Modelling Robust Optimization in DEA With Ratio Data: A Case Study of Commercial Banks
محورهای موضوعی : Financial Mathematics
Javad Gerami
1
(
Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
)
کلید واژه: Data Envelopment Analysis, Ratio Analysis , Robust Optimization, Common Set of Weights Uncertainty , Banking, ,
چکیده مقاله :
In many practical problems, we face situations where the data ratio is important for the decision-maker (DM). Data envelopment analysis ratio-based (DEA-R) and ratio analysis models are presented to deal with the above issue in data envelopment analysis (DEA). If the data is uncertain, it is no longer possible to use the basic DEA-R and ratio analysis models to evaluate the efficiency of decision-making units (DMUs). In this paper, we will first discuss robust optimization modelling based on DEA-R models. In this regard, we consider a case where the inputs have an uncertain numerical value and the outputs have certain values. In the following, we present the ratio analysis model based on the set of common weights of all the ratios of input to output components and obtain this model for robust optimization. To show the validity of the proposed approach, we use it to evaluate the efficiency of 38 excellent banks that compete in the global market and compare the results of the proposed approach in this paper with the results of previous approaches.
In many practical problems, we face situations where the data ratio is important for the decision-maker (DM). Data envelopment analysis ratio-based (DEA-R) and ratio analysis models are presented to deal with the above issue in data envelopment analysis (DEA). If the data is uncertain, it is no longer possible to use the basic DEA-R and ratio analysis models to evaluate the efficiency of decision-making units (DMUs). In this paper, we will first discuss robust optimization modelling based on DEA-R models. In this regard, we consider a case where the inputs have an uncertain numerical value and the outputs have certain values. In the following, we present the ratio analysis model based on the set of common weights of all the ratios of input to output components and obtain this model for robust optimization. To show the validity of the proposed approach, we use it to evaluate the efficiency of 38 excellent banks that compete in the global market and compare the results of the proposed approach in this paper with the results of previous approaches.
[1] Afsharian, M., Ahn, H., Guntram Harms, S., A review of DEA approaches applying a common set of weights: The perspective of centralized management, European Journal of Operational Research, 2021; 294: 3–15. Doi: 10.1016/j.ejor.2021.01.001.
[2] Arabmaldar, A., Jablonsky, J., Hosseinzadeh Saljooghi, F., A new robust DEA model and super effi-ciency measure. Optimization, 2017; 66 (5): 723–736.Doi: 10.1080/02331934.2017.1295047.
[3] Arabmaldar, A., Mensah, E. K., Toloo, M., Robust worst-practice interval DEA with non-discretionary factors, Expert Systems with Applications, 2021;182: 115256. Doi: 10.1016/j.eswa.2021.115256.
[4] Arabmaldar, A., Sahoo, B. K., Ghiyasi, M., A generalized robust data envelopment analysis model based on directional distance function. European Journal of Operational Research, 2023; 311(2):617–632. Doi:10.1016/j.ejor.2023.05.005.
[5] Arabmaldar, A., Hatami-Marbini, A., Loske, D., Hammerschmidt, M., Klumpp, M., Robust data envel-opment analysis with variable budgeted uncertainty, European Journal of Operational Research, Availa-ble online 3 January 2024 In Press, Corrected Proof. Doi:10.1016/j.ejor.2023.11.043.
[6] Bazaraa, M. S., Jarvis, J. J., Sherali, H. D., Linear programming and network flows (4th ed.). Hoboken, New Jersey: John Wiley & Sons, 2010.
[7] Ben-Tal, A., Nemirovski, A., Robust solutions of uncertain linear programs. Operations Research Let-ters, 1999; 25(1): 1–13. Doi:10.1016/S0167-6377(99)00016-4.
[8] Ben-Tal, A., Nemirovski, A., Robust solutions of Linear Programming problems contaminated with un-certain data. Mathematical Programming, 2000; 88(3):411–424. Doi:10.1007/PL00011380.
[9] Ben-Tal, A., Nemirovski, A., Lectures on modern convex optimization: Analysis, algorithms, and engi-neering applications. Philadelphia: Society for Industrial and Applied Mathematics, 2001.
[10] Bertsimas, D., Pachamanova, D., Sim, M. (2004). Robust linear optimization under general norms. Operations Research Letters, 2004; 32(6):510–516. Doi: 10.1016/j.orl.2003.12.007.
