an approach utilizing epsilon-constraint and nsga-ii for circular manufacturing supply chain networks

Circular manufacturing supply chains offer a novel and compelling perspective within the realm of supply chain sustainability. consequently, the development of a suitable solution approach for circular manufacturing supply chains holds significant value. this study presents appropriate solution approaches for a mathematical model that has been formulated for a circular supply chain. to address the small-sized problem, the epsilon-constraint method is proposed. this method aids in obtaining a pareto set of optimal solutions, facilitating the evaluation of trade-offs among three objectives. given the np-hard nature of the problem, the non-dominated sorting genetic algorithm (nsga-ii) is employed to approximate the pareto front for larger problem sizes. a comparative analysis is conducted between the outcomes achieved in smaller dimensions using the epsilon-constraint method and those generated by the metaheuristic algorithm. the results indicate that the error percentage of the objective function, when compared to the epsilon method, remains consistently below 1%, underscoring the effectiveness of the proposed algorithm. these methodologies empower decision-makers to offer efficient, optimal solutions, enabling them to select the most suitable alternative based on budgetary considerations and organizational policies.