A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> Abstract A new multiple criteria decision-making (MCDM) method, called the Balancing and Ranking Method, is presented. The method overcomes some of the deficiencies of other MCDM methods, such as subjective evaluation of criteria weights, scoring of options, statistical estimation of weights and specification of the utility function for criteria. The new method uses a three-step procedure to derive an overall complete final order of options. First, an outranking matrix is derived, which indicates the frequency with which one option is superior to all other options based on each criterion. Second, the outranking matrix is triangularized to obtain an implicit pre-ordering or provisional order of options. Third, the provisional order of options is subjected to various screening and balancing operations that require sequential application of a balancing principle to the so-called advantages–disadvantages table that combines the criteria with the pair-wise comparisons of options. The new method is used to rank five farming systems (FS) for a claypan soil region in the Midwestern US. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> Abstract Ranked voting data arise when voters select and rank more than one candidate with order of preference. Cook and Kress [Management Science 36 (11) (1990) 1302] introduced data envelopment analysis (DEA) to analyze ranked voting data. By using DEA, each candidate may use the most favorable weights for him/her to estimate his/her own preference score. However DEA often suggests that more than one unit are equally efficient. So, a method to discriminate these efficient candidates is needed. Some methods of such purpose are proposed. However, these methods have a weak point that the order of efficient candidates may be changed by existence of an inefficient candidate. In this paper, we propose a new method. Our method does not use information about inefficient candidates to discriminate efficient candidates. It is based on a very simple idea, and is realizable visually. So, we hope that it is acceptable to election officials. <s> BIB002 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> In data mining applications, it is important to develop evaluation methods for selecting quality and profitable rules. This paper utilizes a non-parametric approach, Data Envelopment Analysis (DEA), to estimate and rank the efficiency of association rules with multiple criteria. The interestingness of association rules is conventionally measured based on support and confidence. For specific applications, domain knowledge can be further designed as measures to evaluate the discovered rules. For example, in market basket analysis, the product value and cross-selling profit associated with the association rule can serve as essential measures to rule interestingness. In this paper, these domain measures are also included in the rule ranking procedure for selecting valuable rules for implementation. An example of market basket analysis is applied to illustrate the DEA based methodology for measuring the efficiency of association rules with multiple criteria. <s> BIB003 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> Data envelopment analysis models usually split decision making units into two basic groups, efficient and inefficient. Efficiency score of inefficient units allows their ranking but efficient units cannot be ranked directly because of their maximum efficiency. That is why there are formulated several models for ranking of efficient units. The paper presents two original models for ranking of efficient units in data envelopment analysis—they are based on multiple criteria decision making techniques—goal programming and analytic hierarchy process. The first model uses goal programming methodology and minimizes either the sum of undesirable deviations or maximal undesirable deviation from the efficient frontier. The second approach is analytic hierarchy process model for ranking of efficient units. The two presented models are compared with several super-efficiency models and other approaches for ranking decision making units in DEA models including definitions based on distances from optimistic and pessimistic envelopes and cross efficiency evaluation models. The results of the analysis by all presented models are illustrated on a real data set—evaluation of 194 bank branches of one of the Czech commercial banks. <s> BIB004 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550-554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi's. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples. <s> BIB005 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Ranking with Multicriteria <s> Abstract Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights. <s> BIB006
Decision-Making (MCDM) Methodologies and DEA Li and Reeves [56] for increasing discrimination power of DEA presented a multiple-objective linear program (MOLP). As the authors mentioned using minimax and minsum efficiency in addition to the standard DEA objective function help to increase discrimination power of DEA. Strassert and Prato BIB001 presented the balancing and ranking method which uses a three-step procedure for deriving an overall complete or partial final order of options. In the first step, derive an outranking matrix for all options Journal of Applied Mathematics 13 from the criteria values. Considering this matrix it is possible to show the frequency with which one option is ranked higher than the other options. In the second step, by triangularizing the outranking matrix establish an implicit preordering or provisional ordering of options. The outranking matrix shows the degree to which there is a complete overall order of options. In the third step, based on information given in an advantages-disadvantages table, the provisional ordering is subjected to different screening and balancing operations. Chen BIB003 utilized a nonparametric approach, DEA, to estimate and rank the efficiency of association rules with multiple criteria in following steps. Proposed postprocessing approach is as follows. Step 1. Input data for association rule mining. Step 2. Mine association rules by using the a priori algorithm with minimum support and minimum confidence. Step 3. Determine subjective interestingness measures by further considering the domain related knowledge. Step 4. Calculate the preference scores of association rules discovered in Step 2 by using Cook and Kress's DEA model. Step 5. Discriminate the efficient association rules found in Step 3 by using Obata and Ishii's BIB002 discriminate model. Step 6. Select rules for implementation by considering the reference scores generated in Step 5 and domain related knowledge. Jablonsky BIB004 presented two original models, super SBM and AHP, for ranking of efficient units in DEA. As the author mentioned these models are based on multiple criteria decision-making techniques-goal programming and analytic hierarchy process. Super SBM model for ranking units is as follows:  Wang and Jiang BIB005 presented an alternative mixed integer linear programming models in order to identify the most efficient units in DEA technique. As the authors mentioned presented models can make full use of inputoutput information with no need to specify any assurance regions for input and output weights to avoid zero weights Hosseinzadeh Lotfi et al. BIB006 provided an improved threestage method for ranking alternatives in multiple criteria decision analysis. In the first stage, based on the best and worst weights in the optimistic and pessimistic cases, obtain the rank position of each alternative, respectively. The obtained weight in the first stage is not unique; thus it seems necessary to introduce a secondary goal that is used in the second stage. Finally, in the third stage, the ranks of the alternatives compute in the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multicriteria decision-making (MCDM) model, and it is solved by mixed integer programming. As the authors mentioned and provided in their paper this model can be converted into an LP problem In the previous model, the rank vector for each alternative is computed by the ideal rank.