[11] Bertsimas, D., Sim, M., Robust discrete optimization and network flows. Mathematical Programming, 2003; 98(1-3): 49–71. Doi:10.1007/s10107-003- 0396-4.
[12] Bertsimas, D., Sim, M., The Price of robustness, Operations Research, 2004; 52(1), P. 35–53. Doi:10.1287/opre.1030.0065.
[13] Bertsimas, D., Sim, M., Tractable approximations to robust conic optimization problems. Mathemati-cal Programming, 2006; 107(1-2): 5–36. Doi:10. 1007/s10107-005-0677-1.
[14] Charnes, A., Cooper, W. W., Rhodes, E., Measuring the efficiency of decision making units. European Journal of Operational Research, 1978; 2(6): 429–444. Doi:10.1016/0377-2217(78)90138-8.
[15] Chen, Y.-W., Larbani, M., Chang, Y.-P., Multi objective data envelopment analysis. Journal of the Operational Research Society, 2009; 60(11): 1556–1566. doi:10.1057/jors.2009.92.
[16] Chen, Wen-Chih, McGinnis, Leon F., Reconciling ratio analysis and DEA as performance assessment tools, European journal of operational research, 2007;178(1): 277-291. Doi:10.1016/j.ejor.2005.06.071.
[17] Contreras I., Lozano, S. Hinojosa, M. A., A bargaining approach to determine common weights in DEA. Operational Research, 2019; 21(3): 2181-2201. Doi:10.1007/s12351-019-00498-w.
[18] Contreras I. (2021). A review of the literature on DEA models under common set of weights, Journal of Modelling in Management, 2021; 15(4):1277-1300. Doi:10.1108/JM2-02-2019-0043.
[19] Despic O., Despic, M., Paradi J. C., DEA-R: Ratio-based comparative efficiency model, its mathemati-cal relation to DEA and its use in applications, Journal of Productivity Analysis, 2007; 28:33–44. Doi:10.1007/s11123-007-0050-x
[20] Dehnokhalaji, A., Khezri, S., Emrouznejad, A., A box-uncertainty in DEA: A robust performance measurement framework. Expert Systems with Applications, 2022; 187:115855. Doi:10.1016/j.eswa.2021.115855.
[21] Dyson, R. G., Thanassoulis, E., Reducing weight flexibility in data envelopment analysis. Journal of the Operational Research Society, 1988; 39(6): 563–576. Doi:10.2307/2582861.
[22] Emrouznejad, A., Amin, Gh. R., DEA models for ratio data: Convexity consideration. Applied Mathe-matical Modelling, 2009; 33, 486–498. Doi: 10.1016/j.apm.2007.11.018.
[23] Fernandez-Castro, A., Smith, P., Towards a general non-parametric model of corporate performance. Omega, 1994; 22(3): 237–49. Doi:10.1016/0305-0483(94)90037-x.
[24] Ghazi, A., Hosseinzadeh Lotfi, F., Assessment and budget allocation of Iranian natural gas distribu-tion company- A CSW DEA based model, Socio-Economic Planning Sciences, 2018 ; 66: 112-118. Doi: 10.1016/j.seps.2018.07.009.
[25] Gerami, J., Mozaffari, M. R. and Wanke, P.F., A multi-criteria ratio-based approach for two-stage data envelopment analysis, Expert Systems with Applications, 2020; 158: 113508. Doi: 10.1016/j.eswa.2020.113508.
[26] Gerami, J., Kiani Mavi, R., Farzipoor Saen, R., and Kiani Mavi, N., A novel network DEA-R model for evaluating hospital services supply chain performance. Annals of Operations Research, 2020;324(1-2):1041-1066. Doi: 10.1007/s10479-020-03755-w.
[27] Gerami, J., Mozaffari, M. R., Wanke, P.F., Correa, H., A novel slacks-based model for efficiency and super-efficiency in DEA-R, Operational Research, 2020; 22(4): 3373-3410. Doi: 10.1007/s12351-021-00679-6.
[28] Ghiyasi, M., Soltanifar, M., Sharafi, H., A novel invrse DEA- model with application in hospital efficiency. Socio-economic planning sciences, 2022; 84: 101427. DOI: 10.1016/j.seps.2022.101427.
