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A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data

Author

Listed:
  • Ali Ebrahimnejad

    (Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran)

  • Madjid Tavana

    (Business Systems and Analytics Department, La Salle University, Philadelphia, PA 19141, USA3Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany)

  • Seyed Hadi Nasseri

    (Department of Mathematics, University of Mazandaran, Babolsar, Iran)

  • Omid Gholami

    (Department of Mathematics, University of Mazandaran, Babolsar, Iran)

Abstract

Data envelopment analysis (DEA) is a widely used mathematical programming technique for measuring the relative efficiency of decision-making units which consume multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally used in classical DEA models, real-life problems often involve uncertainties characterized by fuzzy and/or random input and output data. We present a new input-oriented dual DEA model with fuzzy and random input and output data and propose a deterministic equivalent model with linear constraints to solve the model. The main contributions of this paper are fourfold: (1) we extend the concept of a normal distribution for fuzzy stochastic variables and propose a DEA model for problems characterized by fuzzy stochastic variables; (2) we transform the proposed DEA model with fuzzy stochastic variables into a deterministic equivalent linear form; (3) the proposed model which is linear and always feasible can overcome the nonlinearity and infeasibility in the existing fuzzy stochastic DEA models; (4) we present a case study in the banking industry to exhibit the applicability of the proposed method and feasibility of the obtained solutions.

Suggested Citation

  • Ali Ebrahimnejad & Madjid Tavana & Seyed Hadi Nasseri & Omid Gholami, 2019. "A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 147-170, January.
    • Handle: RePEc:wsi:ijitdm:v:18:y:2019:i:01:n:s0219622018500396
    DOI: 10.1142/S0219622018500396
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    1. Qin, Rui & Liu, Yan-Kui, 2010. "Modeling data envelopment analysis by chance method in hybrid uncertain environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 922-950.
    2. Konstantinos Triantis & Olivier Girod, 1998. "A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment," Journal of Productivity Analysis, Springer, vol. 10(1), pages 85-102, July.
    3. Tsionas, Efthymios G. & Papadakis, Emmanuel N., 2010. "A Bayesian approach to statistical inference in stochastic DEA," Omega, Elsevier, vol. 38(5), pages 309-314, October.
    4. Adel Hatami-Marbini & Madjid Tavana & Alireza Ebrahimi, 2011. "A fully fuzzified data envelopment analysis model," International Journal of Information and Decision Sciences, Inderscience Enterprises Ltd, vol. 3(3), pages 252-264.
    5. William Cooper & Zhimin Huang & Vedran Lelas & Susan Li & Ole Olesen, 1998. "Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA," Journal of Productivity Analysis, Springer, vol. 9(1), pages 53-79, January.
    6. HATAMI-MARBINI, Adel & TAVANA, Madjid & EBRAHIMI, Alireza, 2011. "A fully fuzzified data envelopment analysis model," LIDAM Reprints CORE 2322, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. TAVANA, Madjid & SHIRAZ, Rashed Khanjani & HATAMI-MARBINI, Adel & AGRELL, Per J., 2012. "Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)," LIDAM Reprints CORE 2412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Udhayakumar, A. & Charles, V. & Kumar, Mukesh, 2011. "Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems," Omega, Elsevier, vol. 39(4), pages 387-397, August.
    9. Huang, Zhimin & Li, Susan X., 1996. "Dominance stochastic models in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 95(2), pages 390-403, December.
    10. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    11. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    13. Rashed Khanjani Shiraz & Madjid Tavana & Khalil Paryab, 2014. "Fuzzy free disposal hull models under possibility and credibility measures," International Journal of Data Analysis Techniques and Strategies, Inderscience Enterprises Ltd, vol. 6(3), pages 286-306.
    14. Cooper, William W. & Deng, H. & Huang, Zhimin & Li, Susan X., 2004. "Chance constrained programming approaches to congestion in stochastic data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 155(2), pages 487-501, June.
    15. Bruni, M.E. & Conforti, D. & Beraldi, P. & Tundis, E., 2009. "Probabilistically constrained models for efficiency and dominance in DEA," International Journal of Production Economics, Elsevier, vol. 117(1), pages 219-228, January.
    16. Li, Susan X., 1998. "Stochastic models and variable returns to scales in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 104(3), pages 532-548, February.
    17. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
    18. Wenshuai Wu & Gang Kou, 2016. "A group consensus model for evaluating real estate investment alternatives," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-10, December.
    19. Olesen, Ole B. & Petersen, Niels Christian, 2016. "Stochastic Data Envelopment Analysis—A review," European Journal of Operational Research, Elsevier, vol. 251(1), pages 2-21.
    20. Madjid Tavana & Rashed Khanjani Shiraz & Adel Hatami-Marbini, 2014. "A new chance-constrained DEA model with birandom input and output data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(12), pages 1824-1839, December.
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    Cited by:

    1. Pejman Peykani & Farhad Hosseinzadeh Lotfi & Seyed Jafar Sadjadi & Ali Ebrahimnejad & Emran Mohammadi, 2022. "Fuzzy chance-constrained data envelopment analysis: a structured literature review, current trends, and future directions," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 197-261, June.
    2. Mustafa Kemal Yilmaz & Ali Osman Kusakci & Ekrem Tatoglu & Orkun Icten & Feyzullah Yetgin, 2019. "Performance Evaluation of Real Estate Investment Trusts using a Hybridized Interval Type-2 Fuzzy AHP-DEA Approach: The Case of Borsa Istanbul," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1785-1820, November.

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