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.
Data envelopment analysis (DEA) is a methodology for measuring best relative efficiencies of a group of peer decision-making units (DMUs) that take multiple inputs to produce multiple outputs. However, the traditional DEA model only aims to maximize the efficiency of the DMU under evaluation. This usually leads to very small weights (even zero weights) being assigned to some inputs or outputs. Correspondingly, these inputs or outputs have little or even no contribution to efficiency, which is unfair and irrational. The purpose of this paper is to address this problem. Two new weight-optimized models are proposed based upon the perspective of cross evaluation. Using the results of an Advanced Manufacturing Technology (AMT) example, it is found that all AMTs are fully sorted. The decision maker can easily choose the best AMT. In addition, unreasonable weights of AMTs are effectively avoided.
The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with exact values. But it cannot handle imprecise data. Imprecise data, for example, can be expressed in the form of the interval data or mixtures of interval data and exact data. In order to solve this problem, this study proposes three new interval DEA models from different points of view. Two examples are presented to illustrate and validate these models.