Análise de Tópicos Relevantes em Programação Linear e Aplicações no Ensino de Engenharia - Dornellas, Carlos Antonio [UNESP] (2014)
This research presents a theoretical analysis of some relevant topics related to linear programming via simplex method. The motivation of analyzing these topics makes them more didactic and easy to understand. As these kinds of methodologies are fast and unequivocal, they are applicable in various real-world engineering problems particularly in the field of power system optimization. In linear programming (LP), the simplex method has been the main technique to optimize the linear problem as well as the linearized problem (a problem with the nonlinear nature). The simplex method solves a linear programming problem using a conceptually refined strategy. In order to understand all of the available versions of the simplex method that can be used to find the solution of a linear programming problem and in order to have a detail study on them, it is necessary to understand: the optimality of such problems, where a linear programming problem is limited, the logic of optimization of the primal simplex method, in which condition a simplex method needs artificial variables, the revised primal simplex method, the duality theory in linear programming, the logic of optimization of the dual simplex methodology, the theory of sensitivity analysis and post-optimization in linear programming, and the logic of the primal or dual simplex for the boundary variables. The output of this research is to prepare a didactic reference and a user manual to help the beginner researchers in operations research. Therefore, a theoretical analysis and reformulation of some relevant topics related to the simplex method for solving LP problems is presented