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 and Zahra Ghelej Beigi
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Adel Hatami-Marbini: Université catholique de Louvain
Madjid Tavana: La Salle University
Kobra Gholami: Islamic Azad University
Zahra Ghelej Beigi: Islamic Azad University

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 15, 679-701

Abstract: 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.

Keywords: Data envelopment analysis; Fuzzy data; Interval efficiency; Safety; Semiconductor industry; 90B50; 68M20; 90C70 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-014-0559-x

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