models
The classification of models is a subjective problem.
They may be distinguished as follows:
1. Models by Degree of abstraction
2. Models by Function/ Purpose
3. Models by Structure
4. Models by Nature of an environment
5. Models by the Extent of generality
6. Models by Behaviour
7. Models by Method
8. Models by the Use of Digital Computers

1. Models by degree of abstraction
With then aforesaid liberty in the definition of a model
(i.e. it may or may not be a physical construct)
whatever we sneak or write or read is after all a
model. Surely when we speak or write we describe
some event or whatever which though we cannot do
perfectly well because of our mastery of the language
and the limitations too.
For example in the case of a cricket match commentary
the commentator who is modelling the palsy for his
audience is usually under time limitations. All such
models are language models.

2. Models by Function/ Purpose
Models can also be classified by purpose of its utility. The
purpose of a model may be descriptive, predictive or
prescriptive.
A. Descriptive models: A descriptive model simply describes
some aspects of a situation based on observations, survey.
Questionnaire results or other available data. The result of
an opinion poll represents a descriptive model.
B. Predictive models: Such models can answer ‘what if’ type of
questions, i.e. they can make predictions regarding certain
events. For example, based on the survey results, television
networks such models attempt to explain and predict the
election results before all the votes are actually counted.
C. Prescriptive models: Finally, when a predictive model has
been repeatedly successful, it can be used to prescribe a
source of action. For example, linear programming is a
prescriptive (or normative) model because it prescribes
what the managers ought to do.

3. Models by structure
These models are represented by
A. Iconic or physical models: They are pictorial representations of real
systems and have the appearance of the real thing. An iconic model
is said to be scaled down or scaled up according to the dimensions of
the model which may be smaller or greater than that of the real item,
e.g., city maps, houses blueprints, globe, and so on. These models
are easy to observe and describe, but are difficult to manipulate and
are not very useful for the purpose of prediction.
B. Analogue models: These are more abstract than the iconic ones for
there is no look alike correspondence between these models and real
life items. The models in which one set of properties is used to
represent another set of properties are called analogue models. After
the problem is solved, the solution is reinterpreted in terms of the
original system. These models are less specific, less concrete, but
easier to manipulate than iconic models.

3. Models by structure
C. Mathematic / Symbolic models: They are most abstract
in nature. They employ a set of mathematical symbols to
represent the components of the real system. These
variables are related together by means of mathematical
equations to describe the behaviour of the system. The
solution of the problem is then obtained by applying well
developed mathematical techniques to the model.
The symbolic model is usually the easiest to manipulate
experimentally and it is the most general and abstract. Its
function is more explanatory than descriptive.

4. Models by nature of an environment
These models can be further classified into
A. Deterministic models: They are those in which all
parameters and functional relationships are assumed to
be known with certainty when the decision is to be made.
Linear programming and break-even models are the
examples of deterministic models.
B. Probabilistic / Stochastic models: These models are those
in which at least one parameter or decision variable is a
random variable. These models reflect to some extent the
complexity of the real world and the uncertainty
surrounding it.

5. Models by the extent of
generality
These models can be further categorized into
(a) Specific models: When a model presents a system at
some specific time, it is known as a specific model. In
these models, if the time factor is not considered, they are
termed as static models.
An inventory problem of determining economic order
quantity for the next period assuming that the demand in
planning period would remain same as that of today is an
example of static model.
b) General models: Simulation and Heuristic models fall
under the category of general models. These models are
used to explore alternative strategies which have been
overlooked previously.

6. Models by Behaviour
A. Static models: These models do not consider the
impact of changes that takes place during the
planning horizon, i.e. they are independent of
time. Also, in a static model only one decision is
needed for the duration of a given time period.
B. Dynamic models: In these models, time is
considered as one of the important variables and
admits the impact of changes generated by time.
Also, in dynamic models, not only one but a series
of interdependent’ decisions is required during
the planning horizon.

7. Models by Method of Solution
A. Analytical models: These models have a specific mathematical
structure-and thus can be solved by known analytical or
mathematical techniques. For example, a general linear
programming model as well as the specially structured
transportation and assignment models are analytical models.
B. Simulation models: They also have a mathematical structure but
they cannot be solved by purely using the ‘tools’ and ‘techniques’ of
mathematics. A simulation model is essentially computer-assisted
experimentation on a mathematical structure of a real time
structure in order to study the system under a variety of
assumptions. Simulation modelling has the advantage of being more
flexible than mathematical modelling and hence can be used to
represent complex systems which otherwise cannot be formulated
mathematically. On the other hand, simulation has the disadvantage
of not providing general solutions like those obtained from
successful mathematical models.

8. Models by Use of Digital Computers
The development of the digital computer has led to the
introduction of the following types of modelling in OR.
A. Analogue and Mathematical models combined: Sometimes
analogue models are also expressed in terms of
mathematical symbols. Such models may belong to both the
types (ii) and (iii) in classification 1 above. For example,
Simulation model is of analogue type but mathematical
formulae are also used in it. Managers very frequently use
this model to ‘simulate’ their decisions by summarizing the
activities of industry in a scale-down period.
B) Heuristic models: These models are mainly used to explore
alternative strategies (courses of action) that were
overlooked previously, whereas mathematical models are
used to represent systems possessing well defined
strategies. Heuristic models do not claim to find the best
solution to the problem.

8. Models by Use of Digital Computers
C) Function models: Such models are grouped on the basis of the
function being performed. For example, a function may
serve to acquaint to scientist with such things as tables,
carrying data, a blue-print of layouts, a program representing
a sequence of operations (like’ in computer programming).
(Hi) Quantitative models. Such models are used to measure the
observations. For example, degree of temperature, yardstick,
a unit of measurement of length value, etc. Other examples
of quantitative models are:
Transformation models which are useful in converting a
measurement of one scale to another. (e.g., Centigrade vs.
Fahrenheit conversion scale), and
The test models that act as ‘standards’ against which
measurements are compared (e.g., business dealings, a
specified standard production control, the quality of a
medicine).

