Abstract
The slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as “few”, “many”, “small”, or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.
Highlights
Charnes et al [10] wrote a revolutionary paper on data envelopment analysis (DEA) [12] which is one of the most cited articles of European Journal of Operational Research
The present study focuses on the fuzzy slack-based measure (SBM) DEA model’s sensitivity and stability analysis, which has been solved after transforming into crisp linear programming models using credibility measures
Fuzzy numbers replace the missing data. 18 inefficient and 12 efficient State Transport Undertakings (STUs) out of 30 STUs have been obtained after computing the relative efficiency from the fuzzy SBM DEA model
Summary
The α-level-based approach is the most commonly used technique to solve the fuzzy DEA model It calculates the relative efficiency in the interval form (i.e., lower bound efficiency and upper bound efficiency), and ranking of the DMUs becomes another task. The SBM DEA model has been selected to compute the relative efficiency, input, and output targets for this study. Many researchers integrate fuzzy set theory with the SBM DEA model to handle the uncertain data and explore this model in many applications. Arana et al [5] proposed an exciting approach, which focused not just on the computation of efficiency scores and on the input and output improvements These improvements help managers with some helpful information on the variables, and they can concentrate their efforts by which the progress can be possible. They converted the FFLP model into a multi objective optimization problem using
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