نوع مقاله : مقاله پژوهشی - کاربردی

نویسندگان

گروه ریاضی، دانشگاه پیام نور، تهران، ایران.

چکیده

مدل تحلیل پوششی داده‌ها مبتنی بر برنامه‌ریزی آرمانی (GDEA) با افزایش میزان تفکیک‌پذیری و ارائه وزن‌های واقعی به واحدهای تصمیم‌گیری (DMU) به دنبال رفع نواقص مدل تحلیل پوششی داده‌ها (DEA) کلاسیک و پایه‌ای می‌باشد. نتایج تجربی حاکی از عدم رفع کامل نقایص در برخی از نمونه‌های مورد آزمایش توسط مدل‌های GDEA می‌باشند.همچنین در محاسبه جواب بهینه با روش‌های مختلف ارزیابی کارایی واحدها، با دسته‌ای از جواب‌های بهینه پارتو مواجه هستیم که یک مدیر تصمیم‌گیرنده را در انتخاب مناسب‌ترین جواب با چالش جدی مواجه می‌کند. برای رفع این معضل، در گام نخست در این مقاله، با استفاده از مفاهیم منطق فازی، رویکرد F-GDEA را که یک مدل مبتنی بر منطق فازی در حل مدل‌های GDEA است، پیشنهاد می‌دهیم که باعث افزایش قدرت تفکیک‌پذیری روش‌ها در رتبه‌بندی واحدها می‌شود. در گام دوم، با در نظر گرفتن رتبه‌بندی‌های متنوع حاصل از اعمال مدل‌های برنامه‌ریزی مختلف، با استفاده از رویکرد F-GDEA یک رویکرد تلفیقی فازی جدید به نام اختصاری HF-GDEA پیشنهاد می‌دهیم. با این رویکرد پیشنهادی، رتبه‌‌بندی حاصل از روش‌های مختلف را با یکدیگر تلفیق نموده و یک‌ رتبه‌بندی جدید برای واحدهای تصمیم‌گیری ارائه می‌دهیم، به‌عبارت‌دیگر، رویکرد HF-GDEA، امکان مقایسه و درنتیجه انتخاب یک جواب بهینه از بین جواب‌های بهینه پارتو را فراهم می‌سازد. در پایان رویکرد پیشنهادی بر روی دو نمونه کاربردی اعمال و نتایج عددی آن آورده شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

HF-GDEA: hybrid fuzzy approach to Integrate ranking of goal models in DEA

نویسندگان [English]

  • Ham,id Reza Yoosefzade
  • Azam Teimuri
  • Aghile Heidari

Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.

چکیده [English]

The models of Data Envelopment Analysis (DEA) based on Goal Programming (GDEA) seeks to address some drawbacks of classical DEA by increasing the degree of resolution and providing real weights to Decision-Making Units (DMUs). Experimental results indicate that the GDEA models do not completely cope with these in some cases which are tested. Also, in calculating the optimal solution with different methods of evaluating the efficiency of units, we are faced with a group of Pareto optimal solutions that make a decision maker facing a serious challenge in choosing the most appropriate solution. To solve this, in the first step, this paper uses the concepts of fuzzy logic and then proposes the F-GDEA approach based on fuzzy logic in solving the GDEA models, which increases the resolution of the methods to rank the units. In the second step, by using the F-GDEA approach, we propose a new hybridized fuzzy approach called HF-GDEA for short, taking into account the various ranking results from the different programming models. With this new proposed approach, we combine the rankings obtained from different methods and present a new ranking for the DMUs. In other words, the HF-GDEA approach makes it possible to compare and thus select an optimal solution from Pareto's optimal solutions set. Finally, the proposed approach is applied to two practical examples and their numerical results are presented.

کلیدواژه‌ها [English]

