Journal of Optimization Theory and Applications

, Volume 164, Issue 2, pp 679–701 | Cite as

A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry

  • Adel Hatami-Marbini
  • Madjid Tavana
  • Kobra Gholami
  • Zahra Ghelej Beigi


Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. The conventional DEA methods require accurate measurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are often imprecise or vague. Fuzzy set theory is widely used to quantify imprecise and vague data in DEA models. In this paper, we propose a four-step bounded fuzzy DEA model, where the inputs and outputs are assumed to be fuzzy numbers. In the first step, we create a hypothetical fuzzy anti-ideal DMU and calculate its best fuzzy relative efficiency. In the second step, we propose a pair of fuzzy DEA models to obtain the upper- and the lower-bounds of the fuzzy efficiency, where the lower-bound is at least equal to the fuzzy efficiency of the anti-ideal DMU, and the upper-bound is at most equal to one. In step three, we use multi-objective programming to solve the proposed fuzzy programs. In the fourth step, we propose a new method for ranking the bounded fuzzy efficiency scores. We also present a case study to demonstrate the applicability of the proposed model and the efficacy of the procedures and algorithms in measuring the safety performance of eight semiconductor facilities.


Data envelopment analysis Fuzzy data Interval efficiency Safety Semiconductor industry 

Mathematical Subject Classification (2010)

90B50 68M20 90C70 



The authors would like to thank the anonymous reviewers and the editor-in-chief for their constructive comments and suggestions. Adel Hatami-Marbini also likes to thank the FRS-FNRS for the financial support he received as a chargé de recherches at the Université catholique de Louvain for this research project


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Adel Hatami-Marbini
    • 1
  • Madjid Tavana
    • 2
    • 3
  • Kobra Gholami
    • 4
  • Zahra Ghelej Beigi
    • 5
  1. 1.Louvain School of Management, Center of Operations Research and Econometrics (CORE)Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision SciencesLa Salle UniversityPhiladelphiaUSA
  3. 3.Business Information Systems Department, Faculty of Business Administration and EconomicsUniversity of PaderbornPaderbornGermany
  4. 4.Department of ScienceIslamic Azad UniversityBushehrIran
  5. 5.Department of MathematicsIslamic Azad UniversityIsfahanIran

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