ارزیابی عملکرد واحدهای تصمیم‌گیری بر اساس دیدگاه‌های خوشبینانه و بدبینانه
محورهای موضوعی :
مدیریت صنعتی
Hossein Azizi
1
(
Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.
)
Maziar Salahi
2
(
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Iran
)
تاریخ دریافت : 1397/10/04
تاریخ پذیرش : 1398/02/24
تاریخ انتشار : 1398/06/30
کلید واژه:
بازه‌ی کارآیی,
مدل‌های کراندار,
تحلیل پوششی داده‌ها,
کارآیی‌های خوشبینانه و بدبینانه,
چکیده مقاله :
تحلیل پوششی داده‌ها ( DEA ) روشی برای سنجش عملکرد گروهی از واحدهای تصمیم‌گیری ( DMUها) است که از ورودی‌های متعدد برای تولید خروجی‌های متعدد استفاده می‌کنند. این روش عملکرد DMUها را با مینیمم‌سازی نسبت ورودی وزنی به خروجی وزنی هر DMU، به ترتیب، مشروط به این قید که هیچ یک از کارآیی‌های DMUهای دیگر کوچک‌تر از یک نباشد، اندازه‌گیری می‌کند (در حالت با ماهیت خروجی). کارآیی‌هایی که به این ترتیب اندازه‌گیری می‌شوند، کارآیی خوشبینانه یا بهترین کارآیی نسبی نامیده می‌شوند. روش اندازه‌گیری کارآیی خوشبینانه‌ی DMUها را خودارزیابی می‌نامند. در صورتی که نمره‌ی کارآیی خودارزیابی یک DMU یک باشد، به آن کارآی خوشبینانه می‌گویند؛ در غیر این صورت، به آن غیرکارآی خوشبینانه می‌گویند. رویکرد مشابهی وجود دارد که از مفهوم مرز ناکارآیی برای تعیین بدترین نمره‌ی کارآیی نسبی که می‌توان به هر DMU اختصاص داد، استفاده می‌کند. DMUهای واقع روی مرز ناکارآیی به‌عنوان ناکارآی بدبینانه تعیین می‌شوند، و آنهایی که روی مرز ناکارآ نیستند، به‌عنوان غیرناکارآی بدبینانه اعلام می‌شوند. در این مقاله، این بحث مطرح می‌شود که هر دو کارآیی نسبی را باید با هم در نظر گرفت، و هر رویکردی که فقط یکی از آنها را در نظر گرفته باشد، دچار سوگیری خواهد بود. برای اندازه‌گیری عملکرد کلی DMUها، پیشنهاد می‌شود که هر دو کارآیی را در قالب یک بازه ادغام، و مدل‌های DEAی پیشنهادی برای اندازه‌گیری کارآیی را مدل‌های کراندار می‌نامیم. به این ترتیب، بازه‌ی کارآیی تمام مقادیر ممکن کارآیی را که منعکس کننده‌ی دیدگاه‌های مختلف هستند، در اختیار تصمیم گیرنده قرار می‌دهد.
چکیده انگلیسی:
Data envelopment analysis (DEA) is a methodology for assessing the performances of a group of decision making units (DMUs) that utilize multiple inputs to produce multiple outputs. It measures the performances of the DMUs by maximizing the efficiency of every DMU, respectively, subject to the constraints that none of the efficiencies of the DMUs can be less than one. The efficiencies measured in this way are referred to as optimistic efficiencies or the best relative efficiencies. The way to measure the optimistic efficiencies of the DMUs is referred to as self-evaluation. If a DMU is self-evaluated to have an efficiency score of one, then it is said to be DEA efficient; otherwise, the DMU is said to be non-DEA efficient. There is a comparable approach which uses the concept of inefficiency frontier for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives.
