Models of Operations Research is addressed

Introduction, Meaning and Characteristics of Operations Research is addressed.
MODELS IN OPERATIONS RESEARCH, Classification of Models, degree of abstraction, Purpose Models, Predictive models, Descriptive models, Prescriptive models, Mathematic / Symbolic models, Models by nature of an environment, Models by the extent of generality, Models by Behaviour, Models by Method of Solution, Models by Method of Solution, Static and dynamic models, Iconic models Iconic models, Analogue models.

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1. MODELS IN OPERATIONS RESEARCH SUNDAR B. N.

2. 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.

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

4. 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.

5. 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. 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. 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. 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 .

6. 3. Models by structure These models are represented by 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. 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.

7. 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.

8. 4. Models by nature of an environment These models can be further classified into 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. 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.

9. 5. Models by the extent of generality These models can be further categorized into 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.

10. 6. Models by Behaviour 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. 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.

11. 7. Models by Method of Solution 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. 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.

12. 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. 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.

13. 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).

14. 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

15. 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 .

16. 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:

17. 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.

18. 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.

19. 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:

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

21. 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.

22. 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.

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

24. METHODOLOGIES/APPROACHES OF OPERATIONAL RESEARCH