Document Type : Original Article


1 M.Sc., Mazandaran University of Science and Technology.

2 Assistant Professor, Mazandaran University of Science and Technology.

3 Associate Professor, Mazandaran University of Science and Technology.


With increasing environmental pollution in recent years, researchers have focused on designing a closed loop supply chain network with consideration of environmental issues. In this research an uncertain bi-objective, multi-period, multi-product and multi-level closed-loop supply chain network is presented. Uncertainty in demand, transportation costs are considered and to counteract this uncertainty the robust optimization approach is used. The proposed supply chain network consists of four levels of forward supply chain and four levels of reverse chain. The proposed model is a mixed integer linear programming (MILP) model with the aim maximizing profit and minimizing generated pollution by transportation of products, and operational centers. The proposed model is solved by lingo software, so that the multi-objective model has been handled by utility based goal programming method. Finally, the results are analyzed and the comparison of different scenarios indicates that the objective function has strongly shown the uncertainty parameters and the effect of uncertainty in the parameters simultaneously. Therefore, network modeling based on different scenarios can be a good tool for deciding on confrontation with uncertain and ambiguous parameters.


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