منابع و مأخذ:
Ahmady, Nazanin, Azadi, Majid, Sadeghi, Seyed Amir Hossein, & Farzipoor Saen, Reza. (2013). A novel fuzzy data envelopment analysis model with double frontiers for supplier selection. International Journal of Logistics Research and Applications, 16(2), 87-98. doi: 10.1080/13675567.2013.772957
Amirteimoori, Alireza. (2007). DEA efficiency analysis: Efficient and anti-efficient frontier. Applied Mathematics and Computation, 186(1), 10-16. doi: https://doi.org/10.1016/j.amc.2006.07.006
Amirteimoori, Alireza, Kordrostami, Sohrab, & Rezaitabar, Aliakbar. (2006). An improvement to the cost efficiency interval: A DEA-based approach. Applied Mathematics and Computation, 181(1), 775-781. doi: https://doi.org/10.1016/j.amc.2006.02.005
Azizi, Hossein. (2011). The interval efficiency based on the optimistic and pessimistic points of view. Applied Mathematical Modelling, 35(5), 2384-2393. doi: https://doi.org/10.1016/j.apm.2010.11.055
Azizi, Hossein, & Ajirlu, Hassan Ganjeh. (2011). Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data. Applied Mathematical Modelling, 35(9), 4149-4156. doi: https://doi.org/10.1016/j.apm.2011.02.038
Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3-4), 181-186. doi: 10.1002/nav.3800090303
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. doi: https://doi.org/10.1016/0377-2217(78)90138-8
Chen, Jin-Xiao. (2012). A comment on DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 219(2), 583-591. doi: https://doi.org/10.1016/j.amc.2012.06.046
Chin, Kwai-Sang, Wang, Ying-Ming, Poon, Gary Ka Kwai, & Yang, Jian-Bo. (2009). Failure mode and effects analysis by data envelopment analysis. Decision Support Systems, 48(1), 246-256. doi: https://doi.org/10.1016/j.dss.2009.08.005
Entani, Tomoe, Maeda, Yutaka, & Tanaka, Hideo. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136(1), 32-45. doi: https://doi.org/10.1016/S0377-2217(01)00055-8
Entani, Tomoe, & Tanaka, Hideo. (2006). Improvement of efficiency intervals based on DEA by adjusting inputs and outputs. European Journal of Operational Research, 172(3), 1004-1017. doi: https://doi.org/10.1016/j.ejor.2004.11.010
Foroughi, Ali Asghar, & Aouni, Belaïd. (2012). Ranking units in DEA based on efficiency intervals and decision-maker's preferences. International Transactions in Operational Research, 19(4), 567-579. doi: 10.1111/j.1475-3995.2011.00834.x
Hatami-Marbini, Adel, Saati, Saber, & Tavana, Madjid. (2010). An ideal-seeking fuzzy data envelopment analysis framework. Applied Soft Computing, 10(4), 1062-1070. doi: https://doi.org/10.1016/j.asoc.2009.12.031
Jahanshahloo, G. R., & Afzalinejad, M. (2006). A ranking method based on a full-inefficient frontier. Applied Mathematical Modelling, 30(3), 248-260. doi: https://doi.org/10.1016/j.apm.2005.03.023
Jahed, Rasul, Amirteimoori, Alireza, & Azizi, Hossein. (2015). Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis. Measurement, 69, 264-279. doi: https://doi.org/10.1016/j.measurement.2015.03.014
Liu, Fuh-hwa Franklin, & Chen, Cheng-Li. (2009). The worst-practice DEA model with slack-based measurement. Computers & Industrial Engineering, 57(2), 496-505. doi: https://doi.org/10.1016/j.cie.2007.12.021
Mirhedayatian, Seyed Mostafa, Vahdat, Seyed Ebrahim, Jafarian Jelodar, Mostafa, & Farzipoor Saen, Reza. (2013). Welding process selection for repairing nodular cast iron engine block by integrated fuzzy data envelopment analysis and TOPSIS approaches. Materials & Design, 43, 272-282. doi: https://doi.org/10.1016/j.matdes.2012.07.010
Serrano-Cinca, Carlos, MarMoliero, Cecillo, & Chaparro, Fernando. (2004). Spanish savings banks: a view on intangibles. Knowledge Management Research & Practice, 2(2), 103-117. doi: 10.1057/palgrave.kmrp.8500025