[29] Hatami-Marbini, A., Emrouznejad, A., Tavana, M., A taxonomy and review of the fuzzy data envel-opment analysis literature: Two decades in the making. European Journal of Operational Research, 2011; 214(3): 457–472. Doi: 10.1016/j.ejor.2011.02.001.
[30] Hatami-Marbini, A., Tavana, M., Agrell, P.J., Hosseinzadeh Lotfi, F., Ghelej Beigi, Z., A common-weights DEA model for centralized resource reduction and target setting. Computers & Industrial Engi-neering, 2015; 79:195–203. Doi:10.1016/j.cie.2014.10.024.
[31] Hatami-Marbini, A., Toloo, M., Data Envelopment Analysis Models with Ratio Data: A revisit. Com-puters & Industrial Engineering, 2019; 133, 331-338. Doi: 10.1016/j.cie.2019.04.041.
[32] Hatami-Marbini, A., Saati, S., Measuring performance with common weights: network DEA, Neural Computing and Applications, 2020; 32(8): 3599- 3617. Doi: 10.1007/s00521-019-04219-4.
[33] Hatami-marbini, A., Arabmaldar, A., Robustness of Farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application, European Journal of Operational Re-search, 2021;
Doi: 10.1016/j.ejor.2021.03.019.
[34] Hatami-Marbini, A., Arabmaldar, A., John, A., Robust productivity growth and efficiency measure-ment with undesirable outputs: Evidence from the oil industry. OR Spectrum, 2022; 44, 1213–1254. DOI: 10.1007/s00291-022-00683-y.
[35] Hosseinzadeh Lotfi, F., Hatami-Marbini, A., Agrell, P.J., Aghayi, N., Gholami, K., Allocating fixed resources and setting targets using a common-weights DEA approach, Computers & Industrial Engineer-ing, 2013 ; 64(2):631–640. Doi: 10.1016/j.cie.2012.12.006.
[36] Jahanshahloo, Gh. R., Sadeghi, J., Khodabakhshi, M. (2017). Proposing a method for fixed cost allo-cation using DEA based on the efficiency invariance and common set of weights principles, Mathematical Methods of Operations Research, 2017;85(2): 223-240. Doi: 10.1007/s00186-016-0563-z.
[37] Kao, C., Hung, H.-T., Data envelopment analysis with common weights: The compromise solution approach, Journal of the Operational Research Society, 2005; 56(10): 1196–1203. Doi: 10.1057/palgrave.jors.2601924.
[38] Liu, W.B., Zhang, D. Q., Meng, W., Li, X.X., & Xu, F., A study of DEA models without explicit inputs, Omega, 2011; 39: 472–480. Doi: 10.1016/j.omega.2010.10.005.
[39] Makui, A., Alinezhad, A., Kiani Mavi, A. 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, 2008; 1(4): 293–303. Doi: 20.1001.1.17358272.2008.1.4.2.8.
[40] Mozaffari, M. R, Gerami, J., and Jablonsky, J., Relationship between DEA models without explicit inputs and DEA-R models. Central European Journal of Operations Research, 2014; 22,:1–12. Doi: 10.1007/s10100-012-0273-4.
[41] Mozaffari, M. R, Kamyab, P., Jablonsky, J., and Gerami, J., Cost and revenue efficiency in DEA-R models, Computers & Industrial Engineering, 2014;78: 188–194. Doi: 10.1016/j.cie.2014.10.001.
[42] Mozaffari, M. R., Dadkhah, F., Jablonsky, J., Wanke, P. W., Finding efficient surfaces in DEA-R mod-els. Applied Mathematics and Computation, 2020; 386, :125497. Doi: 10.1016/j.amc.2020.125497.
[43] Mulvey, J. M., Vanderbei, R. J., Zenios, S. a., Robust optimization of large-scale systems. Operations Research, 1995; 43(2):264–281. Doi: 10.21236/ada299402.
[44] Nasrabadi, N., Dehnokhalaji, A., Korhonen, P., Lokman, B., Wallenius, J., Robustness of efficiency scores in data envelopment analysis with interval scale data. European Journal of Operational Research, 2022; 297: 1151–1161. Doi: 10.1016/j.ejor.2021.06.049.
