Negative data in DEA: Recognizing congestion and specifying the least and the most congested decision making units |
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| Affiliation: | 1. National Graduate Institute for Policy Studies, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8677, Japan;2. Benchmarking Research Group, Faculty of Accounting, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Department of Financial Management, National Defense University, No. 70, Sec. 2, Zhongyang North Rd., Beitou, Taipei 112, Taiwan;4. Faculty of Industrial Management, Universiti Malaysia Pahang, 26300 Gambang, Pahang, Malaysia;1. Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah 06010 UUM, Malaysia;2. College of Administration and Economics, University of Anbar, Ramadi, Iraq;1. Dongguk Business School, Dongguk University—Seoul, 30, Pildong-ro 1-gil, Jung-gu, Seoul 100-715, South Korea;2. International Center for Auditing and Evaluation, Nanjing Audit University, Nanjing 211815, PR China;3. Robert A. Foisie School of Business, Worcester Polytechnic Institute, Worcester, MA 01609, USA;1. Department of Transportation and Logistics Management, National Chiao Tung University, Taiwan;2. National Graduate Institute for Policy Studies, Japan;3. Department of Accounting and Information Technology, National Chung Cheng University, Taiwan |
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| Abstract: | One of the important concepts of data envelopment analysis (DEA) is congestion. A decision making unit (DMU) has congestion if an increase (decrease) in one or more input(s) of the DMU leads to a decrease (increase) in one or more its output(s). The drawback of all existing congestion DEA approaches is that they are applicable only to technologies specified by non-negative data, whereas in the real world, it may exist negative data, too. Moreover, specifying the strongly and weakly most congested DMUs is a very important issue for decision makers, however, there is no study on specifying these DMUs in DEA. These two facts are motivations for creating this current study. Hence, in this research, we first introduce a DEA model to determine candidate DMUs for having congestion and then, a DEA approach is presented to detect congestion status of these DMUs. Likewise, we propose two integrated mixed integer programming (MIP)-DEA models to specify the strongly and weakly most congested DMUs. Note that the proposed approach permits the inputs and outputs that can take both negative and non-negative magnitudes. Also, a ranking DEA approach is introduced to rank the specified congested DMUs and identify the least congested DMU. Finally, a numerical example and an empirical application are presented to highlight the purpose of this research. |
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| Keywords: | Data envelopment analysis (DEA) Strong and weak congestion Negative data in DEA Slack variables Mixed integer programming (MIP) model |
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