Data envelopment analysis for efficiency measurement in the stochastic case

The data envelopment analysis for measuring efficiency of decision-making units is generalized here for stochastic variations of input and output data. The case of one output and many inputs is considered for three types of data variations, e.g. in the objective function, in the constraints and the outputs. It is shown that a minimax method of efficiency measurement through chance-constrained programming methods can be suitably applied for the case of chance constraints. Some empirical applications to measurement of efficiency of public schools are also analyzed to test the sensitivity and robustness of the efficiency ranking and measurement.