[45] Odeck, J., Statistical precision of DEA and Malmquist indices: A bootstrap application to Norwegian grain producers, Omega, 2009;37(5):1007–1017. Doi: 10.1016/j.omega.2008.11.003.
[46] Olesen, O. B., Petersen, N. C., Podinovski, V. V., Efficiency analysis with ratio Measures, European Journal of Operational Research, 2015;245: 446–462. Doi: 10.1016/j.ejor.2015.03.013.
[47] Olesen, O. B., Petersen, N. C. (2016). Stochastic data envelopment analysis - A review, European Journal of Operational Research, 251(1): 2–21. Doi: 10.1016/j.ejor.2015.07.058.
[48] Olesen, O. B., Petersen, N. C., Podinovski, V. V. (2017). Efficiency measures and computational ap-proaches for data envelopment analysis models with ratio inputs and outputs, European Journal of Oper-ational Research, 2017; 261: 640–655. Doi: 10.1016/j.ejor.2017.02.021.
[49] Omrani, H., Common weights data envelopment analysis with uncertain data: A robust optimization approach, Computers & Industrial Engineering, 2013;66(4):1163–1170. Doi: 10.1016/j.cie.2013.07.023.
[50] Omrani, H., Adabi, F., Adabi, N., Designing an efficient supply chain network with uncertain data: A robust optimization - Data envelopment analysis approach, Journal of the Operational Research Society, 2017; 68(7): 816–828. Doi:10.1057/jors.2016.42.
[51] Omrani, H., Alizadeh, A., Naghizadeh, F., Incorporating decision makers’ preferences into DEA and common weight DEA models based on the best–worst method (BWM), Soft Computing, 2020; 24(6): 3989-4002. Doi: 10.1007/s00500-019-04168-z.
[52] Omrani, H., Alizadeh, A., Emrouznejad, A., Teplova, T., A Robust Credibility DEA Model with Fuzzy Perturbation Degree: An Application to Hospitals Performance, 2022; 189, 116021. Doi: 10.1016/j.eswa.2021.116021
[53] Omrani, H., Valipour, M., Emrouznejad, A., A novel best worst method robust data envelopment analysis: Incorporating decision makers’ preferences in an uncertain environment, Operations Research Perspectives, 2021; 8:100184. Doi: 10.1016/j.orp.2021.100184.
[54] Omrani, H., Alizadeh, A., Emrouznejad, A., Teplova A., A Robust Credibility DEA Model with Fuzzy Perturbation Degree: An Application to Hospitals Performance, Expert Systems with Applications, 2022; 189: 116021. Doi: 10.1016/j.eswa.2021.116021.
[55] Roll, Y., Cook, W.D., Golany, B., Controlling factor weights in data envelopment Analysis, IIE Trans, 1991; 23(1): 2–9. Doi:10.1080/07408179108963835.
[56] Roll, Y., Golany, B. (1993). Alternate methods of treating factor weights in DEA, Omega, 1993; 21(1):99–109. Doi:10.1016/0305-0483(93)90042-j.
[57] Sadjadi, S. J., Omrani, H., Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies, Energy Policy, 2008; 36(11): 4247–4254. Doi: 10.1016/j.enpol.2008.08.004.
[58] Sadjadi, S. J., Omrani, H., A bootstrapped robust data envelopment analysis model for efficiency es-timating of telecommunication companies in Iran, Telecommunications Policy, 2010; 34(4):221–232.
Doi: 10.1016/j.telpol.2009.09.003.
[59] Sadjadi, S. J., Omrani, H., Abdollahzadeh, S., Alinaghian, M., Mohammadi, H., A robust super-efficiency data envelopment analysis model for ranking of provincial gas companies in Iran, Expert Sys-tems with Applications, 2011; 38(9): 10875–10881. Doi: 10.1016/j.eswa.2011.02.120.
[60] Salahi, M., Torabi, N., Amiri, A., An optimistic robust optimization approach to common set of weights in DEA, Measurement, 2016; 93: 67–73. Doi: 10.1016/j.measurement.2016.06.049.
[61] Salahi, M., Toloo, M., Hesabirad, Z., Robust Russell and enhanced Russell measures in DEA. Journal of the Operational Research Society, 2019; 70(8), 1275–1283. Doi:10.1080/01605682.2018.1489353.