Wang, Ying-Ming, & Chin, Kwai-Sang. (2009). A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers. International Journal of Production Research, 47(23), 6663-6679. doi: 10.1080/00207540802314845
Wang, Ying-Ming, & Chin, Kwai-Sang. (2011). Fuzzy data envelopment analysis: A fuzzy expected value approach. Expert Systems with Applications, 38(9), 11678-11685. doi: https://doi.org/10.1016/j.eswa.2011.03.049
Wang, Ying-Ming, Chin, Kwai-Sang, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using geometric average efficiency. Journal of the Operational Research Society, 58(7), 929-937. doi: 10.1057/palgrave.jors.2602205
Wang, Ying-Ming, & Lan, Yi-Xin. (2011). Measuring Malmquist productivity index: A new approach based on double frontiers data envelopment analysis. Mathematical and Computer Modelling, 54(11), 2760-2771. doi: https://doi.org/10.1016/j.mcm.2011.06.064
Wang, Ying-Ming, & Lan, Yi-Xin. (2013). Estimating most productive scale size with double frontiers data envelopment analysis. Economic Modelling, 33, 182-186. doi: https://doi.org/10.1016/j.econmod.2013.04.021
Wang, Ying-Ming, & Luo, Ying. (2006). DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 173(2), 902-915. doi: https://doi.org/10.1016/j.amc.2005.04.023
Wang, Ying-Ming, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using interval efficiencies. Journal of Computational and Applied Mathematics, 198(1), 253-267. doi: https://doi.org/10.1016/j.cam.2005.12.025
Wu, Desheng. (2006). A note on DEA efficiency assessment using ideal point: An improvement of Wang and Luo’s model. Applied Mathematics and Computation, 183(2), 819-830. doi: https://doi.org/10.1016/j.amc.2006.06.030
Xu, Ji Heng, Li, Ling, Liu, Jian Yong, Fu, Cheng Qun, & Zheng, Ji Lin. (2011). Imprecise DEA Model Based on TOPSIS. Applied Mechanics and Materials, 63-64, 723-727. doi: 10.4028/www.scientific.net/AMM.63-64.723
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Ahmady, Nazanin, Azadi, Majid, Sadeghi, Seyed Amir Hossein, & Farzipoor Saen, Reza. (2013). A novel fuzzy data envelopment analysis model with double frontiers for supplier selection. International Journal of Logistics Research and Applications, 16(2), 87-98. doi: 10.1080/13675567.2013.772957
Amirteimoori, Alireza. (2007). DEA efficiency analysis: Efficient and anti-efficient frontier. Applied Mathematics and Computation, 186(1), 10-16. doi: https://doi.org/10.1016/j.amc.2006.07.006
Amirteimoori, Alireza, Kordrostami, Sohrab, & Rezaitabar, Aliakbar. (2006). An improvement to the cost efficiency interval: A DEA-based approach. Applied Mathematics and Computation, 181(1), 775-781. doi: https://doi.org/10.1016/j.amc.2006.02.005
Azizi, Hossein. (2011). The interval efficiency based on the optimistic and pessimistic points of view. Applied Mathematical Modelling, 35(5), 2384-2393. doi: https://doi.org/10.1016/j.apm.2010.11.055
Azizi, Hossein, & Ajirlu, Hassan Ganjeh. (2011). Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data. Applied Mathematical Modelling, 35(9), 4149-4156. doi: https://doi.org/10.1016/j.apm.2011.02.038
Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3-4), 181-186. doi: 10.1002/nav.3800090303
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. doi: https://doi.org/10.1016/0377-2217(78)90138-8
Chen, Jin-Xiao. (2012). A comment on DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 219(2), 583-591. doi: https://doi.org/10.1016/j.amc.2012.06.046
Chin, Kwai-Sang, Wang, Ying-Ming, Poon, Gary Ka Kwai, & Yang, Jian-Bo. (2009). Failure mode and effects analysis by data envelopment analysis. Decision Support Systems, 48(1), 246-256. doi: https://doi.org/10.1016/j.dss.2009.08.005
Entani, Tomoe, Maeda, Yutaka, & Tanaka, Hideo. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136(1), 32-45. doi: https://doi.org/10.1016/S0377-2217(01)00055-8
