Cross-Efficiency aggregation based on the denominator rule

Abstract

In this paper we propose an alternative cross-efficiency aggregation scheme that is based on the theory underlying the aggregation of self-appraisal efficiency scores. For this purpose, we apply the denominator rule to aggregate the cross-efficiency scores obtained from the multiplier form of the DEA model. This results in a share-weighted average cross-efficiency that takes explicitly into account the relative importance of each element of the cross efficiency matrix by means of either the opportunity cost of resources used or the value of outputs produced, depending upon the orientation chosen to measure efficiency. It turns out that the proposed share-weighting average cross-efficiency uses the simple arithmetic average of the estimated input and output weights from the self-appraisal form of the DEA model to compute the ultimate cross-efficiency. As this is a set of common (across decision-making units) input and output weights, it allows for complete ranking and comparison of all (efficient and inefficient) decision-making units.