Classifications of Operation Research Models.
The various classification schemes of operation Research models are discussed below:
1. Classification 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 canot 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. Business case studies are such models in our4 context
Language models are far more abstract than the concrete model like a globe of the earth or the model planes mounted in wind tunnels since they (the concrete models) are at once suggestive of the shape or properties or characteristics sought after or the modeled entity. However even more abstract than the language models are the mathematical models (viz., the break even equation or linear programming formulation of the product mix problem). Because to get the idea of the real life situation they represent requires mathematical training and on the top of that considerable concentration.
2. Classification according to Structure.
(a) Iconic (physical) Model. Iconic model is a physical representation of some item either in an idealized form or on a different scale i.e. a representation is an iconic model to the extent that its properties are the same as possessed by what it represents. A photograph, cyclograph, a blueprint and a painting are iconic models of persons or objects. The toy aero plane is an iconic model of a real aero plane, A globe is an iconic model of the earth, an iconic model is said to be scaled down when the dimensions of the model are smaller than those of the real object for example a globe representing the earth or a blueprint representing a floor of a building. The model is said to be scaled up when it is bigger than the real item in biology, the structure of a cell may be depicted by an enlarged model for teaching purposes and similarly an atom in physics.
Commonly an iconic model represents a static event. Characteristics that are not considered in the analysis for which the model is constructed are not included in the model. For example, in the use of a model in the study of the structure of an atom the colour of the model is irrelevant because this particular fact does not afford any scientific study of the atom. Models of automobiles used in the study of a parking problem need is its dimensions i.e., tow dimensions (photo blueprints maps) or three dimensions (small airplane globe atom). When a model surpasses the third dimension it is no longer possible to construct it physically.
(b) Analogue (schematic) Model. It represents a system or an object of the inquiry by utilizing a set of properties different from what the original system possesses. After the model is solved the solution is re-interpreted in terms of the original system. For example an analogue computer is the physical representation of the variables in a problem. Also graphs are very simple analogues. They represent properties like force, speed, age, time, etc.., in terms of distance. A graph is well suited for representing quantitative relationship between any two properties and predicts how a change in one property effects the other.
An organizational chart is a common analogue model. It represents the relationships existing between the various members of the organization. A man machine chart is also schematic model. It represents a time varying interaction of men and machines ovier a complete work cycle. A flow process chart is another schematic model which irepresents the other of occurrence of various events to make a product. Contour lines on a map are analogue of the flow of electricity through wires. Similarly demand curves and frequency distribution curves used in statistics are example of analogue models.
Simiarly a map is an analogue model which shows roads highways towns and their inter-relationship. Hence an analogue model represents one set of properties by another set of properties. Analogue models can represent dynamic situation and they are customarily used more than iconic models because of their vast capacity to depict the characteristics of the event under consideration.
(c ) symbolic Models (syn, Mahemaical Models) are those which employ a set of symbols (i.e. letters numbers etc.) and functions to represent the decision variables and their relationships to describe the behaviour or the system the symbols used generally mathematical or logical in character. They are by far the most widely employed in an O.R. study because of the great deal of complexity associated with an organization. A symbolic or mathematical model consists of a set of equations which define and specify the relationship and interactions among various elements of decision problem under study. The solution of the problem is then obtained by applying well-developed mathematical techniques to the model.
The advantages of mathematical models over other types of models may be summarized as under.
- Are precise abstract and general rather than restricted
- Transformation of a model from a verbal to a mathematical from makes far greater clarification of existing and likely relationships and interactions among variables.
- Promote greater case of communication because mathematical terminology is standardized unlike that of social sciences.
- Being logical are more objective while verbal constructs lean heavily on intuition.
- Analysis that is not feasible through verbal models may be advanced by mathematical models since they tend themselves to analysis and manipulation by utilizing the laws of mathematical
Remark. The nature and structure of mathematical models A mathematical model includes principally there basic set of elements these are:
(i) Decision variables and parameters. These decision variables are the unknowns (for decision) which are to determined by solving the model. The parameters are the known values that relate the decision variables to the constraints and objective function. The parameters of the model may either be or probabilistic (stochastic)
(ii) Constraints. To account for the technological economic and other limitations of the system the model include constraints (implicit or explicit) that restrict the decision variables to a range of feasible values.
