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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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    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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