MODELS IN OPERATIONS RESEARCH
A model in Operations Research is a mathematical or
theoretical description of the various variables of a
system representing the basic aspects or the most
important features of a typical problem under
investigation. The objective of the model is to identify the
significant factors and interrelationships.
It helps in deciding how the changes in one or more
variables of a model may affect other variables or the
system as a whole. Operations Research models are
broadly classified as follows:
i) Mathematical and descriptive models, and
ii) Static and dynamic models

Mathematical and descriptive models
In mathematical models, various variables/parameters explaining
different operations of a system are expressed in
mathematical terms and the relations are explained by means
of mathematical equations or inequalities. The variables can
be exact (deterministic) or probabilistic. In deterministic
models, the variables and their relationships are stated
exactly. The probabilistic models are developed for problems
involving risk and uncertainty. Therefore, in these models,
decision variables take the form of probability distributions. For
example, the variables in linear programming, transportation
and assignment problems.
The models in which various operations are explained in non-
mathematical language are called descriptive models and serve
as preliminary models for the development of mathematical
models.

Static and dynamic models
A probabilistic mathematical model is called static or
dynamic according as the distribution of parameters
remains unchanged or changes with time. An inventory
model is a static model wherein the re-ordering of goods
is determined using average demand and average time
and not on the basis of changes that take place in any
particular period. However, an inventory model in which
the re-order point is determined by a certain stock level
at any point of time is dynamic.
Operations Research models are mainly of three kinds:
Iconic, Symbolic and Analogue. Let us understand briefly
them as under:

Iconic models
Iconic models are physical replicas of real life systems and
are based on a smaller scale than the original. In many
cases, they provide a pictorial presentation of various
aspects of a system. Such models are designed for the
purpose of understanding the behaviour of the operation
of the system when conducting experiments on the real
life systems is risky and/or costly affair.
Flight simulators, missile firing simulators are examples of
iconic models. Photographs, paintings, maps, drawings,
clay, wooden or metallic models of systems are also iconic
models.
For example, a toy car can be considered as an iconic model
of an automobile. Similarly, a blueprint representing the
floor of a building is an iconic model, and the globe is an
iconic model of earth.

Symbolic models
Symbolic models reflect the structure of a system,
denoting various components of a system and their
interrelationships employing letters, numbers and
various other types of mathematical symbols.
For example, the buyers' behaviour at varying price level
can be represented symbolically by the demand curve in
Economics.
A model for processing inventory cost in inventory
problems is another example of symbolic model. Such
models are very well suited for determination of various
changes in the system.

Analogue models
Analogue models are helpful in representing all the significant properties of a
system which are not represented by iconic or symbolic models. They are
also physical, but not the exact replica of the system. They are used to
explain the system by analogy.
For example, the geological structure of earth cannot be represented by the
globe, an iconic model of earth, if different colours are not used. If different
colours are taken on the globe to represent the geological structure of the
earth, it is known as Analogue model.
There is no unique method for solving all mathematical
models. The nature of the method of solution depends on the type and
complexity of the mathematical model. In Operations Research, the
solutions are generally determined by algorithms which provide fixed
computational rules. These rules are applied repetitively/iteratively to the
problem, with each repetition/ iteration moving the solution closer to the
optimum. The three main methods for the solution of a mathematical
model are:

The three main methods for the solution
of a mathematical model are:
I. Analytic or deductive methods,
II. Numerical or inductive methods, and
III. Monte Carlo techniques or simulations.

Analytic methods involve graphs and elementary differential calculus.
In numerical methods, numerical values are substituted for various variables
involved in the model by trial and error. Then the set of values, which
maximises the effectiveness of the system is taken as the required
solution.
Monte Carlo techniques are applied on systems, which are not represented
adequately by theoretical models. In these techniques, the knowledge of
the important characteristics and rules along with random sampling is used
to determine the probability distributions of various components of the
model.
Some mathematical models may be so complex that it is impossible to solve
them by any of the available optimisation algorithms. In such cases, it may
be necessary to abandon the search for the optimal solution and simply
seek a better solution using heuristics.
Heuristic models use intuitive rules or guidelines to find the solution to any
problem. These models do not guarantee an optimum solution and give
solutions depending on the assumptions based on past experience.
These models, however, operate faster and are very useful for solving large
size problems. However, they require a good amount of creativity and
experience on the part of decision makers.

Characteristics of a Good Model
A model doesn't always have the characteristic of
being yardstick it can be explanatory.
 It should be capable of taking into account, new
formulation without having any changes in its
frame.
Assumptions made in the model should be as small
as possible.
Variables used in the model must be less in number
ensuring that it is simple and coherent.
It should not take much time in its construction for
any problem.

Advantages of a Model
1. Problems under consideration become controllable.
2. It provides a logical and systematic approach to the
problem.
3. It provides the limitations and scope of an activity.
4. It helps in finding useful tools that eliminate duplication
of methods applied to solve problems.
5. It helps in finding solutions for research and
improvements in a system.
6. It provides an economic description and explanation of
either the operation, or the systems it represents.

METHODOLOGIES/APPROACHES OF
OPERATIONAL RESEARCH
Formula
te the
Problem
Observ
e the
System
Formulat
e a
Mathema
tical
Model of
the
Problem
Verify the
Model and
Use the
Model for
Prediction
Select a
Suitable
Alternative
Present the
Results and
Conclusion
s of the
Study
Implement
and
Evaluate
Recommen
dation

Models of Operations Research is addressed

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