Efficient Neutrosophic Optimization for Minimum Cost Flow Problems

In the domain of optimization, linear programming (LP) is recognized as an exceptionally effective method for ensuring the most favorable outcomes. Within the context of LP, the minimum cost flow (MCF) problem is fundamental, with its primary objective being to reduce the transportation costs for a single item moving through a network, under the constraints related to capacity. This network is made up of supply nodes, directed arcs, and demand nodes and each arc has an associated cost and capacity constraint, these factors are certain. However, in practical scenarios, these factors are susceptible to variation due to causal uncertainty. The neu-trosophic set theory has surfaced as a challenging approach to tackle the uncertainty that is often encountered in optimization processes. In this manuscript, our primary objective is to address the minimal cost flow (MCF) problem while accounting for the uncertainty inherent in the neutrosophic set. We specifically focus on the cost aspect as SVTN numbers and introduce a new approach based on a customized ranking function handmade for the MCF problem a pioneering endeavor within the field of neutrosophic sets. Additionally, we present numerical example to validate the effectiveness and robustness of our model.