Note: Ranking DMUs with Infeasible Super-Efficiency DEA Models

Abstract

I t has been suggested in the data envelopment analysis (DEA) literature that it is impossible to obtain a full ranking of decision-making units (DMUs) when infeasible subproblems arise in the so-called super-efficiency DEA models under different returns to scale (RTS) assumptions other than constant returns to scale (CRS) and consequently the application of the super-efficiency DEA models under different RTS conditions other than CRS should be restricted. The implications of the infeasibility in super-efficiency DEA models with respect to the efficiency ranking of the DMUs is explored. Based on the analysis, we show that it is still possible to obtain the full ranking of the entire observation set when infeasibilities arise in super-efficiency DEA models.

Data Envelopment Analysis of Helsinki-Tallinn Transportation Chains

“…Super-efficiency gives opportunity for this (it is actually a two-staged process, where the ordinary frontier is at first estimated and then the highest performing options are removed from the data and the frontier is recalculated) as variance grows between the options and the highest performing is clearly detected (e.g. [26]). …”

“…Data Envelopment Analysis is based on linear programming and it fits the scale curves on multidimensional non-parametric data during the efficiency estimation process. Research does not only report ordinary DEA efficiency in the range from 0-100%, but it gives super-efficiency values, which are more suitable in situations, where differences between the evaluated units are minor [26].…”

Research on Optimization for Units Start During Power System Restoration

“…An improved DEA model, that is, super efficiency DEA model [13,14] is fully applied to compare and rank the decision making unit in this paper. In the units recovery model, according to start units selection principle, each optional start units are launched as decision unit, then combined with the improved DEA model, the input and output index of the unit relative efficiency evaluation are established.…”

Equivalent standard DEA models to provide super-efficiency scores

“…; a m Þ þ 1. If a super-efficient DMU remains efficient after scaling its inputs by a, then it belongs to the super-efficient category of DMUs (SE) identified as infeasible by Xue and Harker; 18 ie, at least one output belonging to DMU o is strictly larger than a convex combination of that output among all other DMUs in the reference set. …”

“…18 Infeasibility arises in either orientation whenever there is no referent DMU for the excluded DMU. A necessary condition for infeasibility is that the excluded DMU be 'extreme-efficient'.…”