  • Goal Programming
  • Multi-Objective Optimization
  • Data envelopment analysis (DEA)
  • Fuzzy logic
  • Pareto solutions
Aldamak, A., & Zolfaghari, S. (2017). Review of efficient units in data envelopment analysis. Measurement science, 39(10), 1261-1264.
Amin, G. R., Al-Muharrami, S., & Toloo, M. (2019). A combined goal programming and inverse dea method for target setting in mergers. Expert systems with applications, 115, 412-417.
Amiri, M., Alimi, A., Abtahi, S. (2007). Offering a model in data envelopment analysis to obtain common set of weights using fuzzy logic. Industrial management studies, 6(17), 135-151. (In Persian). https://jims.atu.ac.ir/article_4452.html
Azizi, H. (2012). Efficiency assessment in data envelopment analysis using efficient and inefficient frontiers. IQBQ, 16 (3), 153-173. (In Persian). http://mri.modares.ac.ir/article-19-118-fa.html
Borzoei, S., & Zohreh-bandian, M. (2013). Common weights for the evaluation of decision-making units with nonlinear virtual inputs and outputs. International journal of data envelopment analysis, ‎1(3), 167-173.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring efficiency of decision making units. ‎European journal of operational research, 2(6), 429–444.
Chen, Y. (2005). On preference structure in data envelopment analysis. International journal of information technology & decision making4(03), 411-431.
Chiang, C. I., & Tzeng, G. H. (2000). A multiple objective programming approach to data envelopment analysis. In New frontiers of decision making for the information technology era (pp. 270-285).  https://doi.org/10.1142/9789812792907_0015
Estellita Lins, M. P., Angulo-Meza, L., & Moreira da Silva, A. C. (2004). A multi-objective approach to determine alternative targets in data envelopment analysis. Journal of the operational research society55(10), 1090-1101.
Golany, B. (1988). An interactive MOLP procedure for the extension of DEA to effectiveness analysis. Journal of the operational research society, 39(8), 725-734
Halme, M., Joro, T., Korhonen, P., Salo, S., & Wallenius, J. (1999). A value efficiency approach to incorporating preference information in data envelopment analysis. Management science, 45(1), 103-115.    
Hatami-Marbini, A., Tavana, M., Agrell, P. J., Lotfi, F. H., & Beigi, Z. G. (2015). A common-weights DEA model for centralized resource reduction and target setting. Computers & industrial engineering79, 195-203.
Hemati, M., & Abbasi, S. (2016). Representing a multi-step technique of the common weights and TOPSIS in order to ranking of units. Modern research in decision making, 1(2), 193-215. (In Persian). http://journal.saim.ir/article_21123.html?lang=en
Jafarian Moghadam, A. R., & Gheisari, K. (2010). Dynamic multi-objective model of fuzzy data envelopment analysis. Industrial management, 2(1), 19-36. (In Persian). https://journals.ut.ac.ir/article_21308_2.html?lang=en
Jahanshahloo, G. R., Lotfi, F. H., Khanmohammadi, M., Kazemimanesh, M., & Rezaie, V. (2010). Ranking of units by positive ideal DMU with common weights. Expert systems with applications37(12), 7483-7488.
Joro, T., Korhonen, P., & Wallenius, J. (1998). Structural comparison of data envelopment analysis and multiple objective linear programming. Management science44(7), 962-970.
Kao, C., & Hung, H. T. (2005). Data envelopment analysis with common weights: the compromise solution approach. Journal of the operational research society56(10), 1196-1203.
Kwon, H. B., Marvel, J. H., & Roh, J. J. (2016). Three-stage performance modeling using DEA–BPNN for better practice benchmarking. Expert systems with applications71, 429-441.
Liu, F. H. F., & Peng, H. H. (2008). Ranking of units on the DEA frontier with common weights. Computers & operations research35(5), 1624-1637.
Maddahi, R., & Yazdani, H. R. (2020). Ranking of decision-making units using data envelopment analysis taking into account multiple time periods. Journal of decision making and operations research, 5(1), 72-82. (In Persian). http://www.journal-dmor.ir/article_114162.html
Makuei, A., Alinezhad, A., KIANI, M. R., & Zohrehbandian, M. (2008). A goal programming method for finding common weights in DEA with an improved discriminating power for efficiency. Journal of industrial and systems engineering, 1(4), 293-303.
Omrani, H. (2013). Common weights data envelopment analysis with uncertain data: a robust optimization approach. Computers & industrial engineering66(4), 1163-1170.
Sadeghi Moghdam, M. R., & Gharib, A. H. (2013). Performance evaluation using fuzzy data envelopment analysis model and application of fuzzy constraints to control weights and find general weights. Journal of industrial management, university of Tehran, 5(2), 74-84. (In Persian). https://www.sid.ir/fa/journal/ViewPaper.aspx?id=231595
Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: critique and extensions. New directions for program evaluation1986(32), 73-105.
Silalahi, A., Natalia, C., & Martio, C. P. (2020). Integration of data envelopment analysis and goal programming in supplier selection optimization. Integration29(7s), 3178-3186.
Soleimani-Chamkhorami, K., Hosseinzadeh Lotfi, F., Jahanshahloo, G., & Rostamy-Malkhalifeh, M. (2020). A ranking system based on inverse data envelopment analysis. IMA journal of management mathematics31(3), 367-385.
Stewart, T. J. (1996). Relationships between data envelopment analysis and multicriteria decision analysis. Journal of the operational research society47(5), 654-665.
Thanassoulis, E., & Dyson, R. G. (1992). Estimating preferred target input-output levels using data envelopment analysis. European journal of operational research56(1), 80-97.
Trigui, S., Cheikhrouhou, O., Koubaa, A., Baroudi, U., & Youssef, H. (2017). FL-MTSP: a fuzzy logic approach to solve the multi-objective multiple traveling salesman problem for multi-robot systems. Soft computing21(24), 7351-7362.
Yu, J. R., Tzeng, Y. C., Tzeng, G. H., Yu, T. Y., & Sheu, H. J. (2004). A fuzzy multiple objective programming to DEA with imprecise data. International journal of uncertainty, fuzziness and knowledge-based systems12(05), 591-600.
Zhu, J. (1996). Data envelopment analysis with preference structure. Journal of the operational research society47(1), 136-150.