Effect of variations on efficiency of decision-making units with respect to output, output estimated by production functions, and output differences

In this paper we study some relationships between Data Envelopment Analysis (DEA) and a production function, given an output and multiple inputs of several units (observations). We examine how small- and large-scale variations in the output of a given sample, measured by the coefficient of variation and by different distributions, affect the number of efficient units. The effect was examined by two types of samples that differed in the level of homogeneousness of the Cobb–Douglas production function. The first sample had a production function with a decreasing return to scale (DRTS), while the other had a production function with an increasing return to scale (IRTS). We determined the number of efficient units according to the DEA model (both the CCR and BCC versions) by the following three types of outputs: 1) the actual sample output; 2) the output estimated by the production function; 3) the error – the difference between the actual and the estimated outputs. This was done for each of the samples at different levels of disturbance (measured by the coefficient of variation) and for different types of distribution functions. We also examined the extent of the effect of the coefficient of variation and the Kurtosis on the number of efficient units achieved for each type of output for each of the samples and for the different types of efficiency. Furthermore, we checked whether there is a correspondence between the units defined as efficient (inefficient) by comparing three types of outputs. For cases in which we found a low correspondence, we examined whether the ranking of the organizational units resulting from the ratio between actual output and estimated output corresponds to the results of the DEA model.