A robust mixed flexible-possibilistic programming approach for multi-objective closed-loop green supply chain network design

In recent years, due to governmental legislation, environmental groups’ pressures, customer green expectation, etc., closed-loop green supply chains have gained paramount consideration. Accordingly, this study develops a novel multi-objective mixed integer nonlinear programming model for a closed-loop green supply chain network design problem. The proposed model aims to minimize the total costs, total CO2 emissions, and robustness costs in both forward and reverse directions, simultaneously. To cope with flexible constraints and epistemic uncertainty in the model’s parameters, a robust flexible-possibilistic programming approach is tailored. The model is solved using an efficient interactive solution approach, in which, the presented model is analyzed under various carbon emission mechanisms to assess the influence of these mechanisms on the achieved solution. An illustrative example in the copier industry is also provided to validate the applicability of the presented optimization model. Numerical results indicate the superiority of the carbon cap-and-trade policy in most of the cases.