What is a whole number of linear programming?
Integer linear programming occurs when trying to solve linear systems, and at the same time determine that all unknown variables must be integers or integers. Linear systems are sets of equations that describe the situation for which the programmer is trying to find a solution. They usually consist of one equation that must be maximized or minimized and one or more restrictive equation that limits unknown variables. To make the system linear, any limitation must be a linear equation; This means that they must not contain any cases of unknown variables with exponents greater than one.
Regular linear systems can be easily solved using a computer. The program can identify the solution by finding a derivative and setting it straight zero. It can then verify that the point is maximum or minimum by checking its immediate neighborhood of the function. As long as the derivative is defined at any point along the function, the computer has only a limited number of control solutions.
linear programming becomes integer linear programming with the addition of the entire restriction. This means that the problem remains the same, but the answer must consist of integer values for unknown values: it must be integers. Sometimes it means that the solution will be compared to the case where fractions are allowed, suboptimal; However, it is a reflective real world in which items often come in discrete units. As a result, integer linear programming is important for business applications because companies want to maximize profits as much as possible, but they cannot decide to sell a fraction of the product.
Once integer restrictions are introduced, the problem with the solution of the linear system is NP-comprehensive. This means that the time that is necessary for the computer to solve the system is vague. With the limitation of the whole number, the computer cannot use the derivative tool because there is no warranty that the zero derivative point falls oninteger. The solution will be a whole number with the highest or lowest value of all integers, so the computer would have to check them all - a process that could take an infinite amount of time.
programmers have developed heuristics or problem solving methods to deal with the complexity of these problems. One way to solve the problems with linear programming of the whole program is the algorithm of the branch and binding, in which the computer solves a number of problems related to the original way to narrow the available range of values to one solution. However, it may take a long time for difficult problems.