Dual Artificial Variable-Free Simplex Algorithm for Solving Neutrosophic Linear Programming Problems

Abstract

This paper presents a simplified form of dual simplex algorithm for solving linear programming problems with fuzzy and neutrosophic numbers which supplies some great benefits over phase 1 of traditional dual simplex algorithm. For instance, it could start with any infeasible basis of linear programming problems; it doesn't need any kind of artificial variables or artificial constraints, so the number of variables of the proposed method is less than the number of variables in the traditional dual simplex algorithm, therefore; the run time for the proposed algorithm is also faster than the phase 1 of traditional dual simplex algorithm, and the proposed method overcomes the traditional dual simplex algorithm for both the fuzzy approach and the neutrosophic approach according to the iterations number. We also use numerical examples to compare between the fuzzy and the neutrosophic approaches, the results show that the neutrosophic approach is more accurate than the fuzzy approach. Furthermore, the proposed algorithm overcomes the phase 1 of traditional dual simplex algorithm for both the fuzzy and neutrosophic approach.

Keywords

• fuzzy number
• neutrosophic number
• rank function
• simplex method