A Review of Ranking Models in Data Envelopment Analysis <s> Benchmarking Ranking Techniques <s> This article describes a new DEA (data envelopment analysis) ranking approach that combines efficiency analysis (by DEA) with index measurement (by DEA sensitivity analysis). The sensitivity analysis, incorporated into the index measurement, omits an efficient DMU (decision making unit) to obtain the index numbers of all the DMUs. The proposed DEA ranking approach is theoretically linked to a non-parametric rank sum test. Using the rank sum test, this article statistically examines whether two groups of DMUs have different distribution functions of efficiency. As an illustrative case study, this article applies the proposed approach to Japanese Agriculture Cooperatives. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Benchmarking Ranking Techniques <s> This research proposes a new ranking system for extreme efficient DMUs (Decision Making Units) based upon the omission of these efficient DMUs from reference set of the inefficient DMUs. We state and prove some facts related to our model. A numerical example where the proposed method is compared with traditional ranking approaches is shown. <s> BIB002 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Benchmarking Ranking Techniques <s> This study aims to resolve the problems associated with ranking fairly for both efficient and inefficient decision making units (DMUs) by proposing an 'interactive benchmark' model. The main concept is derived as a result of taking one certain DMU as a fixed benchmark and estimating the efficiency scores of the remaining DMUs based on that benchmark pair by pair. The process is repeated until all of the DMUs have served as the fixed benchmark. The DMUs can then be evaluated on a fair basis by computing the average efficiency scores using the above rolling procedure. The model is applied to fourteen financial holding companies (FHCs) in Taiwan using a production transfer model that is adopted by Seiford and Zhu [L.M. Seiford, J. Zhu, Profitability and marketability of the top 55 US commercial banks, Management Science 45 (9) (1999) 1270-1288]. The empirical results can serve as valuable reference to both policy-makers and investors. <s> BIB003 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Benchmarking Ranking Techniques <s> Decision making units (DMUs) can be ranked using data envelopment analysis (DEA) technologies. This paper develops a new ranking system under the condition of variable returns to scale (VRS) based on a measure of cross-dependence efficiency (MCDE), where the evaluation for an efficient DMU is dependent of the efficiency changes of all inefficient units due to its absence in the reference set, while the appraisal of inefficient DMUs depends on the influence of the exclusion of each efficient unit from the reference set. The infeasibility problem that arises from the conventional super-efficiency models is eliminated. A new approach to ranking inefficient units is embedded in the proposed ranking system. Through an example, advantages of our proposal are demonstrated. A real application illustrates the effectiveness of the cross-dependence based ranking system. <s> BIB004
Sueyoshi et al. BIB001 proposes a "benchmark approach" for baseball evaluation. This method is the combination of DEA and (Offensive earned-run average) OERA. As the authors noted, using this method it is possible to select best units and also their ranking orders. They mentioned that using only DEA may result in a shortcoming in assessment as many efficient units can be identified. Thus, the authors used slackadjusted DEA model and OERA to overcome this difficulty. Jahanshahloo et al. BIB002 presented a new model for ranking DMUs based on alteration in reference set. The idea is based on this fact that efficient units can be the target unit for inefficient units  Finally the ranking order for each efficient unit b can be computing by Note that this method cannot rank nonextreme efficient units. Lu and Lo BIB003 provided an interactive benchmark model for ranking units. The idea is based upon considering a fixed unit as a benchmark and calculating the efficiency of other units, pair by pair, to this unit. This procedure continues when all units are accounted for as a benchmark unit. Consider DMU as a unit under evaluation and DMU as a benchmark. Assume  Then using (∑ =1 * )/ , = 1, . . . , , the efficiency of benchmark DMU can be obtained. Using the following index which indicates the increment in efficiency of a unit by moving from peer appraisal to self-appraisal, it is now possible to rank units. Note that the less the magnitude of this index is the better rank for corresponding unit will be obtained where TE BCC and STD IBM are, respectively, efficiency in BCC model and normalization of TE IBM of DMU . Chen BIB004 provided a paper for ranking efficient and inefficient units in DEA. They noted that the evaluation of efficient units is based upon the alterations in efficiency of all inefficient units by omitting in reference set. At first, solve the following model which measures the efficiency of DMU when DMU is eliminated from the reference set Then, again, solve the previous model, this time for calculating the efficiency score of each inefficient unit when each of efficient units, in turn, is eliminated from the reference set * and calculate the efficiency change Then, calculate the following index called as "MCDE" index for each efficient and inefficient unit: Now, in accordance with the magnitude of the acquired index it is possible to rank units. Those units with higher score have better ranking order.