Abstract: The way to deal with flexible data from their stochastic presence point of view as output or input in the evaluation of efficiency of the decision-making units (DMUs) motivates new perspectives in modeling and solving data envelopment analysis (DEA) in the presence of flexible variables. Because the orientation of flexible data is not pre-determined, and because the number of DMUs is fixed and all the DMUs are independent, flexible data can be treated as random variable in terms of both input and output selection. As a result, the selection of flexible variable as input or output for n DMUs can be regarded as binary random variable. Assuming the randomness of choosing flexible data as input or output, we deal with DEA models in the presence of flexible data whose input or output orientation determines a binomial distribution function. This study provides a new insight to classify flexible variable and investigates the input or output status of a variable using a stochastic model. The proposed model obviates the problems caused by the use of the large M number and using its different values in previous models. In addition, it can obtain the most appropriate efficiency value for decision-making units by assigning the chance of choosing the orientation of flexible variable to the model itself. The proposed method is compared with other available methods by employing numerical and empirical examples.

Key words: Data envelopment analysis, Flexible variables, Stochastic model, Random variable, Classifying