Measuring the performances of decision-making units using geometric average efficiency

The performances of decision-making units (DMUs) can be measured from two different points of view: optimistic or pessimistic, which leads to two different efficiencies for each DMU: the best relative efficiency and the worst relative efficiency. The conventional data envelopment analysis (DEA) considers only the best relative efficiency. It is argued that the two different efficiencies should be considered together and any approach that considers only one of them is biased. This paper proposes to integrate the two different efficiencies into a geometric average efficiency, which measures the overall performance of each DMU. It is found that the geometric average efficiency has better discriminating power than either of the two efficiencies. This is illustrated by two numerical examples.