Ranking Decision Making Units (DMUs) Using Support Vector Machines (SVM) & Ideal DMU

Year 2025, Volume: 9 Issue: 1, 24 - 35, 01.07.2025

Mehmet Ünsal , Volkan Soner Özsoy , H. Hasan Örkcü

https://doi.org/10.56554/jtom.1532492

Abstract

Ranking of decision making units (DMUs) is an important issue in a production process. Therefore, it is one of the most frequently studied subjects in the theory and practice studies in Data Envelopment Analysis literature. Recently, machine learning-based methods have also been used for crutial problems in literature such as ranking of DMUs and determining the efficiency frontier. This study proposes a new hybrid approach to rank DMUs. This approach is based on the Support Vector Machines, which is a machine learning method, and the Ideal DMU, which has an important place in the DEA literature. The theoretical details of this method are explained, and the performance of the model is demonstrated through application and simulation studies.

Keywords

Ranking, Decision making unit, Support Vector Machines, Ideal DMU

References

• Afsharian, M., & Ahn, H. (2017). Multi-period productivity measurement under centralized management with an empirical illustration to German saving banks. OR Spectrum, 39(3), 881-911. https://doi.org/10.1007/s00291- 016-0465-8
• Allen, R., Athanassopoulos, A., Dyson, R. G., & Thanassoulis, E. (1997). Weights restrictions and value judgements in data envelopment analysis: evolution, development and future directions. Annals of Operations Research, 73, 13-34. https://doi.org/10.1023/A:1018968909638
• Azadeh, A., Amalnick, M. S., Ghaderi, S. F., & Asadzadeh, S. M. (2007). An integrated DEA PCA numerical taxonomy approach for energy efficiency assessment and consumption optimization in energy intensive manufacturing sectors. Energy Policy, 35(7), 3792-3806. https://doi.org/10.1016/j.enpol.2007.01.018
• Bal, H., & Örkcü, H. H. (2007). A goal programming approach to weight dispersion in data envelopment analysis. Gazi University Journal of Science, 20(4), 117-125. Retrieved from https://dergipark.org.tr/en/pub/gujs/issue/7399/96859
• Bal, H., Örkcü, H. H., & Çelebioğlu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Computers & Industrial Engineering, 54(3), 502-512. https://doi.org/10.1016/j.cie.2007.09.001
• 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. https://doi.org/10.1287/mnsc.30.9.1078
• Boser, B. E., Guyon, I. M., & Vapnik, V. N. (1992). A training algorithm for optimal margin classifiers. In Proceedings of the fifth annual workshop on Computational Learning Theory (pp. 144-152). https://doi.org/10.1145/130385.130401
• Bouzidis, T., & Karagiannis, G. (2022). An alternative ranking of DMUs performance for the ZSG-DEA model. Socio-Economic Planning Sciences, 81, 101179. https://doi.org/10.1016/j.seps.2021.101179
• Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8
• Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning, 20(3), 273-297. https://doi.org/10.1007/BF00994018
• Davoodi, A., & Rezai, H. Z. (2012). Common set of weights in data envelopment analysis: a linear programming problem. Central European Journal of Operations Research, 20(2), 355-365. https://doi.org/10.1007/s10100- 011-0195-6
• Esteve, M., Aparicio, J., Rodriguez-Sala, J. J., & Zhu, J. (2022). Random Forests and the measurement of superefficiency in the context of Free Disposal Hull. European Journal of Operational Research. 304(2), 729-744. https://doi.org/10.1016/j.ejor.2022.04.024
• Fallahpour, A., Kazemi, N., Molani, M., Nayyeri,S., Ehsani, M. (2018) An Intelligence-Based Model for Supplier Selection Integrating Data Envelopment Analysis and Support Vector Machine. Interdiciplinary Journal of Management Studies, 11 (2), 209-241. https://doi.org/10.22059/ijms.2018.237965.672750
• Franc, V., & Hlavác, V. (2002). Multi-class support vector machine. In 2002 International Conference on Pattern Recognition, 2, 236-239. IEEE. https://doi.org/10.1109/ICPR.2002.1048282
• Giraleas, D., Emrouznejad, A., & Thanassoulis, E. (2012). Productivity change using growth accounting and frontier-based approaches: Evidence from a Monte Carlo analysis. European Journal of Operational Research 222 (3):673–683. https://doi.org/10.1016/j.ejor.2012.05.015
• Gonçalves, A. C., Almeida, R. M., Lins, M. P. E., & Samanez, C. P. (2013). Canonical correlation analysis in the definition of weight restrictions for data envelopment analysis. Journal of Applied Statistics, 40(5), 1032-1043. https://doi.org/10.1080/02664763.2013.772571
