Introducció a la programació lineal: mètode sı́mplex i el problema del transport

Abstract

[en] The following article presents the necessary knowledge to understand and solve linear programming problems. Linear programming was born in 1947, when G.B. Dantzig suggested the simplex method in order to solve planification problems of the United States Air Forces. In this article it is explained how this method works and a series of examples are solved by using a program which has the method’s algorithm implemented. To do this, the definitions and basic concepts of linear programming are explained to understand the linear programming problems from an algebraic point of view. There are also explanations of the necessary concepts and definitions of convex analysis to understand this type of problems from a geometric point of view. On the other hand, the concept of duality and the relation between primal linear programming problems and dual linear programming problems are explained. Finally, this article presents the transportation problem, a linear programming practical case, and the algorithm in order to solve it. This algorithm has been implemented in a program and has been used to solve an example shown in this article.