A new robust optimization approach to most efficient formulation in DEA
محورهای موضوعی : Data Envelopment AnalysisReza Akhlaghi 1 , Mohsen Rostamy-Malkhalifeh 2 , Alireza Amirteimoori 3 , Sohrab Kordrostami 4
1 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
3 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
4 - Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
کلید واژه: Uncertainty, Data Envelopment Analysis (DEA), Robust Optimization, Interval data, Optimistic Counterpart,
چکیده مقاله :
In this article, we investigate a new continuous linear model with constraints for the direct selection of the most efficient unit in the analysis of data coverage presented by Akhlaghi et al. (2021) on uncertainty robust optimization. Considering the importance of incorporating uncertainty into performance evaluation models in the real world and its increasing application in various problems, we propose a robust optimization approach. Given the discrete and non-convex nature of the introduced models for selecting the most efficient decision-making unit, examining the dual and finding an optimistic scenario is practically impossible. Therefore, by utilizing the linear model presented by Akhlaghi et al. (2021) with constraints for identifying the most efficient unit, we can investigate the robustness of the desired model using(BS )Bertsimas and Sim's (2004) robust estimation method while also considering uncertainty. We aim to demonstrate that employing a robust formulation leads to reliable performance in uncertain conditions
In this article, we investigate a new continuous linear model with constraints for the direct selection of the most efficient unit in the analysis of data coverage presented by Akhlaghi et al. (2021) on uncertainty robust optimization. Considering the importance of incorporating uncertainty into performance evaluation models in the real world and its increasing application in various problems, we propose a robust optimization approach. Given the discrete and non-convex nature of the introduced models for selecting the most efficient decision-making unit, examining the dual and finding an optimistic scenario is practically impossible. Therefore, by utilizing the linear model presented by Akhlaghi et al. (2021) with constraints for identifying the most efficient unit, we can investigate the robustness of the desired model using(BS )Bertsimas and Sim's (2004) robust estimation method while also considering uncertainty. We aim to demonstrate that employing a robust formulation leads to reliable performance in uncertain conditions
Akhlaghi, R & Rostamy-Malkhalifeh, M. (2019). A linear programming DEA model for selecting a single efficient unit. International Journal of Industrial Engineering and Operations Research, 1(1), 60-66. http://bgsiran.ir/journal/ojs-3.1.1-4 /index.php/IJIEOR/article/view/12/9.
Akhlaghi, R., Rostamy-Malkhalifeh, M., Amirteimoori, A., & Kordrostami, S. (2021). A Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology. Croatian Operational Research Review, 12(2), 131-137.
Amin, G. R. (2009). Comments on finding the most efficient DMUs in DEA: An improved integrated model. Computers and Industrial Engineering, 56(4), 1701–1702. https://doi.org/10.1016/j.cie.2008.07.014.
Amin, G. R., & Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers and Industrial Engineering, 52(2), 71–77. https://doi.org/10.1016/j.cie.2006.10.003
Arabmaldar A, Jablonsky J, Hosseinzadeh Saljooghi F. A new robust DEA model and super-efficiency measure. Optimization 2017;66(5):723–36.
Arabmaldar A, Mensah EK, Toloo M. Robust worst-practice interval DEA with non-discretionary factors. Expert Syst Appl 2021:115256.
Baker, R. C., & Talluri, S. (1997). A closer look at the use of data envelopment analysis for technology selection. Computers & Industrial Engineering. Elsevier science ltd. https://doi.org/10.1016/S0360-8352(96)00199-4
Beck, A., & Ben-Tal, A. (2009). Duality in robust optimization: Primal worst equals dual best. Operations Research Letters, 37(1), 1–6. https://doi.org/10.1016/j.orl.2008.09.010
Ben-Tal, A., & Nemirovski, A. (1998). Robust Convex Optimization. Mathematics of Operations Research, 23(4), 769–805. https://doi.org/10.1287/moor.23.4.769
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25(1), 1–13. https://doi.org/10.1016/S0167-6377(99)00016-4
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of Linear Programming problems contaminated with uncertain data. Mathematical Programming, 88(3), 411–424. https://doi.org/10.1007/PL00011380
Bertsimas D, Sim M. The Price of robustness. Oper Res 2004;52(1):35–53.
Bertsimas, D., Pachamanova, D., & Sim, M. (2004). Robust linear optimization under general norms. Operations Research Letters, 32(6), 510–516. https://doi.org/10.1016/j.orl.2003.12.007
Cazals C, Florens JP, Simar L. Nonparametric frontier estimation: a robust approach. J Econom 2002;106(1):1–25.