• Guerrero, N. M., Aparicio, J., & Valero-Carreras, D. (2022). Combining Data Envelopment Analysis and Machine Learning. Mathematics, 10(6), 909. https://doi.org/10.3390/math10060909
• Hearst, M. A., Dumais, S. T., Osuna, E., Platt, J., & Scholkopf, B. (1998). Support vector machines. IEEE Intelligent Systems and their applications, 13(4), 18-28. https://doi.org/10.1109/5254.708428
• Huang, G., Chen, H., Zhou, Z., Yin, F., & Guo, K. (2011). Two-class support vector data description. Pattern Recognition, 44(2), 320-329. https://doi.org/10.1016/j.patcog.2010.08.025
• Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Khanmohammadi, M., Kazemimanesh, M., & Rezaie, V. (2010). Ranking of units by positive ideal DMU with common weights. Expert Systems with Applications: An International Journal, 37(12), 7483-7488. https://doi.org/10.1016/j.eswa.2010.04.011
• Jahanshahloo, G. R., Memariani, A., ., Hosseinzadeh Lotfi, F, & Rezai, H. Z. (2005). A note on some of DEA models and finding efficiency and complete ranking using common set of weights. Applied Mathematics and Computation, 166(2), 265-281. https://doi.org/10.1016/j.amc.2004.04.088
• Kao, H. Y., Chang, T. K., & Chang, Y. C. (2013). Classification of hospital web security efficiency using data envelopment analysis and support vector machine. Mathematical Problems in Engineering, 2013, 542314 .
• Kuosmanen, T., & Johnson, A. L. (2010). Data envelopment analysis as nonparametric least-squares regression. Operations Research, 58(1), 149-160. https://doi.org/10.1287/opre.1090.0722
• Lam, K. F. (2010). In the determination of weight sets to compute cross-efficiency ratios in DEA. Journal of the Operational Research Society, 61(1), 134-143. https://doi.org/10.1057/jors.2008.138
• Liu, F. H. F., & Peng, H. H. (2008). Ranking of units on the DEA frontier with common weights. Computers and Operations Research, 35(5), 1624-1637. https://doi.org/10.1016/j.cor.2006.09.006
• Lozano, S., Soltani, N., & Dehnokhalaji, A. (2020). A compromise programming approach for target setting in DEA. Annals of Operations Research, 288(1), 363-390. https://doi.org/10.1007/s10479-019-03486-7
• Mecit, E. D., & Alp, I. (2012). A new restricted model using correlation coefficients as an alternative to crossefficiency evaluation in Data Envelopment Analysis. Hacettepe Journal of Mathematics and Statistics, 41(2), 321-335. Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/7755/101371
• Mecit, E. D., & Alp, I. (2013). A new proposed model of restricted data envelopment analysis by correlation coefficients. Applied Mathematical Modelling, 37(5), 3407-3425. https://doi.org/10.1016/j.apm.2012.07.010
• Michali, M., Emrouznejad, A., Dehnokhalaji, A., & Clegg, B. (2021). Noise-pollution efficiency analysis of European railways: A network DEA model. Transportation Research Part D: Transport and Environment, 98, 102980. https://doi.org/10.1016/j.trd.2021.102980
• Örkcü, H. H., Ünsal, M. G., & Bal, H. (2015). A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity. Annals of Operations Research, 235(1), 599-623. https://doi.org/10.1007/s10479-015-1916-3
• Pecha, M., Horák, D. (2020). Analyzing l1-loss and l2-loss Support Vector Machines Implemented in PERMON Toolbox. In: Zelinka, I., Brandstetter, P., Trong Dao, T., Hoang Duy, V., Kim, S. (eds) AETA 2018 - Recent
• Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2018. Lecture Notes in Electrical Engineering, vol 554. Springer, Cham. https://doi.org/10.1007/978-3-030-14907-9_2
• Petridis,K., Tampakoudis, I., Drogalas, G., Kiosses, N. (2022) A Support Vector Machine model for classification of efficiency: An application to M&A. Research in International Business and Finance 61,101633. https://doi.org/10.1016/j.ribaf.2022.101633
• Podinovski, V. V. (1999). Side effects of absolute weight bounds in DEA models. European Journal of Operational Research, 115(3), 583-595. https://doi.org/10.1016/S0377-2217(98)00124-6
• Premachandra, I. M. (2001). A note on DEA vs principal component analysis: An improvement to Joe Zhu's approach. European Journal of Operational Research, 132(3), 553-560. https://doi.org/10.1016/S0377- 2217(00)00145-4
• Ramasubramanian, K., Singh, A. Machine Learning Using R, 2nd Edition, Apress, Delhi India, 2019. https://doi.org/10.1007/978-1-4842-4215-5
• Ramón, N., Ruiz, J. L., & Sirvent, I. (2012). Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players. Expert Systems with Applications, 39(5), 4882- 4889. https://doi.org/10.1016/j.eswa.2011.10.004
