#### Types of Mathematical Models:

Models may be classified as:

(1) Iconic (Sale) Model:

An iconic model is a physical replica of a system usually based on a different scale than the original. These may appear in three dimensions such as airplane, car or bridge model to scale. Photographs are another type of iconic model but in only two dimensions.

(2) Analog Model:

An analog model does not look like the real system but behaves like it. These are usually two dimensional charts or diagrams, e.g., organisation charts, showing structure, authority, and responsibility relationships. Analog models are more abstract than iconic ones.

(3) Mathematical Model:

The complexity of relationships in some systems cannot be represented physically or the physical representation may be cumbersome and take time to construct. Therefore a more abstract model is used with the aid of symbols. Most management science analysis is executed with the aid of mathematical models which utilize mathematical symbols. These are general rather than specific and can describe diverse situations. Furthermore they can be manipulated easily for purposes of experimentation and prediction.

When the concept of a model is extended to the area of mathematics, it is useful to know in a quantitative sense how important or how pertinent the variables are in the model with regard to their impact on the solution. The mathematical models depict explicit relationships and interrelationships among the vari­ables and other factors deemed important in solving problems.

#### The Structure of Mathematical Models:

Mathematical models are typically in the form of equations or other mathematical statements.

For example, the relationship between cost, revenue and profit can be expressed as:

P = R – C …. (i)

where

P symbolizes profit,

R symbolizes revenues, and

C symbolizes cost.

The components of a system, when described by a mathematical model, are expressed in terms of variables (such as C and R above). In general, a distinction is made between independent (cause) and dependent (effect) variables.

#### Characteristics of Mathematical Models:

To be used successfully in a typical Management Science (MS) project, a mathematical model must meet the following criteria:

(i) The model should be as simple and understandable as possible.

(ii) The Model should be reasonable.

(iii) The Model should be easy to maintain and control,

(iv) The model should be adaptive. The parameters and structure of the model should be easy to change as new insights and information evolve.

(v) The model should be complete on important issues, i.e., all important variables and factors should have been taken into consideration.

1. Use of models avoids constructing costly plants and warehouses in locations that do not best meet the present and future needs of the customers.

2. A model indicates gaps that are not immediately apparent, and after testing, the character of the failure might give a clue to the model’s deficiencies.

3. Models have the advantage of time, since results can be obtained within a relatively-short time.

4. Because of the constant squeeze on profits, the cost and time saving that MS models allow make them decision-making tools of great value to the manager.