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 our goal.
An example of such functions is the calculation of the strength and mass of the structure, the power of the installation, the volume of output, the cost of transportation, and others.
The objective function allows you to answer several questions:
- profitable or not this or that event;
- is the movement going in the right direction;
- how well the choice was made, etc.
If we are not able to influence the parameters of the function, then we can say that we cannot do anything, except to analyze it and that's it. But to be able to change something, there are usually mutable function parameters. The main task is to change the values to those at which the function becomesoptimal.
Objective functions cannot always be represented as a formula. It could be a table, for example. Also, the condition can be in the form of several objective functions. For example, if you want to ensure maximum reliability, minimum costs and minimum material consumption.
Optimization problems should have the most important initial condition - the objective function. If we have not defined 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, much less favorable conditions.
Optimization problems can be conditional and unconditional. The first type involves restrictions, that is, certain conditions when setting a task. The second kind is to find the maximum or minimum of the function given the existing parameters. Often, such problems involve finding a minimum.
In the classical understanding of optimization, such values of parameters are selected for which the objective function satisfies the desired results. It can also be described as the process of selecting the best possible option. 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 example:
- the number of systems that hit the maximum point is limited (a monopoly or oligopoly has already been established);
- no monopoly, but no resources (lack of qualification in any competition);
- the absence of the maximum point itself, or rather “ignorance” of it (a man dreams of some beautiful woman, but it is not known whether such a woman 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 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, an objective consumption function is set. It shows the amount of goods consumed and the degree of satisfaction of consumer needs, as well as the relationship between them.
