فهرست نشریات علمی دسترسی آزاد ایران

The Linear Programming (LP) model's strong modeling capabilities make it a valuable tool for solving real-world problems and optimizing objectives. The classical Minimal Cost Flow (MCF) problem is one such application of the LP model. These problems typically assume fixed parameters, whereas real-world scenarios often involve uncertainty in demand, cost, supply, and capacity. To address such uncertainty, neutrosophic logic extends fuzzy logic, enabling more effective handling of ambiguity, inconsistency, and incompleteness in data. This article explores the MCF problem with capacitated arcs and addresses it using neutrosophic arc costs represented by Single-Valued Triangular Neutrosophic Numbers (SVTN) numbers. Two algorithms are developed to provide methodologies for solving the neutrosophic MCF problem with uncertain cost parameters. Algorithm 1 introduce a strategy for obtaining the optimal solution by converting the Neutrosophic Minimal Cost Flow (NMCF) problem into a classical MCF problem. Algorithm 2 transforms each cost parameter into a weighted value and applies the possibilistic mean to produce an equivalent classical MCF problem. To validate the effectiveness of the proposed approach, three different types of numerical examples are examined, each demonstrating the applicability and performance of the two algorithms. The proposed method not only addresses current challenges but also resolves issues that previous models have not effectively handled, with a comparative analysis provided in this article.