MATHEMATICAL MODEL

MATHEMATICAL MODEL

A product model is an abstraction of a real system, eliminating the complexities and making relevant assumptions, applies a mathematical technique and obtained a symbolic representation of it.

A mathematical model comprises at least three basic sets of elements:

• Decision variables and parameters

The decision variables are unknowns to be determined from the model solution. The parameters represent the values known to the system or that can be controlled.

• Restrictions

Constraints are relations between decision variables and magnitudes that give meaning to the solution of the problem and delimit values feasible. For example if one of the decision variables representing the number employees of a workshop, it is clear that the value of that variable can not be negative.

• Objective Function

The objective function is a mathematical relationship between variables decision parameters and a magnitude representing the target or product system. For example if the objective is to minimize system costs operation, the objective function should express the relationship between cost and decision variables. The optimal solution is obtained when the value of cost is minimal for a set of feasible values of the variables. Ie there to determine the variables x1, x2, ..., xn that optimize the value of Z = f (x1, x2, ..., xn) subject to constraints of the form g (x1, x2, ..., xn) b. Where x1, x2, ..., Xn are the decision variables Z is the objective function, f is a function mathematics.

HOW TO DEVELOP A MATEMATICAL MODEL

1. Find a real world problem.

2. Formulate a mathematical model of the problem, identifying variables (dependent and independent) and establishing hypotheses simple enough to be treated mathematically.

3. Apply mathematical knowledge that has to reach mathematical conclusions.

4. Compare the data obtained as predictions with real data. If the data are different, the process is restarted.

CLASSIFICATION OF MODELS

• Heuristic Models: (Greek euriskein 'find, invent'). Are those that are based on the explanations of natural causes or mechanisms that give rise to the phenomenon studied.

• Empirical models: (Greek empeirikos on the 'experience'). They are using direct observations or the results of experiments studied phenomenon.

Mathematical models are also different names in various applications. The following are some types to which you can adapt a mathematical model of interest. According to its scope models:

• Conceptual models :Are those that reproduce by mathematical formulas and algorithms more or less complex physical processes that occur in nature.

• Mathematical model of optimization :Mathematical optimization models are widely used in various branches of engineering to solve problems that are by nature indeterminate, ie have more than one possible solution.

CATEGORIES FOR ITS APPLICATION

For use commonly used in the following three areas, however there are many others such as finance, science and so on.

• Simulation: In situations accurately measurable or random, for example linear programming aspects precisely when, and probabilistic or heuristic when it is random.

• Optimization :To determine the exact point to resolve any administrative problems, production, or other status. When the optimization is complete or nonlinear, combination, refers to mathematical models little predictable, but they can fit into any existing alternative and approximate quantification.

• Control: To find out precisely how is something in an organization, research, area of operation, etc..

fuente:

• http://www.investigacion-operaciones.com/Formulacion%20Problemas.htm

• Ríos, Sixto (1995). Modelización. Alianza Universidad.