Abstract
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 is 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 of 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 that remain the efficient DMU being 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 being efficient, an α-percentile of efficiency score.
