Data envelopment analysis with missing data

Missing data is a chronic disease in applications of data envelopment analysis. Very often, ‎important input or output variables are not completely specified and/or the decision-‎making units do not report all the required statistics. Therefore, the missing values in the ‎inputs and outputs cannot be studied using the original data envelopment analysis models. ‎This paper introduces methods for finding missing data when the existing data is certain. ‎In this article, after explaining the essential concepts of missing values, we describe some ‎methods of missing value imputation that reduce the complexity of data analysis. There ‎are several methods for imputing missing data, including various methods of simple ‎imputation and multiple imputation. This paper is the first systematic attempt to utilize data ‎containing missing values using statistical approaches in the DEA. In particular, we ‎examine what happens if we keep empty entries in the data set and assign a certain ‎numeric value to them. To show how the proposed methods work, they will be used to ‎evaluate a set of secondary public schools in Greece in some of which there are missing ‎input or output values.‎