(iii) Objective function. The objective function defines the measure of effectiveness of the system as a mathematical function of the decision variables. An optimal solution to the model is obtained when the values of the decision variables yield a best value of the objective function of subject to the constraints. A poor or inappropriate formulation of the objective function can only lead to a poor solution to the problem a common example of this occurs when some aspects of the system are neglected. For example in determining the optimal production level of a certain product the objective function may reflect only the goals of the production department while neglecting the goals of marketing and finance in such cases. The model yields as suboptimal solution which may not serve the best interest of the entire organization.
3. Classification by purpose. Models can be classified by purpose. The purpose of a model may be to describe predict or prescribe.
(a) Descriptive models. A descriptive model simply describes some aspects of a situation based on observation survey questionnaire results or other available data the result of an opinion poll represents a descriptive model. Descriptive models describe, and predict facts and relationships among the variables of the problem. These are used to observe and study the performance of a complex system with a view to understanding it better. No optimal solutions are attempted only the system parameters are depicted in the form of equations. In a descriptive model. It is possible to get information as to how one or more factors change as a result of changes in other factors. They are useful for explanatory and predictive purposes.
(b) Normative or prescriptive models develop objective decision rules or criteria for optimal solutions. Some problems lend themselves to prescriptive format. These are well-structured problems and could be dealt with as if their solution does not have noticeable reactions on the other components or problems of the system of which they are a part. Normative models are applicable to repetitive problems. The solution process of which could be programmed with little managerial involvement. Linear programming is a normative or prescriptive model, because it prescribes what the managers outght to do.
4. Classification by Nature of the Environment.
(a) Deterministic Models. In deterministic models, parameters are completely defined and the outcomes related to particular course of action are certain. Certainty is the state of nature assumed in deterministic models. In other words, deterministic models represent completely closed systems and the results of the models assume single values only. For any given set of input variables the same output variables always result. Linear programming and Break-even models are examples of deterministic models.
(b) Probabilities Models. These models handle those situations in which the consequence or payoff of managerial actions cannot be predicted with certainty. These models are the products of are environment of risk and uncertainty. The input and or the output variables take the form of probability distributions and assume more than single values. The advantage of a probabilistic model is that it offers an evaluation of the likelihood of any event or result. In other words probabilistic models reflect to some extent the complexity of the real world and the uncertainty surrounding it. They are probably semi closed models.
5. Classification according to behavior characteristics.
(a) Static Models. These models do not consider the impact of changes that takes place durying the planning horizon i.e. they are independent of time. Also in static model only one decision is needed for the duration of a given time period. In a static model, cause and effect are almost immediate and no time lag is allowed. Alternatively the effects of time are considered linear and as such do not affect the model output basically. Static models are easier to handle and understand.
(b) Dynamic models. These models consider time as one of the important variables and admit the impact of change generated by time. Also in dynamic models, not one, but a series of interdependent decision, is required during the planning horizon. The time dimensions has a definite impact on the model so solution, and on the interpretation of the results.
6. Classification according to procedure of solution.
(a) Analytical models. These models have specified mathematical structure and they can be solved by known analytical or mathematical techniques. For example, the general linear programming model as well as the special structured transportation and assignments models is analytical models.
(b) Simulation and heuristic Models. The development of the ditital computer has led to the introduction of two other of modelling in O.R. these are (i). Simulation and (ii). Heuristic models. Simulation modelling has the advantage of being more flexible than mathematical modelling and hence may be used to represent complex systems which otherwise cannot be formulated mathematically. On the other hand simulation has the disadvantage of not yielding general solutions like those obtained from successful mathematical models.
Heuristic models are essentially models that employ some intuitive rules or guidelines in the hope of generating new strategies which will yield improved solutions. This is in contrast to mathematical and simulation models where the strategies are generally well-defined. Heuristic models do not claim to find the optimum solution to the problem and gives a solution to a problem depending on the assumption based on past experience. The advantage of such models is that they operate faster as compared to other models and are very useful for solving large size problems. These models however require an ample amount of creativity and experience on the part of decision maker.
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