The depletion of natural resources and the degradation of the ecosystem have led many countries to adopt closed-loop supply activities in both their industrial and service sectors. With the widespread use of Internet technology, these aspects motivate the incorporation of e-commerce with the classical closed-loop supply chain. This study suggests a novel mixed-integer linear programming (MILP) model that addresses the integration of e-commerce with a multi-echelon closed-loop supply chain with a multi-period planning time horizon by considering dual channels in manufacturing, and recovery facilities. To validate the model, we obtain optimal decision variables and examine the robustness and applicability of the model, and comprehensive computational experiments are performed. Moreover, sensitivity analysis is carried out to illustrate the efficacy of e-commerce integration by considering the two channels in the closed-loop supply chain. Accordingly, the total cost of the dual-channel CLSC decreases with an increase in customer demand via online retailers, the returned end of life (EOL) products, recycling ratio, and recovery ratio. Some useful managerial implications are provided based on the conducted analysis.

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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).

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