In this paper, a new mixed integer mathematical model for a closed-loop supply-chain network that includes both forward and reverse flows with multi-periods and multi-parts is proposed. The proposed model guarantees the optimal values of transportation amounts of manufactured and disassembled products in a closed-loop supply chain while determining the location of plants and retailers. Finally, computational results are presented for a number of scenarios to show and validate the applicability of the model.
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Özceylan et al. (2012) studied this question.
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