What should be the objective function

The objective function is a function with some variables, on which the achievement of optimality directly depends. It can also act as several variables that characterize an object. We can say that, in fact, it shows how we have progressed in achieving the task.

An example of such functions can be the calculation of the strength and weight of the structure, the capacity of the installation, the volume of output, the cost of transportation, and others.

The objective function allows you to answer several questions:

- whether or not an event is profitable or not;

- Is the movement in the right direction?

- how correctly the choice is made, etc.

If we do not have the ability to influence the parameters of a function, then we can say that we can do nothing, except that we can analyze everything. But in order to be able to change something, there are usually variable parameters of the function. The main task is to change the values to those at which the function will become optimal.

Target functions can not always be represented in the form of a formula. This can be a table, for example. Also the condition can be in the form of several objective functions. For example, if you want to provide maximum reliability, minimum costs and minimum material consumption.

Optimization tasks should have the most important initial condition - the objective function. If we do not define it, then we can assume that optimization does not exist. In other words, if there is no goal, then there are no ways to achieve it, let alone favorable conditions.

Tasks for optimization are conditional and unconditional. The first kind presupposes limitations, that is, certain conditions in the formulation of the problem. The second kind is to find the maximum or minimum of the function with the existing parameters. Often, such problems require a minimum.

In the classical understanding of optimization, such parameter values are selected for which the objective function satisfies the desired results. Also, it can be designated as the process of selecting the best option possible. For example, choose the best allocation of resources, the design variant, etc.

There is such a thing as incomplete optimization. It can be formed for several reasons. For example:

- the number of systems in the maximum point is limited (a monopoly or an oligopoly has already been established);

- there is no monopoly, but there are no resources (lack of qualification in any competition);

- the absence of the very point of maximum, or rather "ignorance" of it (a man dreams of some beautiful woman, but it is not known if such exists in nature), etc.

In the conditions of market relations of management of marketing and production activity of firms and enterprises, the basis for decision-making is information about the market, and the validity of this decision is checked already when entering the market with the corresponding product or service. In this case, the starting point is the study of consumer demand. To find solutions, the target consumption function is established. It shows the amount of consumed goods and the degree of satisfaction of the needs of the consumer, as well as the relationship between them.