egészértékprogramozás

Integer programming, or egészértékprogramozás in Hungarian, is a subfield of mathematical optimization that deals with linear programming problems where all variables are constrained to be integers. In a standard linear programming problem, variables can take on any real value. However, many real-world problems require integer solutions. For example, one cannot produce a fraction of a car or hire a fraction of an employee. Integer programming provides a framework to model and solve such problems.

The general form of an integer programming problem involves minimizing or maximizing a linear objective function subject to a set of linear constraints, with the additional condition that all decision variables must be integers. If all variables are required to be integers, it's called a pure integer programming problem. If some variables are allowed to be continuous and others must be integers, it's a mixed integer programming problem. Problems where variables can only take values of 0 or 1 are known as binary integer programming problems, which are a special case of pure integer programming and are widely used for decision-making problems like selection or assignment.

Solving integer programming problems is generally more computationally challenging than solving linear programming problems. While linear programs can often be solved efficiently using algorithms like the simplex method, integer programming problems are NP-hard. Common solution techniques include branch and bound, cutting plane methods, and heuristics. These methods systematically explore the solution space, often by solving a series of related linear programming relaxations, to find an optimal integer solution. Integer programming has found applications in diverse fields such as operations research, logistics, finance, scheduling, and resource allocation.