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.