Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

An empirical application of data envelopment analysis in credit rating

Data Envelopment Analysis (DEA) is a nonparametric optimization technique that evaluates the relative efficiency of decision-making units and is used in this thesis as an empirical estimator of credit rating. The purpose of this research is to combine different DEA models and technique and obtain the best model that captures different aspects of credit risk. Various models are evaluated by combining four Slack DEA models with Principal Component Analysis (PCA), Absolute Weights Restriction, and Stochastic DEA. We found that Goal Vector Approach Stochastic PCA (SGV+PCA), applied to a sample consisting of five sectors, is the best model. SGV+PCA DEA model obtains a high correlation with Standard & Poor’s (S&P) credit rating and with Market Price; it also classified twelve bankrupted companies within the 17% of the less efficient companies in the sample, suggesting that the model is a good financial health estimator and is a potential tool for credit rating analysis.

An empirical application of data envelopment analysis in credit rating

Data Envelopment Analysis (DEA) is a nonparametric optimization technique that evaluates the relative efficiency of decision-making units and is used in this thesis as an empirical estimator of credit rating. The purpose of this research is to combine different DEA models and technique and obtain the best model that captures different aspects of credit risk. Various models are evaluated by combining four Slack DEA models with Principal Component Analysis (PCA), Absolute Weights Restriction, and Stochastic DEA. We found that Goal Vector Approach Stochastic PCA (SGV+PCA), applied to a sample consisting of five sectors, is the best model. SGV+PCA DEA model obtains a high correlation with Standard & Poor’s (S&P) credit rating and with Market Price; it also classified twelve bankrupted companies within the 17% of the less efficient companies in the sample, suggesting that the model is a good financial health estimator and is a potential tool for credit rating analysis.

A Unified Mathematical Model for Stochastic Data Envelopment Analysis

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.

Developing a new super-efficiency DEA model in the presence of both zero data and stochastic data: a case study in the Iranian airline industry

PurposeThe purpose of this study is to propose a novel super-efficiency DEA model to appraise the relative efficiency of DMUs with zero data and stochastic data. Our model can work with both variable returns to scale (VRS) and constant returns to scale (CRS).Design/methodology/approachThis study proposes a new stochastic super-efficiency DEA (SSDEA) model to assess the performance of airlines with stochastic and zero inputs and outputs.FindingsThis paper proposes a new analysis and contribution to the knowledge of efficiency assessment with stochastic super-efficiency DEA model by (1) using input saving and output surplus index for efficient DMUs to get the optimal solution; (2) obtaining efficiency scores from the proposed model that are equivalent to original stochastic super-efficiency model when feasible solutions exist. A case study is given to illustrate the applicability of our proposed model. Also, poor performance reasons are identified to improve the performance of inefficient airlines.Originality/valueFor the first time, a new SSDEA model for ranking DMUs is proposed. The introduced model produces a feasible solution when dealing with zero input or output. This paper applies the input saving and output surplus concept to rectify the infeasibility problem in the stochastic DEA model.

Multi-Attribute Decision Making Based on Stochastic DEA Cross-Efficiency with Ordinal Variable and Its Application to Evaluation of Banks’ Sustainable Development

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs’ optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.