Mathematical programming providesimplementation of methods for finding the optimal solution. The solution of such types of problems is connected with the study of functions on extremality. Methods of mathematical programming are quite common in the applied field of cybernetics.
A large number of tasks appearing insociety, are often associated with phenomena that are based on a conscious basis of decisions. It is precisely with the necessary choice of a possible mode of action used in different areas of human life activity that the problems of mathematical programming find their application.
The history of the development of society shows thata limited amount of information has always prevented the right decision, and the optimal solution was mainly based on intuition and experience. In the future, with the increase in the amount of information for decision-making, direct calculations began to be used.
The picture on the modernenterprise, where due to a wide range of products produced there the flow of input information is simply huge. Its processing is possible only with the use of modern electronic technologies. And if you need to choose the optimal solutions from the solutions offered, then you can not do without electronics.
Therefore mathematical programming goes through the following main stages.
The first stage involves ranking all factors in importance and establishing a regularity between them, which they are able to comply with.
The second stage is the construction of a problem model inmathematical expression. In other words, it is an abstraction of reality, represented using mathematical symbols. The mathematical model is able to establish the relationship between the control parameters and the selected phenomenon. This stage should include the construction of such a characteristic, in which each optimal or smaller value corresponds to the optimal situation from the position of the decision being made.
Based on the results of the above steps, a mathematical model that uses certain mathematical knowledge is formed.
The third stage involves a studyvariables that have a significant impact on the objective function. This period should provide for the possession of certain mathematical knowledge that will help in solving problems arising in the second stage of decision-making.
The fourth stage is to compareThe results of the calculations obtained in the third stage with the modeled object. In other words, at this stage, the adequacy of the model with the modeled object is established, within the limits of achieving the necessary accuracy of the initial data. Decision-making at this stage depends on the result of the study. So, when the unsatisfactory results of the comparison are received, the input data about the object being modeled is refined. If there is a need, then the formulation of the task is carried out with the subsequent construction of a new mathematical model, the solution of the stated mathematical problem and a new comparison of the results.
Mathematical programming allows us to use two basic directions of calculations:
- the solution of deterministic problems that assume the certainty of all the initial information;
- stochastic programming that allowssolve problems containing elements of uncertainty or, when the parameters of these problems are of a random nature. For example, production planning is often carried out in conditions of incomplete display of real information.
In general, mathematical programming has in its structure the following sections of programming: linear, nonlinear, convex and quadratic.
