مدل‌های تحلیل پوششی داده‌های بدترین عملکرد برای اندازه‌گیری کارآیی فازی
محورهای موضوعی :
مدیریت صنعتی
Hossein Azizi
1
,
Haidar Rasul Jahed
2
,
Leila Farrokhi
3
1 - Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran
2 - M.Sc., Instructor, Germi Branch, Islamic Azad University, Germi, Iran
3 - M.Sc., Instructor, Germi Branch, Islamic Azad University, Germi, Iran
تاریخ دریافت : 1396/10/20
تاریخ پذیرش : 1396/10/20
تاریخ انتشار : 1391/08/01
کلید واژه:
Data envelopment analysis,
تحلیل پوششی داده‌ها,
داده‌های ورودی فازی و خروجی فازی,
کارآیی فازی,
مرز بدترین عملکرد,
حساب فازی,
fuzzy input and output data,
worst-practice frontier,
fuzzy arithmetic,
چکیده مقاله :
تحلیل پوششی داده‌ها (DEA) در شکل کلاسیک خود که مبتنی بر مفهوم مرز تولید کارآ ست، بهترین نمره‌ی کارآیی ممکن را تعیین می‌کند که می‌توان آن را به هر یک از اعضای مجموعه‌ای از واحدهای تصمیم‌گیری (DMU) اختصاص داد. DMU بر اساس این نمرات به عنوان کارآی خوشبینانه یا غیرکارآی خوشبینانه تقسیم‌بندی می‌شوند، و DMU کارآی خوشبینانه، مرز کارآیی را مشخص می‌کنند. DEA کلاسیک را می‌توان برای شناسایی واحدهای دارای عملکرد خوب (کارآ) در مطلوب‌ترین سناریو استفاده کرد. به منظور شناسایی واحدهای دارای عملکرد بد، مانند بنگاه‌های ورشکسته در نامطلوب‌ترین سناریو (بدترین حالت)، رویکرد مشابهی به نام تحلیل بدترین کارآیی وجود دارد، که از مرز تولید ناکارآ برای تعیین بدترین نمره‌ی کارآیی نسبی ممکن که می‌توان به هر DMU اختصاص داد، استفاده می‌کند. DMU واقع شده بر مرز تولید ناکارآ به عنوان ناکارآی بدبینانه تعیین می‌شوند، و آنهایی که روی مرز تولید کارآ و تولید ناکارآ نیستند، به عنوان نامعین DEA اعلام می‌شوند. DEA نیازمند آن است که داده‌های ورودی‌ها و خروجی‌ها به طور دقیق معلوم باشند. ولی در کاربردهای واقعی همیشه چنین نیست. لیکن مقادیر مشاهده شده‌ی ورودی‌ها و خروجی‌ها در مسایل دنیای واقعی گاه فازی هستند. بسیاری از پژوهشگران روش‌های فازی مختلفی را برای کار با داده‌های فازی در DEA پیشنهاد کرده‌اند. این مقاله دو مدل DEA فازی جدید ارائه می‌کند که بر اساس حساب فازی برای کار با فازی بودن داده‌های ورودی و خروجی در DEA ایجاد شده‌اند. مدل‌های DEA فازی جدید به صورت مدل‌های برنامه‌ریزی خطی فرمول‌بندی می‌شوند و می‌توان آنها را برای تعیین کارآیی فازی گروهی از DMU مورد استفاده قرار داد. مدل‌های DEA فازی مرز بدترین عملکرد پیشنهاد شده در این مقاله، DMU دارای بدترین عملکرد را که مرز بدترین عملکرد (مرز ناکارآیی) را تشکیل می‌دهند، به صورت دقیق شناسایی می‌کنند. این مسأله به خصوص برای ارزیابی ریسک اعتبار مفید واقع می‌شود، ولی در هر کاربرد دیگری نیز می‌تواند سودمند باشد، زیرا واحدهایی که بدترین عملکرد را دارند، غالباً در همان جایی قرار دارند که بیشترین احتمال بهبود در آنجا وجود دارد. برای نشان دادن کاربرد رویکرد جدید، یک مثال ارائه خواهد شد.
