Modelling Robust Optimization in DEA With Ratio Data: A Case Study of Commercial Banks
Subject Areas : Financial Mathematics
1 - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
Keywords: Data Envelopment Analysis, Ratio Analysis , Robust Optimization, Common Set of Weights Uncertainty , Banking, ,
Abstract :
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.
References:
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[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.
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