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

summary: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 of the intervening factors, called proportional dual-role factors, are presented that one part of each proportional dual-role factor plays the input role and the other plays the output role. To address this issue, the current study proposes radial and non-radial DEA models for evaluating the overall and stage efficiencies of the closed-loop supply chains when there are proportional dual-role factors. To illustrate, a proportional dual-role factor is divided into portions of the input of the first stage and the output of the second stage such that the optimal overall and stage efficiency scores of closed-loop supply chain are obtained. A case study is used to illustrate the proposed approach. The experimental results obtained from real world data show the convincing performance of our proposed method