Analyzing the impact of sustainability on EPQ model: Investigating price and sustainability level dependent demand using center-radius optimization techniques with Metaheuristic algorithms in interval valued environment

In real-world production inventory systems, uncertainties related to demand, production, defectiveness, and costs pose significant challenges. These uncertainties—arising from incomplete information, unpredictability, complexity, or system variability—complicate decision-making and planning. To address these challenges, various methodologies, including interval, fuzzy, stochastic, and fuzzy-stochastic approaches, have been developed. The interval-based approach, in particular, provides a practical way to represent uncertainty, encompassing factors like epistemic uncertainty, which arises from inherent randomness or variability. This study introduces a green production model within an interval-based framework, incorporating interval-valued representations of defective rates and stochastic demand. Differential equations governing inventory levels are formulated in interval form and solved using advanced parametric techniques. Unlike traditional models that focus on cost minimization or profit maximization, this paper adopts an optimization approach centered on the profit-cost ratio function, reflecting the negative relationship between production rate and inventory on hand and sharpening the manufacturer's goal. The study also explores the business practice of 'buy now, pay later' (BNPL), technically a delay-in-payments approach, which is used to boost sales. The BNPL scheme is integrated into the optimization model, and the related problem is solved through the center-radius technique. Metaheuristic algorithms are employed to derive the optimal solution. A numerical example validates the model, while sensitivity analyses explore variations in algorithmic and inventory parameters. Statistical analysis using ANOVA tests further supports the findings. A case study illustrates how the concept can be used in practice, solved with Maple and Python. This comprehensive analysis highlights the model's effectiveness in managing uncertainty and optimizing performance in real-world production inventory systems.