Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points
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ORIGINAL ARTICLE
Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points Ali Ebrahimnejad1
· Naser Amani2
Received: 4 July 2020 / Accepted: 28 September 2020 © The Author(s) 2020
Abstract Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranking fuzzy relative closeness indexes based on which the DMUs are ranked. The developed framework greatly reduces the complexity of computation compared with commonly used existing methods in the literature. To validate the proposed methodology and proposed ranking method, a numerical example is illustrated and compared the results with an existing approach. Keywords Data envelopment analysis · Fuzzy relative efficiency · Undesirable outputs · Ideal and anti-ideal units
Introduction Performance evaluation is a critically important procedure for the companies and organizations operating in the modern business world, where survival in the fiercely competitive business environment requires maintaining high levels of performance and efficiency. Thus, performance evaluations of business and production units in its many aspects have long been of interest to organizational managers and corporate executives. One of the major challenges ahead of proper performance evaluation is the lack of access to an accurate production function because of the complexity of the production process, the change in production technology, the impact of external factors on performance, the large size of data and operations, and the abrupt changes in policy
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Ali Ebrahimnejad [email protected]; [email protected]
1
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2
Department of Applied Mathematics, University of Texas at Austin, Austin, USA
to address acute problems. Access to production function is of immense importance for microeconomic analyses, as it allows managers to easily evaluate the performance of business units. Parametric methods have long been among the leading methods of estimation of production function and thereby unit performance. In these methods, user assumes a particular f
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