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Iranian Journal of Management Studies
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Autumn 2017, Page 751-959
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Amirteimoori, A., Kordrostami, S., Nasrollahian, P. (2017). A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values. Iranian Journal of Management Studies, 10(4), 905-916. doi: 10.22059/ijms.2017.235592.672706
Alireza Amirteimoori; Sohrab Kordrostami; Pooya Nasrollahian. "A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values". Iranian Journal of Management Studies, 10, 4, 2017, 905-916. doi: 10.22059/ijms.2017.235592.672706
Amirteimoori, A., Kordrostami, S., Nasrollahian, P. (2017). 'A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values', Iranian Journal of Management Studies, 10(4), pp. 905-916. doi: 10.22059/ijms.2017.235592.672706
Amirteimoori, A., Kordrostami, S., Nasrollahian, P. A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values. Iranian Journal of Management Studies, 2017; 10(4): 905-916. doi: 10.22059/ijms.2017.235592.672706

A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values

Article 6, Volume 10, Issue 4, Autumn 2017, Page 905-916  XML PDF (275 K)
Document Type: Research Paper
DOI: 10.22059/ijms.2017.235592.672706
Authors
Alireza Amirteimoori1; Sohrab Kordrostami2; Pooya Nasrollahian 1
1Department of Applied Mathematics, Islamic Azad University, Rasht Branch, Rasht, Iran
2Department of Applied Mathematics, Islamic Azad University, Lahijan Branch, Lahijan, Iran
Abstract
Using super-efficiency, with regard to ranking efficient units, is increasing in DEA. However, this model has some problems such as the infeasibility. Thus, this article studies infeasibility of the input-based super-efficiency model (because of the zero inputs and outputs), and presents a solution by adding two virtual DMUs with mean values (one for inputs and one for outputs). Adding virtual DMUs to Production Possibility Set (PPS) changed the basic super-efficiency model, so a new model is proposed for solving this problem. Finally, the newly developed model is illustrated with a real-world data set.
Keywords
DEA; super-efficiency; infeasibility; mean values
Main Subjects
Optimization, Stochastic Models and Simulation
Article Title [Persian]
روشی برای حل مشکل نشدنی بودن ابرکارایی به کمک داده های مجازی با مقادیر میانگین
Authors [Persian]
علیرضا امیرتیموری1; سهراب کردرستمی2; پویا نصراللهیان1
1دانشکده علوم پایه ، دانشگاه آزاد اسلامی واحد رشت ، رشت، ایران
2دانشکده علوم پایه ، دانشگاه آزاد اسلامی واحد لاهیجان، لاهیجان، ایران
Abstract [Persian]
استفاده از ابرکارایی در تحلیل پوششی داده­ها برای رتبه­بندی واحدهای کارا روز به روز در حال افزایش است. با این حال، این مدل دارای مشکلاتی همچون نشدنی بودن می­باشد. بنابراین در این مقاله به بیان این مشکل در مدل ورودی محور پرداخته شده( به خاطر وجود ورودی و خروجی صفر) و راه­حلی با اضافه کردن واحدهای مجازی با مقدار میانگین پیشنهاد شده­است. اضافه کردن واحد مجازی به مجموعه امکان تولید سبب تغییر در مدل  ابرکارایی پایه می­شود، بنابراین، مدل­های جدید برای حل این مشکل ارائه شده­است. در انتها،  یک مثال با داده­های واقعی برای روشن شدن مطلب بیان شده­است.
Keywords [Persian]
تحلیل پوششی داده‌ها، ابرکارایی، نشدنی بودن، مقدار میانگین
References
  1. Andersen, P., & Petersen, N. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10) , 1261-1264.
  2. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092.
  3. Banker, R. D., & Thrall, R. (1992). Estimation of returns to scale using data envelopment analysis. European Journal of Operational Research, 62(1), 74-84.
  4. Charnes, A., Cooper, W., & Rhodes, E. (1979). Measuring the efficiency of decision-making units. European Journal of Operational Research, 3(4), 339.
  5. Charnes, A., Haag, S., Jaska, P., & Semple, J. (1992). Sensitivity of efficiency classifications in the additive model of data envelopment analysis. International Journal of Systems Science, 23(5), 789-798.
  6. Charnes, A., Rousseau, J. J., & Semple, J. H. (1996). Sensitivity and stability of efficiency classifications in data envelopment analysis. Journal of Productivity Analysis, 7(1), 5-18.
  7. Chen, Y. (2004). Ranking efficient units in DEA. OMEGA, 32, 213-219.
  8. Esmaeili, F. S., & Rostamy-Malkhalifeh, M. (2017). Data envelopment analysis with fixed inputs, undesirable outputs and negative data. Data Envelopment Analysis and Decision Science, 2017(1), 1-6.
  9. Mehrabian S., Alirezaee M. R., & Jahanshahloo G. R. (1999).  A complete efficiency ranking of decision making units in data envelopment analysis. Computer Optimization Apply, 14, 261-266.
  10. Rezai, F. R., Balf, H. Z., Jahanshahloo, G., & Lotfi, F. H. (2012). Ranking efficient DMUs using the Tchebycheff norm. Applied Mathematical Modeling, 36(1), 46-56.
  11. Seiford L. M., & Thrall R. M. (1990). Recent developments in DEA: The mathematical programming approach to frontier analysis. Journal of Econometrics, 46, 7-38.
  12. Seiford, L. M., & Zhu, J. (1998). Stability regions for maintaining efficiency in data envelopment analysis. European Journal of Operational Research, 108(1), 127-139.
  13. Seiford, L. M., & Zhu, J. (1999). Infeasibility of super-efficiency data envelopment analysis models. INFOR: Information Systems and Operational Research, 37(2), 174-187.
  14. Sueyoshi, T. (1999). DEA non-parametric ranking test and index measurement: Slack-adjusted DEA and an application to Japanese agriculture cooperatives. Omega, 27(3), 315-326.
  15. Thrall R. M. (1996). Duality, classification and slack in data envelopment analysis. The Annals of Operational Research, 66, 109-138.
  16. Tone, K. (2002). A slacks-based measure of super-efficiency in data envelopment analysis. European Journal of Operational Research, 143(1), 32-41.
  17. Zhu, J. (1996). Robustness of the efficient DMUs in data envelopment analysis. European Journal of Operational Research, 90(3), 451-460.
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