average - revenue efficiency and optimal scale sizes in non-parametric analysis

Data envelopment analysis (dea) is a non-parametric method for measuring the relative efficiency of decision-making units (dmus) with multiple inputs and outputs through the use of linear and mathematical programming. one of the important results in dea is the most productive scale size (mpss) of dmus. an optimal scale size (oss) must be an mpss, hence this paper introduces a new definition of oss based on the maximization of unit revenues. in particular, an efficiency measure is proposed based on the ratio between the ray average revenue (rar) of an input vector of dmus evaluated at its oss and its final revenue. the measure is called average revenue –efficiency (are). in a recent research has defined the oss from the cost orientation. whereas the cost does not cover all orientations. in this paper, a more general concept is suggested where contains revenue and cost and cost-revenue. three different scale sizes are compared. to illustrate the real applicability of the proposed approach, we use two data sets