On value efficiency analysis and targeted benevolence cross efficiency

In this article, we examine the relation between cross efficiency and Value Efficiency Analysis, two Data Envelopment Analysis related models for peer appraisal assessment. Particularly, we show that the Targeted Benevolence cross efficiency formulation is equivalent to the Value Efficiency Analysis model if either (i) the “reference” unit, i.e. the one whose vector of optimal multipliers is used to evaluate all others in the Targeted Benevolence formulation, or (ii), its radial projection if it is inefficient, is chosen as the Most Preferred Solution in Value Efficiency Analysis. An immediate implication of this result is an alternative and most frequently shorter way to compute the Targeted Benevolence cross-efficiency matrix, as we can do so by solving a series of Value Efficiency Analysis problems, each of which uses a different unit or its radial projection if it is not efficient as the Most Preferred Solution. For this purpose, we provide a four-step algorithm, from which it is clear that in most of the cases it is not necessary to solve all the relevant problems. This depends on the number of inefficient units that are (radially) projected in the strongly efficient frontier and the number of different sets of peers for these units.