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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. 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
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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

9. 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
10. Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning, 20(3), 273-297. https://doi.org/10.1007/BF00994018
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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 .
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. Ramasubramanian, K., Singh, A. Machine Learning Using R, 2nd Edition, Apress, Delhi India, 2019. https://doi.org/10.1007/978-1-4842-4215-5
37. 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
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. 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
50. 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
51. 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
52. 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
53. 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
54. 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.
55. 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
56. 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
57. 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
58. 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