Robust Optimization for a Bi-Objective Green Closed-Loop Supply Chain with Heterogeneous Transportation System and Presorting Consideration

In this study, we propose a robust bi-objective optimization model of the green closed-loop supply chain network considering presorting, a heterogeneous transportation system, and carbon emissions. The proposed model is an uncertain bi-objective mixed-integer linear optimization model that maximizes profit and minimizes carbon emissions by considering uncertain costs, selling price, and carbon emissions. The robust optimization approach is implemented using the combined interval and polyhedral, “Interval+ Polyhedral,” uncertainty set to develop the robust counterpart of the proposed model. Robust Pareto optimal solutions are obtained using a lexicographic weighted Tchebycheff optimization approach of the bi-objective model. Intensive computational experiments are conducted and a robust Pareto optimal front is obtained with a probability guarantee that the constraints containing uncertain parameters are not violated (constraint satisfaction).