• Rezaie, V., Ahmad, T., Daneshfard, C., Khanmohammadi, M., & Nejatian, S. (2013). An Integrated modeling based on data envelopment analysis and support vector machines: A case modeling of Tehran Social Security Insurance Organization. World Applied Sciences Journal (Mathematical Applications in Engineering), 21, 138- 142. https://doi.org/10.5829/idosi.wasj.2013.21.mae.99940
• Saati, S., Hatami-Marbini, A., Agrell, P. J., & Tavana, M. (2012). A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial & Management Optimization, 8(3), 623-637. http://dx.doi.org/10.3934/jimo.2012.8.623
• Saradhi, V.V., & Girish, K.R. (2015). Effective Parameter Tuning of SVMs Using Radius/Margin Bound Through Data Envelopment Analysis, Neural Process Letters 41:125–138. https://doi.org/10.1007/s11063-014-9338-9
• Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation, 1986(32), 73-105. https://doi.org/10.1002/ev.1441
• Suthaharan, S. (2016). Support Vector Machine. In: Machine Learning Models and Algorithms for Big Data Classification. Integrated Series in Information Systems, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7641-3_9
• Thompson, R. G., Singleton Jr, F. D., Thrall, R. M., & Smith, B. A. (1986). Comparative site evaluations for locating a high-energy physics lab in Texas. Interfaces, 16(6), 35-49. https://doi.org/10.1287/inte.16.6.35
• Tsionas, M. (2022). Efficiency estimation using probabilistic regression trees with an application to Chilean manufacturing industries. International Journal of Production Economics, 249, 108492. https://doi.org/10.1016/j.ijpe.2022.108492
• Ünsal, M. G. & Orkcu, H. H. (2017). Ranking decision making units with the integration of the multidimensional scaling algorithm into PCA-DEA. Hacettepe Journal of Mathematics and Statistics, 46(6), 1187- 1197. Retrieved from https://dergipark.org.tr/en/pub/hujms/issue/38350/444401
• Ünsal, M. G., & Nazman, E. (2020). Investigating socio-economic ranking of cities in Turkey using data envelopment analysis (DEA) and linear discriminant analysis (LDA). Annals of Operations Research, 294(1), 281-295. https://doi.org/10.1007/s10479-017-2748-0
• Ünsal, M. G., & Örkcü, H. H. (2016). A note for weight restriction in the ARIII model based on correlation coefficients. Applied Mathematical Modelling, 40(23-24), 10820-10827. https://doi.org/10.1016/j.apm.2016.06.052
• Valero-Carreras, D., Aparicio, J., & Guerrero, N. M. (2021). Support vector frontiers: A new approach for estimating production functions through support vector machines. Omega, 104, 102490. https://doi.org/10.1016/j.omega.2021.102490
• Valero-Carreras, D., Aparicio, J., & Guerrero, N. M. (2022). Multi-output Support Vector Frontiers. Computers & Operations Research, 143, 105765. https://doi.org/10.1016/j.cor.2022.105765
• Wang, Y. M., Chin, K. S., & Luo, Y. (2011). Cross-efficiency evaluation based on ideal and anti-ideal decision making units. Expert Systems with Applications, 8(38), 10312-10319. https://doi.org/10.1016/j.eswa.2011.02.116
• Wang, Y. M., Luo, Y., & Liang, L. (2009). Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis. Journal of Computational and Applied Mathematics, 223(1), 469- 484. https://doi.org/10.1016/j.cam.2008.01.022
• Wanke, P., & Barros, C.P. (2017) Efficiency thresholds and cost structure in Senegal airports, Journal of Air Transport Management 58, 100-112. https://doi.org/10.1016/j.jairtraman.2016.10.005
• Yang, X., & Dimitrov, S. (2017). Data envelopment analysis may obfuscate corporate financial data: using support vector machine and data envelopment analysis to predict corporate failure for nonmanufacturing firms. INFOR: Information Systems and Operational Research, 55(4), 295-311. https://doi.org/10.1080/03155986.2017.1282290
• Yeh, C. C., Chi, D. J., & Hsu, M. F. (2010). A hybrid approach of DEA, rough set and support vector machines for business failure prediction. Expert Systems with Applications, 37(2), 1535-1541.
• Zhang, Q., Wang, C. (2019). DEA efficiency prediction based on IG–SVM. Neural Computing and Applications, 31:8369–8378 https://doi.org/10.1007/s00521-018-3904-4
• Zhao, L., Wang, B., He, J., Jiang, X. (2022) SE-DEA-SVM evaluation method of ECM operational disposition scheme. Journal of Systems Engineering and Electronics 33 (3), 600 – 611. https://doi.org/10.23919/JSEE.2022.000058
• Zhu, N., Zhu, C., Emrouznejad, A. (2021) A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies, Journal of Management Science and Engineering 6(4), 435-448. https://doi.org/10.1016/j.jmse.2020.10.001
• Zhu, J. (1998). Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities. European Journal of Operational Research, 111(1), 50-61. https://doi.org/10.1016/S0377-2217(97)00321-4