Mathematical Modelling with Advanced Optimization Techniques for Renewal and Sustainable Products

The increasing global emphasis on sustainability necessitates robust mathematical modelling and optimization techniques to enhance the efficiency of renewable and sustainable products. This paper explores advanced deterministic and stochastic models, including linear and nonlinear programming, dynamic systems, game theory, and variational methods, to optimize resource utilization and minimize environmental impact. Multi-objective optimization approaches, such as Pareto optimization and constrained optimization methods, are examined for balancing economic and ecological sustainability. Case studies in renewable energy, sustainable supply chains, and eco-friendly product lifecycle modelling demonstrate the practical applicability of these mathematical frameworks. The study also highlights key challenges in solving large-scale sustainability models and identifies future research directions.