A full ranking methodology in data envelopment analysis based on a set of dummy decision making units |
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| Affiliation: | 1. Departamento de Ciencias de la Ingeniería, Facultad de Ingeniería, Universidad Andres Bello, Antonio Varas 880, Santiago, Chile;2. Yahoo! Research Latin America, Blanco Encalada 2120, Santiago, Chile;1. Department of Electrical Engineering, Pohang University of Science and Technology, Pohang 37673, Korea;2. Department of Creative IT Excellence Engineering and Future IT Innovation Laboratory, Pohang University of Science and Technology, Pohang 37673, Korea;1. Intelligent Data Analytics Research Program Dept. Aselsan Research Center, Ankara, Turkey;2. Department of Electrical Engineering, Stanford University, CA, USA;3. Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey;4. National Magnetic Resonance Research Center (UMRAM), Bilkent University, Ankara, Turkey;1. School of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, GPO Box 2434, 2 George Street Brisbane Qld 4000, Australia;2. Emergency Medicine, Princess Alexandra Hospital, 2 Ipswich Rd, Woolloongabba, Brisbane, Qld 4102, Australia;3. Intensive Care Unit, Princess Alexandra Hospital, 2 Ipswich Rd, Woolloongabba, Brisbane, Qld 4102, Australia;4. School of Electrical Engineering and Computer Science, Science and Engineering Faculty, Queensland University of Technology, GPO Box 2434, 2 George Street Brisbane Qld 4000, Australia |
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| Abstract: | In this paper, we propose a new methodology for ranking decision making units in data envelopment analysis (DEA). Our approach is a benchmarking method, seeks a common set of weights using a proposed linear programming model and is based on the TOPSIS approach in multiple attribute decision making (MADM). To this end, five artificial or dummy decision making units (DMUs) are defined, the ideal DMU (IDMU), the anti-ideal DMU (ADMU), the right ideal DMU (RIDMU), the left anti-ideal DMU (LADMU) and the average DMU (AVDMU). We form two comprehensive indexes for the AVDMU called the Left Relative Closeness (LRC) and the Right Relative Closeness (RRC) with respect to the RIDMU and LADMU. The LRC and RRC indexes will be used in the new proposed linear programming model to estimate the common set of weights, the new efficiency of DMUs and finally an overall ranking for all the DMUs. The change of the ratio between LRC and RRC indexes is capable to be provoked alternative rankings. One of the best advantages of this model is that we can make a rationale ranking which is demonstrated by the realized correlation analysis. Also, the new proposed efficiency score of the DMUs is close to the efficiency score of the DEA (CCR) methodology. Three numerical examples are provided to illustrate the applicability of the new approach and the effectiveness of the new approach in DEA ranking in comparison with other conventional ranking methods. Also, an "error" analysis proves the robustness of the proposed methodology. |
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