Data envelopment analysis

The goal of this article is to extend data envelopment analysis by reverse envelope, worst coefficients and identification of outliers. Reverse data envelopment analysis solves the problem whether there are weights which, if applied to all units, would make the selected unit the worst efficient. In other words, whether it is possible to choose common weights, so no other units would be less efficient than the selected one. It is possible using reverse data envelopment analysis to identify the worst units in some sense. But it does not say anything about their real relative efficiency under the worst conditions. Measurement of the worst and the best possible efficiency gives a better idea about efficiency of decision-making units. Outliers are the units, which lie in extreme positions. These are the units that use the fewest amount in at least one input component and/or produce the highest amount in at least one output component (depending on the model orientation). Very often is a small increase in one output compensated by a significant drop in other output or a small decrease of an input is compensated by a big increase of another one. They are efficient because they lie on a production frontier, so there is no other unit, which managed to produce better results. But in the same time, they do not fulfill the idea of being efficient because their marginal rate of substitution of inputs or outputs is the worst one. Outliers can be identified as the ones, which lie on the reverse envelope of efficient units. So, they can be easily identified in two steps by current DEA programs. Efficient unit identified by data envelopment analysis can be used as input for statistical (regression) analysis. By elimination of outliers my be regression analysis able to find Out statistically significant information even in data where it would not be possible before. This way could the best practice be modeled, The other possibility is to use reverse data envelopment analysis and model the worst practices. Elimination of outliers may play an important role also here.