A novel multi-objective optimization model for designing a reverse supply chain network

Reverse supply chain management is one of the most effective ways to protect the environment and conserve natural resources while generating significant economic benefits for manufacturing firms. This paper examines the design of a reverse supply chain consisting of various facilities, including collection, inspection, and recycling centers, internal and external remanufacturing plants, suppliers, and secondary markets. The supply chain aims to minimize costs and carbon emissions. Additionally, the proposed model is extended to a multi-objective robust stochastic-based model to consider the uncertainty in the amount and quality of return products. Furthermore, to derive the Pareto solutions, two methods, $\epsilon -$ constraint, and the Metaheuristic algorithm of the multi-objective genetic algorithm are employed. In the multi-objective genetic algorithm, a new representation of solutions is provided, considering all dependencies between the variables and embodying the concept of robustness in the solutions of the Metaheuristic algorithms. According to the research findings, the Metaheuristic algorithm could compete with the exact method of $\epsilon -$ constraint in small-size problems, while the multi-objective genetic algorithm outperforms it in large-size problems. On the other hand, a sensitivity analysis reveals that revenue and emission-related parameters influence the level of expansion in the reverse supply chain, while the standard deviation of uncertain parameters mostly affects the robustness of the solutions. A balanced capacity throughout the supply chain is also recognized as essential for improving profitability and flexibility. Additionally, the model results showed that reducing emissions related to facilities can create opportunities for all the identified objectives within the supply chain.