The linear programming, refers to an algorithm that through it can solve various real situations in which you want to identify and solve certain difficulties that help to increase the production of resources that contain some limitations and thus increase the Benefits.
It is intended to maximize or minimize linear functions of different real variables that contain restrictions within the system of linear inequalities, optimizing its functionality. The optimization process and the results are transformed into a quantitative backup of the decisions when faced with the situations.
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In this article you will find:
Objective of linear programming
This programming is a set of analysis and problem solving techniques that has the purpose of facilitating assists decision-makers in related decisions in situations where a large number of variables.
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Within the development of operations research in general and a certain programming in particular, there has been a favorable impulse due to computers, as for example there is one of great importance such as the method of simplex.
Among the most important objectives that are within this program are:
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- Acquire knowledge about linear programming as well as its different applications in everyday life.
- Follow certain steps to build a model.
- Make proposals in order to solve various situations in relation to programming.
Solution methods in linear programming
Among the troubleshooting methods are the following:
Graphical method
The level lines provide the points on the plane where the objective function acquires the same value.
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Analytical method
It is about the result that is called fundamental theorem of programming, this allows to have knowledge of another method that solves a program by means of two variables.
Inside a program that contains two variables, if you have a single solution that perfects the function objective, it can be found at an extreme point of the demarcated feasible region and not within the region.
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In case the objective function has the same value at two vertices, it takes the same value at the points of the determined segment.
If the feasible region is not demarcated, the objective function will not be able to reach the concrete value, but if it does, it will be found at one of the vertices of the region.
Practical scheme
Programming problems can be shown in a standard way, facilitating the function, objectives and constraints, or they can simply be posed through a statement.
Types of linear programming solutions
If they contain two variables, they can be classified depending on the type of solution they show. These types can be:
Feasible
It occurs when there is a set of solutions that benefit the restrictions. These can also be:
- With unique solution.
- With multiple solution when more than one solution is presented.
- With unbounded solution in case there is no limiting factor for the objective function.
Not factible
This occurs when the set of solutions that determine the constraints does not exist, which means that these constraints are inconsistent.
How to solve a linear programming problem
The corresponding step to solve a programming problem is to identify the basic elements of a mathematical format, where the following methodologies must be followed:
The objective function
This function is directly related to the general question that you want to answer. If different questions are generated in the model, then the objective function is going to be related to the higher level question, therefore the question is the main one.
If, for example, in a certain situation you want to reduce costs, it is likely that the question The main one has to do with increasing utility rather than a question that seeks to minimize the costs.
Decision variables
The relationship found between specific objectives and the general objective are similar, the decision variables behave with respect to the objective function, because these are identified from various questions that come from the main question.
These variables are factors that can be controlled within the system being modeled, therefore, they can possibly acquire different values, of which it is intended to have knowledge of their optimal value, which favors the monitoring of the objective of the general operation of the trouble.
The restrictions
When talking about the restrictions in a programming problem, it refers to everything that limits the freedom of the values that the decision variables can take. The best way to achieve them is by thinking of a hypothetical case where these variables must be given an infinite value and in this way the necessary questions are likely to arise.
In this way, it will be possible to discover that the system has several limitations in a physical sense and context, such as point that the values that a given moment could take the variables that are in conditions restricted.
Application of linear programming
This application constitutes an important field of optimization for different reasons, there is a great number of practical operations research problems that could be posed as research problems the linear programming.
In some cases of network flow and goods flow problems, they can be considered during their development. mathematician how important they are to generate by themselves diverse investigations related to algorithms in their solution.
Various algorithms created to solve other types of optimization problems include specific cases of the linear programming system. Historically, the ideas of this system have stimulated innumerable optimization concepts such as decomposition, duality, the importance of convexity, in addition to its generalizations.
In the same way, it is widely used in microeconomics and in business administration, in order to maximize income or reduce costs of a certain production system.
