A Paradigm Shift in Linear Programming: An Algorithm without Artificial Variables

Abstract

Linear Programming (LP) is pivotal in operations research across various domains. The standard simplex method, while effective, faces challenges initializing when inequality constraints exist, often necessitating artificial variables. This paper presents a paradigm-shifting approach—eliminating artificial variables. The new method simplifies LP by leveraging negative and positive variables, saving significant time and resources compared to traditional Two-Phase and Big-M methods. A numerical example confirms our approach's superior efficiency and speed. This innovation promises to transform LP problem-solving, eliminating artificial variable burdens and streamlining computations.