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Efficiency evaluation of closed-loop supply chains with proportional dual-role measures

Data Envelopment Analysis (DEA) is a beneficial mathematical programming method to measure relative efficiencies. In conventional DEA models, Decision Making Units (DMUs) are usually considered as black boxes. Also, the efficiency of DMUs is evaluated in the presence of the specified inputs and outputs. Nevertheless, in real-world applications, there are situations in which the performance of multi-stage processes like supply chains with forward and reverse flows must be measured such that some...

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