Simplex method of solving linear programming

Since its publication, the simplex method (and its variants) was the main tool for solving linear problems until 1980 when Kha-chiyan proposed an ellipsoidal algorithm (Khachiyan, 1982).

LP has been widely studied in engineering programmes, management, mathematics and other fields due to its applicability. However, LP as an area of study has been attributed to George Dantzig who also developed the simplex method in 1947 (Cottle, 2006). Linear programming (LP) dates from 1939 when Leonid Kan-tarovich first expressed a problem in economics in linear form (Bazaraa et al., 1998). Received: June 21th 2011 Accepted: May 20th 2012 Palabras clave: programaciГіn lineal, optimizaciГіn, proyecciones ortogonales, ecuaciones paramГ©tricas. Este trabajo tiene como propГіsito principal presentar la propuesta de un nuevo procedimiento para la soluciГіn de problemas PL que, partiendo de un punto interior, realiza proyecciones ortogonales mediante rectas paramГ©tricas y se mueve iterativamente entre el interior y la frontera del poliedro que define la regiГіn factible hasta llegar al punto extremo Гіptimo. Se han desarrollado y se siguen proponiendo varios mГ©todos para la resoluciГіn de problemas de este tipo, desde el famoso simplex hasta los algoritmos de punto interior. La programaciГіn lineal (PL) es una de las herramientas de mayor aplicaciГіn en la investigaciГіn de operaciones. Keywords: linear programming, optimisation, orthogonal projection, parametric equation. The proposed algorithm starts from an interior point and then carries out orthogonal projections using parametric straight lines to move between the interior and polyhedron frontier defining the feasible region until reaching the extreme optimal point. This study was aimed at introducing a new method for solving LP problems. Many methods have been developed and several others are being proposed for solving LP problems, including the famous simplex method and interior point algorithms. E-mail: programming (LP) is one of the most widely-applied techniques in operations research. in Mathematics, MoscГє State University Lomonosov.

PhD in Mathematics, MoscГє State University Lomonosov. Affiliation: Universidad Nacional de Colombia. in Chemical engineering, Universidad Nacional de Colombia. MSc in Industrial engineering, Universidad de los Andes, Colombia. PHD in Logistics, Maryland University, United States. Affiliation: Universidad de Los Andes, Colombia. in Chemical Engineering, Universidad Nacional de Colombia. Affiliation: Universidad Militar Nueva Granada, Colombia. in Chemistry Universidad Nacional de Colombia. MSc in mathematics, Universidad Nacional de Colombia. Fedossova 4ДЎ AndrГ©s Leonardo RamГrez Leal. Un nuevo algoritmo para la soluciГіn de problemas de programaciГіn linealДЄ. A new algorithm for solving linear programming problems

Simplex method of solving linear programming