A slacks-based measure of super-efficiency in data envelopment analysis

In most models of Data Envelopment Analysis (DEA), the best performers have the full efficient status denoted by unity (or 100%), and, from experience, we know that usually plural Decision Making Units (DMUs) have this “efficient status”. To discriminate between these efficient DMUs is an interesting subject. This paper addresses this “super-efficiency” issue by using the slacks-based measure (SBM) of efficiency, which the author proposed in his previous paper [European Journal of Operational Research 130 (2001) 498]. The method differs from the traditional one based on the radial measure, e.g. Andersen and Petersen model, in that the former deals directly with slacks in inputs/outputs, while the latter does not take account of the existence of slacks. We will demonstrate the rationality of our approach by comparing it with the radial measure of super-efficiency. The proposed method will be particularly useful when the number of DMUs are small compared with the number of criteria employed for evaluation.

A Slacks-based Measure of Super-Efficiency in Data Envelopment Analysis

Data envelopment analysis (DEA) - Thirty years on

In this paper we examine a neglected aspect of Data Envelopment Analysis: cross-efficiency. We develop the concept of cross-efficiency in a number of new directions. We ground an intuitive understanding of cross-efficiency in the concept of peer-appraisal, as opposed to self-appraisal implied by simple efficiency, and discuss the relative merits of each. We also present mathematical formulations of, and intuitive meanings for three possible implementations of aggressive and benevolent cross-efficiency. We have implemented two of these formulations in computer programs; their performance is compared empirically on a real data set. Finally, we suggest practical uses for cross-efficiency, illustrated with reference to the same data set.

https://link.springer.com/content/pdf/10.1057%2Fjors.1994.84.pdf

Efficiency and cross-efficiency in DEA: derivations, meanings and uses

A survey of data envelopment analysis in energy and environmental studies

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Data envelopment analysis and multiple criteria decision making

There is a need to distinguish among efficient DMUs in Data Envelopment Analysis (DEA). We introduce cross-evaluation in DEA as a logical extension of the reference set count, an idea which is alre...

Cross-Evaluation in DEA - Improving Discrimiation Among DMUs

Two commonly used methods of assigning numerical judgments (i.e., importance weights) to attributes in order to signify their relative importance are point allocation (PA) and direct rating (DR). These methods may seem to be minor variants of each other, yet they produce very different profiles of attribute weights when rank ordered from most to least important. The weights elicited by DR were more reliable than those elicited by PA in a test–retest situation. An important practical implication of this is for multicriteria decision making. Using people’s test–retest data as attribute weights on simulated alternative values revealed that the same alternative would be chosen on 88% of occasions with DR, but only 74% of occasions with PA. Moreover, subjects reacted more favorably to DR than to PA.

Rodney H. Green

Papers

Efficiency and cross-efficiency in DEA: derivations, meanings and uses

Preference voting and project ranking using DEA and cross-evaluation

Data envelopment analysis and multiple criteria decision making

Cross-Evaluation in DEA - Improving Discrimiation Among DMUs

Testing the reliability of weight elicitation methods: Direct rating versus point allocation