Interval efficiency measures in data envelopment analysis with imprecise data |
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| Institution: | 1. Department of Industrial and Information Management, National Cheng Kung University, Tainan 70101, Taiwan, ROC;2. Department of Finance, University of Georgia, Athens, GA 30602-6253, USA;1. National Graduate Institute for Policy Studies, Japan;2. Department of System Engineering, Faculty of Economics, Technical University of Ostrava, Ostrava, Czech Republic Department of Operations Management & Business Statistics, College of Economics and Political Science, Sultan Qaboos University, Muscat, Oman;3. Department of Mathematics, College of Science, Arak Branch, Islamic Azad University, Arak, Iran;1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu Province, China;2. Research Center for Soft Energy Science, Nanjing University of Aeronautics and Astronautics, 29 Jiangjun Avenue, Nanjing 211106, Jiangsu Province, China;3. Center of Operations Research (CIO), University Miguel Hernandez of Elche (UMH), Elche, Alicante 03202, Spain;4. School of Business Administration, Faculty of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, Sichuan Province, China;5. School of Management, University of Science and Technology of China, Hefei 230026, Anhui Province, China |
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| Abstract: | The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units (DMUs) with exact values of inputs and outputs. For imprecise data, i.e., mixtures of interval data and ordinal data, some methods have been developed to calculate the upper bound of the efficiency scores. This paper constructs a pair of two-level mathematical programming models, whose objective values represent the lower bound and upper bound of the efficiency scores, respectively. Based on the concept of productive efficiency and the application of a variable substitution technique, the pair of two-level nonlinear programs is transformed to a pair of ordinary one-level linear programs. Solving the associated pairs of linear programs produces the efficiency intervals of all DMUs. An illustrative example verifies the idea of this paper. A real case is also provided to give some interpretation of the interval efficiency. Interval efficiency not only describes the real situation in better detail; psychologically, it also eases the tension of the DMUs being evaluated as well as the persons conducting the evaluation. |
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