Data envelopment analysis with missing values: an interval DEA approach

Missing values in inputs, outputs cannot be handled by the original data envelopment analysis (DEA) models. In this paper we introduce an approach based on interval DEA that allows the evaluation of the units with missing values along with the other units with available crisp data. The missing values are replaced by intervals in which the unknown values are likely to belong. The constant bounds of the intervals, depending on the application, can be estimated by using statistical or experiential techniques. For the units with missing values, the proposed models are able to identify an upper and a lower bound of their efficiency scores. The efficiency analysis is further extended by estimating new values for the initial interval bounds that may turn the unit to an efficient one. The proposed methodology is illustrated by an application which evaluates the efficiency of a set of secondary public schools in Greece, a number of which appears to have missing values in some inputs and outputs.