A comparative analysis of metaheuristic algorithms in interval-valued sustainable economic production quantity inventory models using center-radius optimization

The real-world production inventory systems involve uncertainties surrounding demand, production, defectiveness, and costs, which pose significant challenges. Various methodologies, including interval, fuzzy, stochastic, and fuzzy-stochastic approaches, have been developed to address these challenges. Among these, the interval approach offers a realistic representation of uncertainty. This study develops a green production model within an interval-based framework, incorporating interval-valued representations of defective rates and demand, which is also stochastic in nature. Differential equations governing inventory levels are formulated in an interval format and solved using advanced parametric techniques. The study extends to profit optimization within this interval-based framework, with the profit maximization problem transformed into a crisp form using interval order relations and center-radius optimization. The optimized solution is obtained through various metaheuristic algorithms. A numerical example validates the proposed model, and sensitivity analyses explore variations in different algorithms and inventory parameters. Additionally, statistical analysis using ANOVA tests is performed. This research contributes to production inventory management by providing a robust framework for handling uncertainty and optimizing performance in real-world scenarios.