On the Simplex-based Methods for Neutrosophic Linear Programming Problems

This paper investigates Neutrosophic Linear Programming (NLP) and focuses on one of the most suitable approaches to solve it, which is called the Simplex-based model. This type of method, inspired by the classic Simplex algorithm, is in search of an optimal basic neutrosophic feasible solution, and several attractive models of it have been proposed in recent years. However, due to neutrosophic logic considers three dimensions of a problem, using a direct generalization of the simplex algorithm (which has been done in existing methods), the computational volume is greatly increased even for the small problems, and as a result, the use of these models in real-world issues will be questioned. To solve this gap, we consider NLP and propose an effective, simple model that can significantly reduce computational tasks and address these deficits in the mentioned models. Some numerical experiments with the comparison results are provided to explain the efficiency and superiority of the proposed approach.