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

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

January 31, 2001 | Kaoru Tone
This paper introduces a slacks-based measure of super-efficiency in Data Envelopment Analysis (DEA), proposed by Kaoru Tone. The method differs from traditional radial measures by directly addressing input/output slacks, allowing for a more accurate discrimination between efficient Decision Making Units (DMUs). The slacks-based measure (SBM) provides an efficiency score between 0 and 1, with a score of 1 indicating that a DMU is on the frontier of the production possibility set with no slacks. The paper discusses the super-efficiency issue using the SBM, proposing a method to rank efficient DMUs. It compares the SBM-based super-efficiency measure with the radial super-efficiency model proposed by Andersen and Petersen, demonstrating the rationality of the SBM approach. The SBM is particularly useful when the number of DMUs is small relative to the number of criteria used for evaluation. The paper also presents an example illustrating the SBM-based super-efficiency measure, showing that it provides a more accurate ranking of efficient DMUs compared to the radial model. The SBM-based super-efficiency measure is further specialized for input and output orientations, enabling direct comparison with radial super-efficiency measures. The paper concludes that the SBM-based super-efficiency measure is a more rational approach to evaluating super-efficiency in DEA, as it accounts for slacks in inputs and outputs, unlike traditional radial measures. The paper also highlights the need for further research on other types of distance measures and the infeasibility of LP issues in DEA.This paper introduces a slacks-based measure of super-efficiency in Data Envelopment Analysis (DEA), proposed by Kaoru Tone. The method differs from traditional radial measures by directly addressing input/output slacks, allowing for a more accurate discrimination between efficient Decision Making Units (DMUs). The slacks-based measure (SBM) provides an efficiency score between 0 and 1, with a score of 1 indicating that a DMU is on the frontier of the production possibility set with no slacks. The paper discusses the super-efficiency issue using the SBM, proposing a method to rank efficient DMUs. It compares the SBM-based super-efficiency measure with the radial super-efficiency model proposed by Andersen and Petersen, demonstrating the rationality of the SBM approach. The SBM is particularly useful when the number of DMUs is small relative to the number of criteria used for evaluation. The paper also presents an example illustrating the SBM-based super-efficiency measure, showing that it provides a more accurate ranking of efficient DMUs compared to the radial model. The SBM-based super-efficiency measure is further specialized for input and output orientations, enabling direct comparison with radial super-efficiency measures. The paper concludes that the SBM-based super-efficiency measure is a more rational approach to evaluating super-efficiency in DEA, as it accounts for slacks in inputs and outputs, unlike traditional radial measures. The paper also highlights the need for further research on other types of distance measures and the infeasibility of LP issues in DEA.
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[slides and audio] A slacks-based measure of super-efficiency in data envelopment analysis