Data envelopment analysis (DEA) has been widely applied to measure the Pareto efficiency of multiple-input and multiple-output decision making units (DMUs). In this paper it is shown that under linear production frontiers DMU efficiency is a weighted arithmetic mean of the efficiencies of the outputs; whereas under loglinear production frontiers DMU efficiency is a weighted geometric mean of the output efficiencies. Furthermore, DMU efficiency can be decomposed with respect to input factors as well, and some results are derived. As a consequence, a modified DEA model is devised, whereby the efficiency of each output (or input) in addition to DMU efficiency is able to be measured in one linear programming solution.
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