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Forward and reverse supply chains form a closed-loop supply chain. In this paper, a mathematical model is proposed for a closed-loop supply chain network by considering global factors, including exchange rates and customs duties. The model is a multi-objective mixed-integer linear programming model under uncertain demand. A solution approach based on fuzzy programming is developed for solving the optimization problem. The model is then applied in a network, which is located in Southwestern Ontario, Canada. A sensitivity analysis is provided to validate the model. This model considers global factors, multi-objectives, and uncertainty simultaneously in a closed-loop supply chain network.