stochastic data envelopment analysis

Estimating the revenue efficiency of entities under evaluation is one of the most important evaluations that can give valuable information about organizations provided that the output prices are known . In this research, a new definition of optimal scale size ( OSS ) based on maximizing the average revenue efficiency (ARE) is presented . Also , the ARE is defined in both convex and non - convex sets, which is independent of returns to scale and the assumption that the vector of input-output prices of units is uniform . Next, due to the presence of uncertain data in many real applications, the introduced ARE model is extended to evaluate systems with random inputs and outputs , and approaches are provided to calculate it . Finally , the proposed method is used in an experimental example and the ARE is calculated for a data set of postal areas in Iran .

Today, the need to use efficiency measurement systems in the modern banking industry has become increasingly apparent. Therefore, the efficiency of banks needs to be forecasted so that future economic growth can be monitored in future decisions. This paper designs a new integrated model based on the Stochastic Data Envelopment Analysis (SDEA) model and the Principal Component Analysis (PCA) method in a dynamic environment to forecast the efficiency of branches in the modern banking industry by considering variable returns to scale for them. In order to deal with the uncertainty in efficiency forecasting, the inputs and outputs of the branches are designed as triangular fuzzy stochastic variables with normal distribution. In this study, Monte Carlo (MC) simulation and meta-heuristic algorithms have been used to solve the proposed model. Finally, in order to evaluate the performance and accuracy of the proposed integrated model, a case study based on modern banking indicators has been presented to forecast the efficiency of the future financial period of the branches and the results have been analyzed.

Data Envelopment Analysis is a management method which applied to performance analysis for decision making units. This paper presents a new hybrid approach based on fuzzy stochastic DEA (FSDEA) and principal component analysis (PCA) to predict efficiency of DMUs. Since the proposed model contains the credibility of fuzzy events in the constraints and the expected value of fuzzy variable in objective function, the solution process is complex. Thus, with the assumption that inputs and outputs are mutually independent triangular fuzzy variables, we then transform the FSDEA model to its equivalent deterministic programming. Then we do PCA on the initial predicted efficiency scores which are obtained from the equivalent deterministic programming under various confidence levels. In order to deal with undesirable initial predicted efficiencies, the required principal components have been selected from the generated ones according to the given choice principal. Then, the principal components are treated as outputs into DEA model to obtain the final predicted efficiencies of DMUs. Finally, the proposed hybrid     PCA-FSDEA approach is applied on real exampleand the computational results will be compared with Fuzzy-SBM model which was proposed by Chen et al. (2013).