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

Author

Listed:
  • Adel Hatami-Marbini

    (Université catholique de Louvain)

  • Madjid Tavana

    (La Salle University
    University of Paderborn)

  • Kobra Gholami

    (Islamic Azad University)

  • Zahra Ghelej Beigi

    (Islamic Azad University)

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.

Suggested Citation

  • Adel Hatami-Marbini & Madjid Tavana & Kobra Gholami & Zahra Ghelej Beigi, 2015. "A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 679-701, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0559-x
    DOI: 10.1007/s10957-014-0559-x
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    References listed on IDEAS

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    2. Liu, Quanlong & Shang, Jianping & Wang, Jingzhi & Niu, Weichao & Qiao, Wanguan, 2023. "Evaluation and prediction of the safety management efficiency of coal enterprises based on a DEA-BP neural network," Resources Policy, Elsevier, vol. 83(C).
    3. Toloo, Mehdi & Keshavarz, Esmaeil & Hatami-Marbini, Adel, 2018. "Dual-role factors for imprecise data envelopment analysis," Omega, Elsevier, vol. 77(C), pages 15-31.
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