# MODELS OF OPERATIONS RESEARCH – Notes for B.com/ BBA students

## MODELS OF OPERATIONS RESEARCH

Most operations research studies involve the construction of a mathematical model. The models of Operations research is a collection of logical and mathematical relationships that represents aspects of the situation under study. Models describe important relationships between variables; include an objective function with which alternative solutions are evaluated, and constraints that restrict solutions to feasible values.

A model is always an abstraction that is of necessarily simpler than the real situation. Elements that are irrelevant or unimportant to the problem are to be ignored; hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem.

Models must be both tractable, capable of being solved, and valid, representative of the original situation. These dual goals are often contradictory and are not always attainable. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model.

## VARIOUS MODELS OF OPERATIONS RESEARCH

The following are the various models of Operations Research:

1.ANALYTICAL MODELS

An analytical model is quantitative in nature, and used to answer a specific question or make a specific design decision. Different analytical models are used to address different aspects of the system, such as its performance, reliability, or mass properties.

Analytical models must be expressed with sufficient precision that they can be formally analyzed, which is typically by a computer.

Analytical models can be further classified as:

• Static Analytical Model
• Dynamic Analytical Model

static model represents the properties of a system that are independent of time, or true for any point in time. The properties being analyzed may have deterministic values, or may include probability distributions on their values.

dynamic model is an analytical model that represents the time-varying state of the system, such as its acceleration, velocity, and position as a function of time.

The selection of a dynamic model versus a static model depends on the type of question that is being answered.

2. SIMULATION MODELS

Simulation models aim to replicate the workings and logic of a real system by using statistical descriptions of the activities involved.

A simulation model has ‘entities’ (e.g. machines, materials, people, etc.) and ‘activities’ (e.g. processing, transporting, etc.). It also has a description of the logic governing each activity. For example, a processing activity can only start when a certain quantity of working material is available, a person to run the machine and an empty conveyor to take away the product. Once an activity has started, a time to completion is calculated, often using a sample from a statistical distribution.

The model is started and continues to run over time, obeying the logical rules that have been set up. Results are then extracted concerning delays, etc.

It is clear that simulation models can replicate a complex production system. They can be used to indicate the level of shared resources needed by the operation (e.g. forklift trucks or operators), the speed of lines, sizes of vessels or storage tanks, etc.

3. ANALOG MODELS

Analog models represent the physiological process using elements that are, to some degree, analogous to those in the actual process. Good analog models can represent the system at a lower level, and in greater detail, than systems models, but not all analog models offer such detail. Analog models provide better representation of secondary features such as energy use, which is usually similar between analog elements and the actual components they represent.

4. SYMBOLIC MODELS

Symbolic Models also known as Mathematical 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 behavior 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 features of symbolic models are as follows:

• It contains a set of representations (or symbols) of something.
• It processes and manipulates those representations based on a set of rules programmed into the model.
• The rules operate on the representations according to their ‘shape’ or syntax, not according to what they represent (their semantics).

5. ICONIC MODELS

Iconic model is also known as 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. Commonly an iconic model represents a static event.