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Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

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Abstract

In the last decade, ranking units in data envelopment analysis (DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. Also, some of these data may be known only in terms of ordinal relations. While the models developed in the past are interesting and meaningful, they didn’t consider both undesirable and ordinal factors at the same time. In this research, we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models. This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units (DMUs) with undesirable and ordinal data. For this purpose, we transform the ordinal data into definite data, and then we consider each undesirable input and output as desirable output and input, respectively. Finally, an application that shows the capability of the proposed method is illustrated.

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran

    Zahra Aliakbarpoor & Mohammad Izadikhah

Authors
  1. Zahra Aliakbarpoor
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  2. Mohammad Izadikhah
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Correspondence to Mohammad Izadikhah.

Additional information

Zahra Aliakbarpoor received her B. Sc. degree in applied mathematics from the Payam-e-Noor University of Sary in 2002. She is now a graduate student of applied mathematics in Islamic Azad University of Arak, and working on her thesis.

Her research interest is data envelopment analysis in the presence of imprecise data.

Mohammad Izadikhah received his B. Sc. degree in applied mathematics from Amir Kabir University of Technology in 2001, and the M. Sc. degree in applied mathematics from Teacher Training University of Tehran in 2003, and the Ph.D. degree in applied mathematics from Islamic Azad University, Science and Research Branch of Tehran in 2007. Since 2007, he has been a faculty member at Islamic Azad University of Arak, and currently, he is an assistant professor in Department of Mathematics at Islamic Azad University of Arak. He has published about 30 refereed journal and conference papers.

His research interests include operations research, data envelopment analysis, multi-objective decision making and fuzzy theory, and operations research with imprecise data.

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Aliakbarpoor, Z., Izadikhah, M. Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis. Int. J. Autom. Comput. 9, 609–615 (2012). https://doi.org/10.1007/s11633-012-0686-5

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  • DOI: https://doi.org/10.1007/s11633-012-0686-5

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