Charnes A, Rousseau JJ, Semple JH. Sensitivity and stability of efficiency classifications in data envelopment analysis. J Product Anal 1996;7(1):5–18.
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
Cooper WW, Park KS, Yu G. IDEA and AR-IDEA: models for dealing with imprecise data in DEA. Manage Sci 1999;45(4):597–607.
Ehrgott, M., Holder, A., & Nohadani, O. (2018). Uncertain data envelopment analysis. European Journal of Operational Research, 268(1), 231-242.
Ertay, T., Ruan, D., & Tuzkaya, U. R. (2006). Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems. Information Sciences 176: 237–262.
Foroughi, A. A. (2011). A new mixed integer linear model for selecting the best decision-making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554. https://doi.org/10.1016/j.cie.2010.12.012.
Gorissen BL, Yanıko ˘glu ˙I, den Hertog D. A practical guide to robust optimization. Omega (Westport) 2015; 53:124–37.
Hatami-marbini A, Arabmaldar A. Robustness of Farrell cost efficiency measurement under data perturbations: evidence from a US manufacturing application. Eur J Oper Res 2021.
Hibiki N, Sueyoshi T. DEA sensitivity analysis by changing a reference set: regional contribution to Japanese industrial development. Omega (Westport) 1999;27(2):139–53
http://dx.doi.org/10.1016/j.ins.2004.12.001
https://doi.org/10.1016/j.cie.2018.10.006
https://doi.org/10.17535/crorr.2021.0011
Kadziński, M., Labijak, A., & Napieraj, M. (2017). Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports. Omega, 67, 1-18.
Karsak, E. E., & Ahiska, S. S. (2008). Improved common weight MCDM model for technology selection. International Journal of Production Research, 46(24), 6933–6944
Khouja, M. (1995). The use of data envelopment analysis for technology selection. Computers & Industrial Engineering. https://doi.org/10.1016/0360-8352(94)00032-I
Mulvey JM, Vanderbei RJ, Zenios SA. Robust optimization of large-scale systems. Oper Res 1995;43(2):264–81.
Olesen OB, Petersen NC. Chance Constrained efficiency evaluation. Manage Sci 1995;41(3):442–57.
Omrani H, Valipour M, Emrouznejad A. A novel best worst method robust data envelopment analysis: incorporating decision makers’ preferences in an uncertain environment. Oper Res Perspect 2021; 8:100184
Omrani, H., Valipour, M., & Emrouznejad, A. (2021). A novel best worst method robust data envelopment analysis: Incorporating decision makers’ preferences in an uncertain environment. Operations Research Perspectives, 8, 100184.
Peykani P, Mohammadi E, Saen RF, Sadjadi SJ, Rostamy-Malkhalifeh M. Data envelopment analysis and robust optimization: a review. Expert Syst 2020(September 2019): e12534.
Sadjadi SJ, Omrani H. A bootstrapped robust data envelopment analysis model for efficiency estimating of telecommunication companies in Iran. Telecomm Policy 2010;34(4):221–32.
Sadjadi SJ, Omrani H. Data envelopment analysis with uncertain data: an application for Iranian electricity distribution companies. Energy Policy 2008;36(11):4247–54
Salahi M, Toloo M, Hesabirad Z. Robust Russell and enhanced Russell measures in DEA. J Oper Res Soc 2019;70(8):1275–83.
Salahi, M., Torabi, N., & Amiri, A. (2016). An optimistic robust optimization approach to common set of weights in DEA. Measurement, 93, 67-73. https://doi.org/10.1080/01605682.2020.1718016
Shang, J., & Sueyoshi, T. (1995). A unified framework for the selection of a Flexible Manufacturing System. European Journal of Operational Research, 85(2), 297–315. https://doi.org/10.1016/0377-2217(94)00041-A
Tavana M, Toloo M, Aghayi N, Arabmaldar A. A robust cross-efficiency data envelopment analysis model with undesirable outputs. Expert Syst Appl 2021; 167:114117.
Toloo, M., & Kresta, A. (2014). Finding the best asset financing alternative: A DEA-WEO approach. Measurement, 55, 288–294.
Toloo, M., & Mensah, E. K. (2018). Robust optimization with nonnegative decision variables: A DEA approach. Computers and Industrial Engineering.
Wang, Y.-M., & Jiang, P. (2012). Alternative mixed integer linear programming models for identifying the most efficient decisionmaking unit in data envelopment analysis. Computers and Industrial Engineering, 62, 546–553.
