Cost optimization of System in Single-valued Neutrosophic Fuzzy Queueing Systems using Genetic Algorithm

Abstract

Queueing theory constitutes a fundamental analytical framework for evaluating the performance, stability, and operational behavior of manufacturing and service systems subjected to stochastic arrival and service processes. The Neutrosophic paradigm offers a powerful extension for modeling uncertainty, imprecision, indeterminacy, and inconsistency inherent in real-world system parameters—capabilities that surpass those of classical probabilistic and fuzzy approaches. The study includes Single-Valued Neutrosophic Queueing Systems (SVNQSs) as a generalized formulation of traditional and fuzzy queueing structures, providing an enriched mathematical apparatus for system analysis, control, and optimization. Within the SVNQS framework, both arrival and service rates are represented by single-valued neutrosophic numbers, enabling a more comprehensive characterization of ambiguous and fluctuating system conditions. Consequently, the associated probability measures, performance indices, and operational metrics are likewise expressed in neutrosophic form. The proposed model further examines the influence of neutrosophic parameters on queueing dynamics and investigates the optimization of total system cost through the application of a Genetic Algorithm (GA). This integrative approach yields deeper insights into decision-making under uncertainty and facilitates enhanced optimization strategies applicable to diverse manufacturing and operational environments. Numerical case studies are provided and successfully solved to demonstrate the applicability of the framework, and due to the computational intricacies involved, dedicated MATLAB routines have been developed to streamline and automate the required computations.