[62] Salahi, M., Toloo, M., Torabi, N., A new robust optimization approach to common weights formula-tion in DEA. Journal of the Operational Research Society, 2020; 72:1390-1402.Doi:10.1080/01605682.2020.1718016.
[63] Shirazi, F., Mohammadi, E., Evaluating efficiency of airlines: A new robust DEA approach with unde-sirable output, Research in Transportation Business and Management, 2020; 33:100467. Doi: 10.1016/j.rtbm.2020.100467.
[64] Soltanifar, M., Hosseinzadeh Lotfi, F., Sharafi, H., Lozano, S., Resource allocation and target setting: a CSW–DEA based Approach. Annals of Operations Research, 2022; 318(1):557-589.
Doi: 10.1007/s10479-022-04721-4.
[65] Soyster, A. L., Convex programming with set inclusive constraints and applications to inexact linear programming, Operations Research, 1973;21(5): 1154–1157. Doi:10.1287/opre.21.5.1154.
[66] Thanassoulis, E., Boussofiane, A., Dyson. R.G., A comparison of data envelopment analysis and ratio analysis as tools for performance assessment, Omega, 1996; 24(3):229-244. Doi: 10.1016/0305-0483(95)00060-7.
[67] Tavana, M., Toloo, M., Aghayi, N., Arabmaldar, A., A robust cross -efficiency data envelopment analysis model with undesirable outputs, Expert Systems with Applications, 2021; 167:114117. Doi: 10.1016/j.eswa.2020.114117.
[68] Toloo, M., Mensah, E. K., Robust optimization with nonnegative decision variables: A DEA ap-proach, Computers & Industrial Engineering, 2019; 127:313–325. Doi: 10.1016/j.cie.2018.10.006.
[69] Toloo, M., Mensah, E. K., Salahi, M. (2022). Robust optimization and its duality in data envelopment analysis. Omega, 2022; 108, P. 102583. Doi:10.1016/j.omega.2021.102583.
[70] Wang, K., Wei, F., Robust data envelopment analysis based MCDM with the consideration of uncer-tain data. Journal of Systems Engineering and Electronics, 2010; 21(6):981–989. Doi: 10.3969/j.issn.1004-4132.2010.06.009.
[71] Wanke, P.F., Ostovan, S., Mozaffari, M. R., Gerami, J., Tan., Stochastic network DEA-R models for two-stage systems, Journal of Modelling in Management, 2023; 18(3):842-875.Doi: 10.1108/jm2-10-2021-0256.
[72] Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H., A study of developing an input oriented ratio-based comparative efficiency model, Expert Systems with Applications, 2011;38:2473–2477. Doi: 10.1016/j.eswa.2010.08.036.
[73] Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H., Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model, Expert Systems with Applications, 2011; 38, 3155–3160.
Doi: 10.1016/j.eswa.2010.08.108.
[74] Wei, C. K., Chen, L. C., Li, R. K., Tsai, C. H., Using DEA-R model in the hospital industry to study the pseudo-inefficiency problem, Expert Systems with Applications, 2011;38: 2172–2176.
Doi: 10.1016/j.eswa.2010.08.003.
[75] Wu, J., Shen, L., Zhang, G., Zhou, Z., & Zhu, Q., Efficiency evaluation with data uncertainty. Annals of Operations Research, 2022; Doi: 10.1007/s10479-022- 04636-0
[76] Zarei Mahmoudabadi, M., Emrouznejad, A., Balanced performance assessment under uncertainty: an integrated CSW-DEA and balanced scorecard (BSC), Annals of Operations Research, in press, 2022, Doi:10.1007/s10479-022-04637-z.
[77] Zhou, X., Xu, Z., Chai, J., Yao, L., Wang, S., Lev, B., Efficiency evaluation for banking systems under uncertainty: A multi-period three-stage DEA model, Omega, 2019; 85: 68–82.Doi: 10.1016/j.omega.2018.05.012.
[78] Zhu, J., Imprecise data envelopment analysis (IDEA): A review and improvement with an application, European Journal of Operational Research, 2003; 144(3): 513–529. Doi: 10.1016/s0377-2217(01)00392-7.
[79] Zohrehbandian, M., Makui, A., Alinezhad, A., A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung’s approach, Journal of the Operational Research Soci-ety, 2010; 61 (4): 604–610. Doi: 10.1057/jors.2009.4.