چکیده انگلیسی:
The classic form of data envelopment analysis (DEA), which is based on the concept of efficient production frontier, determines the best efficiency score that can be assigned to each member of a set of decision-making units (DMUs). Based on these scores, DMUs are classified into optimistic efficient and optimistic non-efficient units, and the optimistic efficient DMUs determine the efficiency frontier. Classic DEA can be used for identification of well-performing (efficient) units in the most favorable scenario. For identification of units with bad performance, such as bankrupt firms in the most unfavorable scenario (the worst case), there is a similar approach, called worst efficiency analysis, which uses the inefficient production frontier in order to determine the worst relative efficiency score that can be assigned to each DMU. DMUs lying on the inefficient production frontier are specified as pessimistic inefficient, while those that are neither on the efficient production frontier nor on the inefficient production frontier is designated as DEA-unspecified units. DEA requires that input and output data are known exactly. However, this is not the case in real-world applications. However, the observed values of the input and output data in real-world problems are sometimes fuzzy. Many researchers have proposed various fuzzy methods for dealing with the fuzzy data in DEA. This paper presents two new fuzzy DEA models based on fuzzy arithmetic that make it possible to work with fuzzy input and output data in DEA. The new fuzzy DEA models are formulated as linear programming models, and they can be used for determining the fuzzy efficiency of a group of DMUs. The worst-practice frontier fuzzy DEA models presented in this paper accurately identify the “worst-practice” DMUs that form the worst practice-frontier (the inefficiency frontier). This is particularly relevant for our application to credit risk evaluation, but this also has general relevance since the worst performers are where the largest improvement potential can be found. An example will be presented to illustrate the application of the new approach.
منابع و مأخذ:
Azizi, H., & Ganjeh Ajirlu, H. (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.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30, 1078–1092.
Charnes, A. & Cooper, W. W. (1962). Programming with fractional function. Naval Research Logistics Quarterly, 9, 181–185.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Dia, M. (2004). A model of fuzzy data envelopment analysis. INFOR, 42, 267–279.
Entani, T., Maeda, Y., & Tanaka, H. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136, 32–45.
Garcia, P. A. A., Schirru, R., & Melo, P. F. F. E. (2005). A fuzzy data envelopment analysis approach for FMEA. Progress in Nuclear Energy, 46, 359–373.
Guo, P., & Tanaka, H. (2001). Fuzzy DEA: A perceptual evaluation method. Fuzzy Sets and Systems, 119, 149–160.
Jahanshahloo, G. R., Soleimani-damaneh, M., & Nasrabadi, E. (2004). Measure of efficiency in DEA with fuzzy input–output levels: A methodology for assessing, ranking and imposing of weights restrictions. Applied Mathematics and Computation, 156, 175–187.
Kao, C., & Liu, S. T. (2000a). Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems, 113, 427–437.
Kao, C., & Liu, S. T. (2000b). Data envelopment analysis with missing data: An application to University libraries in Taiwan. Journal of the Operational Research Society, 51, 897–905.
Kao, C., & Liu, S. T. (2003). A mathematical programming approach to fuzzy efficiency ranking. International Journal of Production Economics, 86, 45–154.
Kao, C., & Liu, S. T. (2005). Data envelopment analysis with imprecise data: An application of Taiwan machinery .rms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(2), 225–240.
León, T., Liern, V., Ruiz, J. L., & Sirvent, I. (2003). A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets and Systems, 139, 407–419.
Lertworasirikul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. W. (2003a). Fuzzy data envelopment analysis (DEA): A possibility approach. Fuzzy Sets and Systems, 139, 379–394.
Lertworasirikul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. W. (2003b). Fuzzy data envelopment analysis: A credibility approach. In J. L. Verdegay (Ed.), Fuzzy sets based heuristics for optimization (pp. 141–158). Berlin, Heidelberg: Springer- Verlag.
Lertworasirikul, S., Fang, S. C., Nuttle, H. L. W., & Joines, J. A. (2003). Fuzzy BCC model for data envelopment analysis. Fuzzy Optimization and Decision Making, 2(4), 337–358.
Liu, F. F. & Chen, C. L. (2009). The worst-practice DEA model with slack-based measurement. Computers & Industrial Engineering, 57, 496–505.
Liu, S. T. (2008). A fuzzy DEA/AR approach to the selection of flexible manufacturing systems. Computers and Industrial Engineering, 54(1), 66–76.
Liu, S. T., Chuang, M. (2009). Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries. Expert Systems with Applications, 36(2), 1105–1113.
Parkan, C., & Wang, Y. M. (2000). Worst Efficiency Analysis Based on Inefficient Production Frontier. Working Paper, Department of Management Sciences, City University of Hong Kong.
Saati, S., & Memariani, A. (2005). Reducing weight flexibility in fuzzy DEA. Applied Mathematics and Computation, 161, 611–622.
Saati, S., Menariani, A., & Jahanshahloo, G. R. (2002). Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optimization and Decision Making, 1, 255–267.
Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers and Mathematics with Applications, 24, 259–266.
Soleimani-damaneh, M., Jahanshahloo, G. R., & Abbasbandy, S. (2006). Computational and theoretical pitfalls in some current performance measurement techniques and a new approach. Applied Mathematics and Computation, 181(2), 1199–1207.
Triantis, K. (2003). Fuzzy non-radial data envelopment analysis (DEA) measures of technical efficiency in support of an integrated performance measurement system. International Journal of Automotive Technology and Management, 3, 328–353.
Triantis, K., & Girod, O. (1998). A mathematical programming approach for measuring technical efficiency in a fuzzy environment. Journal of Productivity Analysis, 10, 85–102.
