Artificial Free Clone Of Simplex Method For Feasibility

TL;DR

This paper introduces an artificial-free phase 1 simplex method that operates in the original variable space, avoiding artificial variables and constraints, and demonstrates its advantages and limitations through counterexamples.

Contribution

The paper presents a new artificial-free phase 1 simplex method that simplifies the process by eliminating artificial variables, with analysis of its behavior under degeneracy.

Findings

The method works in the original variable space, mirroring the simplex pivot sequence.

Counterexamples show potential deviations from the standard simplex path under degeneracy.

The method is simple and suitable for educational purposes.

Abstract

This paper presents a method which is identical to simplex method phase 1, but do not need any artificial variable (or artificial constraints). So, the new method works in original variable space but visits the same sequence of pivots as simplex method does. Recently, (Inayatullah, Khan, Imtiaz & Khan, New artificial-free Phase 1 Simplex Method, 2009) claimed a similar method, here in this paper we have presented a counter example which shows in some special conditions of degeneracy their method may deviate from the simplex path. Because of its simplicity, the method presented in this paper is highly classroom oriented. So, indeed there is no need to work with artificial variables (or artificial constraints) in simplex method any more.