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 a particular 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 mass of a structure, plant capacity, output, transportation costs, and others.
The objective function allows you to answer several questions:
- profitable or not, this or that event;
- whether the movement is in the right direction;
- how correctly the choice is made, etc.
If we do not have the ability to influence the parameters of the function, then we can say that we can’t do anything, except to analyze everything. But in order to be able to change something, usually there are mutable function parameters. The main task is to change the values to those at which the function becomes optimal.
Target functions may not always be presented in the form of a formula. It could be a table, for example. Also, the condition may be in the form of several objective functions. For example, if you want to ensure maximum reliability, minimum cost and minimum material consumption.
Optimization problems should have the most important initial condition - the objective function. If we did 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, and even more favorable conditions.
Optimization tasks are conditional and unconditional. The first type involves restrictions, that is, certain conditions in the formulation of the problem. The second type is to find the maximum or minimum of the function with the existing parameters. Often, such tasks involve finding a minimum.
In the classical understanding of optimization, such parameter values are selected at which the objective function satisfies the desired results. It can also be described as the process of selecting the best option from the possible. For example, choose the best resource allocation, design option, etc.
There is such a thing as incomplete optimization. It can form for several reasons. For instance:
- the number of systems that hit the maximum point is limited (a monopoly or oligopoly has already been established);
- there is no monopoly, but there are no resources (lack of qualifications in any competition);
- the absence of the maximum point itself, or rather “ignorance” of it (a man dreams of a beautiful woman, but it is not known whether this exists in nature), etc.
In the conditions of market relations in the management of sales and production activities of firms and enterprises, the basis for decision-making is information about the market, and the validity of this decision is checked upon 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 consumer needs, as well as the relationship between them.
