Operations Research

Introduction:

Management deals with reality that is at once complex, dynamic, and multifaceted. It is neither possible nor desirable, to consider each and every element of reality before deciding the courses of action. It is impossible because of time available to decide the courses of action and the resources, which are limited in nature. More over in many cases, it will be impossible for a manager to conduct experiment in real environment.

Types of Models:

(a) Classification by Structure

Iconic Models:  These models are scaled version of the actual object. For example a toy of a car is an iconic model of a real car.

Analogue Model:In this model one set of properties are used to represent another set of properties. Say for example, blue colour generally represents water.

Symbolic Models or Mathematical Models:In these models the variables of a problem is represented by mathematical symbols, letters etc.

  •         They explain all the features of the actual object.
  •         In fact a globe is an iconic model of the earth.
  •         These models may be of enlarged version or reduced version. Big objects are scaled down (reduced version) and small objects,
  •          when we want to show the features, it is scaled up to a bigger version.
  •         In fact it is a descriptive model giving the description of various aspects of real object.
  •          The advantagesof these models: are It is easy to work with an iconic model in some cases, these are easy to construct and these are useful in describing static or dynamic phenomenon at some definite time.
  •          The limitationsare, we cannot study the changes in the operation of the system.
  •          For some type of systems, the model building is very costly. It will be sometimes very difficult to carry out experimental analysis on these models.
  •          Many a time we represent various aspects on graph by different colors or different lines all these are analog models.
  •         These are also not much used in operations research. The best examples are warehousing problems and layout problems.
  •          To show the relationships between variables and constraints we use mathematical symbols. Hence these are known as
  •          symbolic models or mathematical models.
  •          These models are used very much in operations research. Examples of such models are Resource allocation model, Newspaper boy problem, transportation model etc.

(b) Classification by utility

 Descriptive model:The descriptive model simply explains certain aspects of the problem or situation or a system so that the user can make use for his analysis.

 Predictive model:These models basing on the data collected, can predict the approximate results of the situation under question.

 Prescriptive models:We have seen that predictive models predict the approximate results. But if the predictions of these models are successful, then it can be used conveniently to prescribe the courses of action to be taken. In such case we call it as Prescriptive model.

 (c) Classification by nature of environment

 Deterministic Models:In this model the operations research analyst assumes complete certainty about the values of the variables and the available resources and expects that they do not change during the planning horizon.

Probabilistic or Stochastic Models:In these models, the values of variables, the pay offs of a certain course of action cannot be predicted accurately because of element of probability. It takes into consideration element of risk into consideration.

(d) Classification depending on the behavior of the problem variables

 Static Models:These models assume that no changes in the values of variables given in the problem for the given planning horizon due to any change in the environment or conditions of the system.

Dynamic Models:In these models the values of given variables goes on changing with time or change in environment or change in the conditions of the given system

(e) Classification depending on the method of getting the solution

 Analytical Models:The given model will have a well-defined mathematical structure and can be solved by the application of mathematical techniques.

Simulation Models:The meaning of simulation is imitation. These models have mathematical structure but cannot be solved by using mathematical techniques.

Only disadvantage of this method is that it does not have general solution method.