Data envelopment analysis with missing data a reliable solution method

In data envelopment analysis (DEA), the input and output data from all of the decision making units (DMUs) to be compared are required. If, for any reason, some data are missing, then the associated DMU must be eliminated to make the approach applicable. This study proposes a fuzzy set approach to deal with missing values. The value of a DMU in an input (or output) which is missing is represented by a triangular fuzzy number constructed from the values of other DMUs in that input (or output). A fuzzy DEA model is then used to calculate the efficiencies, which are usually also fuzzy numbers. We use a problem with complete data to investigate the effect of this approach when 1%, 2%, and 5% of the values are missing. While the conventional DMU-deletion method will overestimate the efficiencies of the remaining DMUs, the fuzzy set approach produces results which are very close to those calculated from complete data. The average error in estimating the true efficiency is less than 0.3%. Most importantly, the fuzzy set approach is able to calculate the efficiencies of all DMUs, including those with some values missing.