Wang, Y. M., Greatbanks, R., & Yang, J. B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153(3), 347–370.
Wang, Y. M., Luo, Y., & Liang, L. (2009). Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Systems with Applications, 36, 5205–5211.
Wu, D., Yang, Z., & Liang, L. (2006). Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis. Applied Mathematics and Computation, 181(1), 271–281.
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Azizi, H., & Ganjeh Ajirlu, H. (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.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30, 1078–1092.
Charnes, A. & Cooper, W. W. (1962). Programming with fractional function. Naval Research Logistics Quarterly, 9, 181–185.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Dia, M. (2004). A model of fuzzy data envelopment analysis. INFOR, 42, 267–279.
Entani, T., Maeda, Y., & Tanaka, H. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136, 32–45.
Garcia, P. A. A., Schirru, R., & Melo, P. F. F. E. (2005). A fuzzy data envelopment analysis approach for FMEA. Progress in Nuclear Energy, 46, 359–373.
Guo, P., & Tanaka, H. (2001). Fuzzy DEA: A perceptual evaluation method. Fuzzy Sets and Systems, 119, 149–160.
Jahanshahloo, G. R., Soleimani-damaneh, M., & Nasrabadi, E. (2004). Measure of efficiency in DEA with fuzzy input–output levels: A methodology for assessing, ranking and imposing of weights restrictions. Applied Mathematics and Computation, 156, 175–187.
Kao, C., & Liu, S. T. (2000a). Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems, 113, 427–437.
Kao, C., & Liu, S. T. (2000b). Data envelopment analysis with missing data: An application to University libraries in Taiwan. Journal of the Operational Research Society, 51, 897–905.
Kao, C., & Liu, S. T. (2003). A mathematical programming approach to fuzzy efficiency ranking. International Journal of Production Economics, 86, 45–154.
Kao, C., & Liu, S. T. (2005). Data envelopment analysis with imprecise data: An application of Taiwan machinery .rms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(2), 225–240.
León, T., Liern, V., Ruiz, J. L., & Sirvent, I. (2003). A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets and Systems, 139, 407–419.
Lertworasirikul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. W. (2003a). Fuzzy data envelopment analysis (DEA): A possibility approach. Fuzzy Sets and Systems, 139, 379–394.
Lertworasirikul, S., Fang, S. C., Joines, J. A., & Nuttle, H. L. W. (2003b). Fuzzy data envelopment analysis: A credibility approach. In J. L. Verdegay (Ed.), Fuzzy sets based heuristics for optimization (pp. 141–158). Berlin, Heidelberg: Springer- Verlag.
Lertworasirikul, S., Fang, S. C., Nuttle, H. L. W., & Joines, J. A. (2003). Fuzzy BCC model for data envelopment analysis. Fuzzy Optimization and Decision Making, 2(4), 337–358.
Liu, F. F. & Chen, C. L. (2009). The worst-practice DEA model with slack-based measurement. Computers & Industrial Engineering, 57, 496–505.
Liu, S. T. (2008). A fuzzy DEA/AR approach to the selection of flexible manufacturing systems. Computers and Industrial Engineering, 54(1), 66–76.
Liu, S. T., Chuang, M. (2009). Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries. Expert Systems with Applications, 36(2), 1105–1113.
Parkan, C., & Wang, Y. M. (2000). Worst Efficiency Analysis Based on Inefficient Production Frontier. Working Paper, Department of Management Sciences, City University of Hong Kong.
Saati, S., & Memariani, A. (2005). Reducing weight flexibility in fuzzy DEA. Applied Mathematics and Computation, 161, 611–622.
Saati, S., Menariani, A., & Jahanshahloo, G. R. (2002). Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optimization and Decision Making, 1, 255–267.
Sengupta, J. K. (1992). A fuzzy systems approach in data envelopment analysis. Computers and Mathematics with Applications, 24, 259–266.
Soleimani-damaneh, M., Jahanshahloo, G. R., & Abbasbandy, S. (2006). Computational and theoretical pitfalls in some current performance measurement techniques and a new approach. Applied Mathematics and Computation, 181(2), 1199–1207.
Triantis, K. (2003). Fuzzy non-radial data envelopment analysis (DEA) measures of technical efficiency in support of an integrated performance measurement system. International Journal of Automotive Technology and Management, 3, 328–353.
Triantis, K., & Girod, O. (1998). A mathematical programming approach for measuring technical efficiency in a fuzzy environment. Journal of Productivity Analysis, 10, 85–102.
Wang, Y. M., Greatbanks, R., & Yang, J. B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153(3), 347–370.
Wang, Y. M., Luo, Y., & Liang, L. (2009). Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert Systems with Applications, 36, 5205–5211.
Wu, D., Yang, Z., & Liang, L. (2006). Efficiency analysis of cross-region bank branches using fuzzy data envelopment analysis. Applied Mathematics and Computation, 181(1), 271–281.
