A Review of Ranking Models in Data Envelopment Analysis <s> Model 4. <s> This paper deals with the selection of the profiles of weights to be used in cross-efficiency evaluations. In an attempt to prevent unrealistic weighting schemes, one of the issues of main interest that we address here is that of the zero weights, since their use implies that some of the variables considered are excluded from the assessments to be made. In the calculation of cross-efficiency scores, we propose to ignore the profiles of weights of the DMUs that cannot make a choice of non-zero weights among their alternate optima. The different units are therefore assessed in a peer-evaluation that does not consider the profiles of weights of some inefficient DMUs. This approach is referred to as "peer-restricted" cross-efficiency evaluation. Aside from avoiding zero weights, the choice of weights that we make also seeks to reduce the differences between the weights profiles selected as much as possible. Thus, in the "peer-restricted" cross-efficiency evaluation in the present paper we also try to avoid that the different DMUs attach very different weights to the same variable. Finally, we extend this approach to derive a common set of weights by exploiting the idea of similarity between profiles of weights. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Model 4. <s> Abstract Ranking DMUs is an important issue in DEA studies. Traditional DEA model usually leads to the failure to ranking all DMUs when DMUs get the same efficiency score, such as efficient DMUs or inefficient DMUs with the same efficiency score. For the sake of comparing and improving capabilities of DMUs, many researchers have sought to fully rank both efficient, as well as inefficient DMUs. In this paper, an extended DEA model considering undesirable outputs using restrictions is presented to realize a unique ranking of DMUs through the new “Maximal Balance Index” based on the optimal shadow prices. Meanwhile, a numerical example and an empirical example are provided to illustrate the difference from previous work and the application of the extended model. In the empirical study, the complete ranking of DMUs incorporating undesirable outputs is proved to be useful and unique. <s> BIB002
Maximization of the relative closeness. The authors mentioned that the bigger the relative closeness of a DMU is the better performance it will have. In a paper, Ramón et al. BIB001 selected the profiles of weights used in cross-efficiency assessment. As the authors said they tried to prevent unrealistic weighting. They have discussed the zero weights as they excluded variables from the evaluation. In the calculation of cross-efficiency scores, they proposed to ignore the profiles of those weights of the unit under evaluation that among their alternate optimal solutions cannot choose nonzero weights. They also proposed the "peer-restricted" cross-efficiency evaluation where the units assessed in a peer evaluation which means profiles of weights of some inefficient units are not considered. Finally, the presented approach extended to derive a common set of weights. Guo and Wu BIB002 provided a complete ranking of DMUs with undesirable outputs using restriction in DEA. As the author mentioned this model is presented to realize a unique ranking of units by "maximal balanced index" according to the obtained optimal shadow prices  , , , ∈ {0, 1} , ̸ = .