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

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Abstract

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.

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Notes

  1. The subscripts 1,2,...,\(n\ \)present the ranking number of DMU\(_{i}\)

  2. The name of the company has been changed to protect their anonymity

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Acknowledgments

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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Authors and Affiliations

  1. Louvain School of Management, Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, L1.03.01, 1348 , Louvain-la-Neuve, Belgium

    Adel Hatami-Marbini

  2. Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA , 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098 , Paderborn, Germany

    Madjid Tavana

  4. Department of Science, Islamic Azad University, Bushehr Branch, Bushehr, Iran

    Kobra Gholami

  5. Department of Mathematics, Islamic Azad University, Mabarakeh Branch, Isfahan, Iran

    Zahra Ghelej Beigi

Authors
  1. Adel Hatami-Marbini
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  2. Madjid Tavana
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  3. Kobra Gholami
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  4. Zahra Ghelej Beigi
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Corresponding author

Correspondence to Madjid Tavana.

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Communicated by Jyh-Horng Chou.

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Hatami-Marbini, A., Tavana, M., Gholami, K. et al. A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry. J Optim Theory Appl 164, 679–701 (2015). https://doi.org/10.1007/s10957-014-0559-x

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