A network design of a closed-loop supply chain (CLSC) with multiple recovery modes under fuzzy environments is studied in this article, in which all the cost coefficients (e.g., for facility establishment, transportation, manufacturing and recovery), customer demands, delivery time, recovery rates and some other factors that cannot be precisely estimated while designing are modeled as triangular fuzzy numbers. To handle these uncertain factors and achieve a compromise between the two conflicting objectives of maximizing company profit and improving customer satisfaction, a fuzzy bi-objective programming model and a corresponding two-stage fuzzy interactive solution method are presented. Applying the fuzzy expected value operator and fuzzy ranking method, the fuzzy model is transformed into a deterministic counterpart. Subsequently, Pareto optimal solutions are determined by employing the fuzzy interactive solution method to deal with the conflicting objectives. Numerical experiments address the efficiency of the proposed model and its solution approach. Furthermore, by comparing these results with the CLSC network design in deterministic environments, the benefits of modeling the CLSC network design problem with fuzzy information are highlighted.
The air transportation hub-and-spoke design problem: comparison between a continuous and a discrete solution method