lineaaroptimeerimine

Lineaaroptimeerimine, often translated as linear programming, is a mathematical method used to determine the best possible outcome in a given situation, with a given objective function, subject to a set of linear constraints. These constraints represent limitations or requirements that must be satisfied. The objective function, also linear, is what needs to be maximized or minimized.

The core idea behind linear programming is to find the optimal values for a set of decision variables. These variables represent quantities that can be controlled or chosen. For example, in a production planning problem, decision variables might represent the number of units of different products to manufacture. The constraints could be limitations on available raw materials, labor hours, or machine capacity. The objective function might be to maximize profit or minimize cost.

Linear programming problems can be solved using various algorithms, with the simplex method being one of the most well-known. The geometric interpretation involves visualizing the feasible region defined by the constraints, which is a convex polyhedron. The optimal solution is found at one of the vertices of this feasible region.

Applications of linear programming are widespread across various fields, including economics, operations research, engineering, and computer science. It is used for resource allocation, production scheduling, transportation logistics, financial portfolio optimization, and many other decision-making processes where resources are limited and objectives need to be met efficiently.