Characteristics on stochastic data envelopment analysis efficiency – Reliability and probability being efficient

Data envelopment analysis (DEA) is a useful non-parametric method to evaluate a relative efficiency of multi-input and multi-output units based on observed data. In general, observed data have inherent uncertainty; however, it is difficult to treat the stochastic data in the conventional DEA model. It required the development of stochastic DEA model, where the uncertainty like a measurement error should be incorporated. We consider in this paper an efficiency analysis of decision making units (DMUs) by using inputs and outputs data with stochastic variations, and discuss some stochastic measures of efficiency taking into account the measurement error. The most interesting characteristic is reliability and robustness of the efficiency result. We propose a measure for reliability of efficient DMUs as the amount of stochastic variations for which the efficient DMU remains efficient. A minimum efficiency score at a specified probability level is also used as a robustness measure. Moreover, we discuss some stochastic measures such as an expected efficiency score, a probability of being efficient, and an alpha-percentile of efficiency score.