A Comparison of Solution Methods for the Multi-Objective Closed Loop Supply Chains

Increased pressure on natural resources, rising production costs, and multiple disposal challenges resulted in a growing global demand for integrated closed sustainable supply chain networks. In this paper, a bi-objective mixed-integer linear programming model is developed to minimize the overall cost and maximize the use of eco-friendly materials and clean technology. The paper evaluates the exact, heuristic, and metaheuristic methods in solving the proposed model in both small and large sizes. The sensitivity analysis was conducted on the LP-metric method as it outperformed the other two exact methods in solving the small size problems. The evaluation of LP-metric, modified ε-constraint, and TH as the exact methods and Lagrange relaxation algorithm as the heuristic method in terms of solution value and CPU time revealed the inability of exact methods in solving the large size problems. The best combination of effective parameters for meta-heuristic algorithms was determined using the Taguchi method. The evaluation of MOPSO, NSGA-II, SPEA-II, and MOEA/D as the metaheuristic methods by means of Number of Pareto Solutions (NPS), Mean Ideal Distance (MID), The Spread of Non-dominance Solutions (SNS), and CPU Time revealed the performance of these methods in solving the proposed model in a large size. The implementation of the VIKOR technique identified the SPEA-II as the best method among the meta-heuristic methods. This study provides a holistic view regarding the importance of selecting an appropriate solution methodology based on the problem dimension to ensure obtaining the optimum and accurate solution within the reasonable processing time.