Robust DEA Models for Performance Evaluation of Systems with Continuous Uncertain Data under CRS and VRS Conditions
الموضوعات :
Mohammad Amirkhan
1
(Department of Industrial Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran.)
الکلمات المفتاحية: Data envelopment analysis, Ranking, Efficiency, Performance Evaluation, Robust Optimization,
ملخص المقالة :
One of the most appropriate and efficient methods for evaluating the performance of homogenous decision-making units (DMU) is data envelopment analysis (DEA). Traditional DEA models are only able to evaluate DMUs with deterministic inputs and outputs, while in real-world problems, data are usually uncertain. So far, various approaches have been introduced to overcome the uncertainty of data. In this paper, two robust DEA models is presented to evaluate the performance of systems with continuous uncertain data under constant return to scale (CRS) and variable return to scale (VRS) conditions. The main advantage of the proposed robust DEA models over the previous robust DEA models is that they are able to formulate uncertainty in both input and output data. Moreover, these models are also developed directly on basic traditional DEA models (not alternative models). To demonstrate the applicability of two developed robust models, a numerical example is presented and the efficacy of models is exhibited.
[1] W.W. Cooper, L.M. Seiford, and K. Tone, "Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software", Boston: Kluwer Academic Publishers, 2000.
[2] M. Amirkhan, H. Didehkhani, K. Khalili-Damghani, and A. Hafezalkotob, "Measuring performance of a three-stage network structure using data envelopment analysis and Nash bargaining game: a supply chain application", International Journal of Information Technology & Decision Making, Vol. 17, No. 05: 1429-1467, 2018.
[3] A. Emrouznejad and M. Tavana, "Performance measurement with fuzzy data envelopment analysis", Studies in Fuzziness and Soft Computing, Springer-Verlag Berlin Heidelberg, 2014.
[4] A. Ben-Tal and A. Nemirovski, "Robust solutions of linear programming problems contaminated with uncertain data" Mathematical programming, Vol. 88, No. 3: 411-424, 2000.
[5] D. Bertsimas and M. Sim, "The price of robustness", Operations Research Letters, Vol. 52, No. 1: 35-53, 2004.
[6] S.J. Sadjadi and H. Omrani, "Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies", Energy Policy, Vol. 36, No. 11: 4247-4254, 2008.
[7] M.E. Bruni, D. Conforti, P. Beraldi, and E. Tundis, "Probabilistically constrained models for efficiency and dominance in DEA", International Journal of Production Economics, Vol. 117, No. 1: 219-228, 2009.
[8] K.C. Land, C.K. Lovell, and S. Thore, "Chance‐constrained data envelopment analysis", Managerial decision economics, Vol. 14, No. 6: 541-554, 1993.
[9] L.A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning—I", Information sciences, Vol. 8, No. 3: 199-249, 1975.
[10] A.L. Soyster, "Convex programming with set-inclusive constraints and applications to inexact linear programming", Operations research, Vol. 21, No. 5: 1154-1157, 1973.
[11] L. El Ghaoui and H. Lebret, "Robust solutions to least-squares problems with uncertain data", SIAM Journal on matrix analysis applications, Vol. 18, No. 4: 1035-1064, 1997.
[12] A. Ben-Tal and A. Nemirovski, "Robust convex optimization", Mathematics of operations research, Vol. 23, No. 4: 769-805, 1998.
[13] S.J. Sadjadi and H. Omrani, "A bootstrapped robust data envelopment analysis model for efficiency estimating of telecommunication companies in Iran", Telecommunications Policy, Vol. 34, No. 4: p. 221-232, 2010.
[14] S.J. Sadjadi, H. Omrani, S. Abdollahzadeh, M. Alinaghian, and H. Mohammadi, "A robust super-efficiency data envelopment analysis model for ranking of provincial gas companies in Iran", Expert Systems with Applications, Vol. 38, No. 9: 10875-10881, 2011.
[15] J.M. Mulvey, R.J. Vanderbei, and S.A. Zenios, "Robust optimization of large-scale systems" Operations research, Vol. 43, No. 2: 264-281, 1995.
[16] A. Hafezalkotob, E. Haji-Sami, and H. Omrani, "Robust DEA under discrete uncertain data: a case study of Iranian electricity distribution companies", Journal of Industrial Engineering International, Vol. 11, No. 2: 199-208, 2015.
[17] D. Bertsimas, D. Pachamanova, and M. Sim, "Robust linear optimization under general norms", Operations Research Letters, Vol. 32, No. 6: 510-516, 2004.
[18] P .Peykani, E. Mohammadi, A. Jabbarzadeh, and A. Jandaghian, "Utilizing robust data envelopment analysis model for measuring efficiency of stock, a case study: Tehran stock exchange", Journal of New Researches in Mathematics, Vol. 1, No. 4: 5-24, 2016.
[19] M. Esfandiari, A. Hafezalkotob, K. Khalili-Damghani, and M. Amirkhan, "Robust two-stage DEA models under discrete uncertain data", International Journal of Management Science and Engineering Management, Vol. 12, No. 3: 216-224, 2017.
[20] S. Yousefi, H. Shabanpour, R. Fisher, and R. Farzipoor Saen, "Evaluating and ranking sustainable suppliers by robust dynamic data envelopment analysis", Measurement, Vol. 83: 72-85, 2016.
[21] M. Rabbani, H. Farrokhi-Asl, and N. Manavizadeh, "Using Robust-DEA optimization approach to analyze performance and efficiency of a mine in north of Iran", Management Science Letters, Vol. 7, No. 2: 97-110, 2017.
[22] M. Amirkhan, H. Didehkhani, K. Khalili-Damghani, and A. Hafezalkotob, "Mixed uncertainties in data envelopment analysis: A fuzzy-robust approach", Expert Systems with Applications, Vol. 103: 218-237, 2018.
[23]. P. Peykani, E. Mohammadi, R. Farzipoor Saen, S.J. Sadjadi, and M. Rostamy-Malkhalifeh, "Data envelopment analysis and robust optimization: A review", Vol. 37, No. 4: 1-30, 2020.
[24] H. Omrani, M. Valipour, and A. Emrouznejad, "A novel best worst method robust data envelopment analysis: Incorporating decision makers" preferences in an uncertain environment", Operations Research Perspectives, Vol. 8: 100184, 2021.
[25] H. Omrani, M. Valipour, and A. Emrouznejad, "A robust cross-efficiency data envelopment analysis model with undesirable outputs", Expert Systems with Applications, Vol. 167: 114117, 2021.
[26] A. Charnes, W.W. Cooper, and E. Rhodes, "Measuring the efficiency of decision making units", European journal of operational research, Vol. 2, No. 6: 429-444, 1978.
[27] R.D. Banker, A. Charnes, and W.W. Cooper, "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis", Management Science, Vol. 30, No. 9: 1078-1092, 1984.
