Worst-practice Data Envelopment Analysis Models for the Measurement of Fuzzy Efficiency

Subject Areas : Industrial Management

Hossein Azizi ¹ , Haidar Rasul Jahed ² , Leila Farrokhi ³

1 - Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran
2 - M.Sc., Instructor, Germi Branch, Islamic Azad University, Germi, Iran
3 - M.Sc., Instructor, Germi Branch, Islamic Azad University, Germi, Iran

Received: 2018-01-10 Accepted : 2018-01-10 Published : 2012-10-22

Keywords:

Abstract :

The classic form of data envelopment analysis (DEA), which is based on the concept of efficient production frontier, determines the best efficiency score that can be assigned to each member of a set of decision-making units (DMUs). Based on these scores, DMUs are classified into optimistic efficient and optimistic non-efficient units, and the optimistic efficient DMUs determine the efficiency frontier. Classic DEA can be used for identification of well-performing (efficient) units in the most favorable scenario. For identification of units with bad performance, such as bankrupt firms in the most unfavorable scenario (the worst case), there is a similar approach, called worst efficiency analysis, which uses the inefficient production frontier in order to determine the worst relative efficiency score that can be assigned to each DMU. DMUs lying on the inefficient production frontier are specified as pessimistic inefficient, while those that are neither on the efficient production frontier nor on the inefficient production frontier is designated as DEA-unspecified units. DEA requires that input and output data are known exactly. However, this is not the case in real-world applications. However, the observed values of the input and output data in real-world problems are sometimes fuzzy. Many researchers have proposed various fuzzy methods for dealing with the fuzzy data in DEA. This paper presents two new fuzzy DEA models based on fuzzy arithmetic that make it possible to work with fuzzy input and output data in DEA. The new fuzzy DEA models are formulated as linear programming models, and they can be used for determining the fuzzy efficiency of a group of DMUs. The worst-practice frontier fuzzy DEA models presented in this paper accurately identify the “worst-practice” DMUs that form the worst practice-frontier (the inefficiency frontier). This is particularly relevant for our application to credit risk evaluation, but this also has general relevance since the worst performers are where the largest improvement potential can be found. An example will be presented to illustrate the application of the new approach. 

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