Entani, Tomoe, & Tanaka, Hideo. (2006). Improvement of efficiency intervals based on DEA by adjusting inputs and outputs. European Journal of Operational Research, 172(3), 1004-1017. doi: https://doi.org/10.1016/j.ejor.2004.11.010
Foroughi, Ali Asghar, & Aouni, Belaïd. (2012). Ranking units in DEA based on efficiency intervals and decision-maker's preferences. International Transactions in Operational Research, 19(4), 567-579. doi: 10.1111/j.1475-3995.2011.00834.x
Hatami-Marbini, Adel, Saati, Saber, & Tavana, Madjid. (2010). An ideal-seeking fuzzy data envelopment analysis framework. Applied Soft Computing, 10(4), 1062-1070. doi: https://doi.org/10.1016/j.asoc.2009.12.031
Jahanshahloo, G. R., & Afzalinejad, M. (2006). A ranking method based on a full-inefficient frontier. Applied Mathematical Modelling, 30(3), 248-260. doi: https://doi.org/10.1016/j.apm.2005.03.023
Jahed, Rasul, Amirteimoori, Alireza, & Azizi, Hossein. (2015). Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis. Measurement, 69, 264-279. doi: https://doi.org/10.1016/j.measurement.2015.03.014
Liu, Fuh-hwa Franklin, & Chen, Cheng-Li. (2009). The worst-practice DEA model with slack-based measurement. Computers & Industrial Engineering, 57(2), 496-505. doi: https://doi.org/10.1016/j.cie.2007.12.021
Mirhedayatian, Seyed Mostafa, Vahdat, Seyed Ebrahim, Jafarian Jelodar, Mostafa, & Farzipoor Saen, Reza. (2013). Welding process selection for repairing nodular cast iron engine block by integrated fuzzy data envelopment analysis and TOPSIS approaches. Materials & Design, 43, 272-282. doi: https://doi.org/10.1016/j.matdes.2012.07.010
Serrano-Cinca, Carlos, MarMoliero, Cecillo, & Chaparro, Fernando. (2004). Spanish savings banks: a view on intangibles. Knowledge Management Research & Practice, 2(2), 103-117. doi: 10.1057/palgrave.kmrp.8500025
Wang, Ying-Ming, & Chin, Kwai-Sang. (2009). A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers. International Journal of Production Research, 47(23), 6663-6679. doi: 10.1080/00207540802314845
Wang, Ying-Ming, & Chin, Kwai-Sang. (2011). Fuzzy data envelopment analysis: A fuzzy expected value approach. Expert Systems with Applications, 38(9), 11678-11685. doi: https://doi.org/10.1016/j.eswa.2011.03.049
Wang, Ying-Ming, Chin, Kwai-Sang, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using geometric average efficiency. Journal of the Operational Research Society, 58(7), 929-937. doi: 10.1057/palgrave.jors.2602205
Wang, Ying-Ming, & Lan, Yi-Xin. (2011). Measuring Malmquist productivity index: A new approach based on double frontiers data envelopment analysis. Mathematical and Computer Modelling, 54(11), 2760-2771. doi: https://doi.org/10.1016/j.mcm.2011.06.064
Wang, Ying-Ming, & Lan, Yi-Xin. (2013). Estimating most productive scale size with double frontiers data envelopment analysis. Economic Modelling, 33, 182-186. doi: https://doi.org/10.1016/j.econmod.2013.04.021
Wang, Ying-Ming, & Luo, Ying. (2006). DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 173(2), 902-915. doi: https://doi.org/10.1016/j.amc.2005.04.023
Wang, Ying-Ming, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using interval efficiencies. Journal of Computational and Applied Mathematics, 198(1), 253-267. doi: https://doi.org/10.1016/j.cam.2005.12.025
Wu, Desheng. (2006). A note on DEA efficiency assessment using ideal point: An improvement of Wang and Luo’s model. Applied Mathematics and Computation, 183(2), 819-830. doi: https://doi.org/10.1016/j.amc.2006.06.030
Xu, Ji Heng, Li, Ling, Liu, Jian Yong, Fu, Cheng Qun, & Zheng, Ji Lin. (2011). Imprecise DEA Model Based on TOPSIS. Applied Mechanics and Materials, 63-64, 723-727. doi: 10.4028/www.scientific.net/AMM.63-64.723
