A Review of Ranking Models in Data Envelopment Analysis <s> =1 <s> Since in evaluating by traditional data envelopment analysis (DEA) models many decision making units (DMUs) are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In this paper a ranking method is suggested which basically differs from previous methods but its models are similar to traditional DEA models such as BCC, additive model, etc. In this ranking method, DMUs are compared against an full-inefficient frontier, which will be defined in this paper. Based on this point of view many models can be designed, and we mention a radial and a slacks-based one out of them. This method can be used to rank all DMUs to get analytic information about the system, and also to rank only efficient DMUs to discriminate between them. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> =1 <s> Data envelopment analysis (DEA) is a methodology for identifying the efficient frontier of production possibility set. Using this efficient frontier, an efficiency score is derived to each decision making units. This study, proposes an alternative efficiency measure by using efficient and anti-efficient frontiers. Numerical experiments show the validity of the proposed efficiency measure and its compatibility with other measures of efficiency. The paper addresses the super-efficiency issue by using this measure. <s> BIB002 </s> A Review of Ranking Models in Data Envelopment Analysis <s> =1 <s> One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a longer distance to the anti-ideal despite the rankings based on the two distance measures possibly not being the same. In order to obtain consistent rankings, this paper proposes a measure of relative distance, which involves the calculation of the relative position of an alternative between the anti-ideal and the ideal for ranking. In this case, minimizing the distance to the ideal is equivalent to maximizing the distance to the anti-ideal, so the rankings obtained from the two criteria are the same. An example is used to discuss the advantages and disadvantages of the proposed method, and the results are compared with those obtained from the TOPSIS method. <s> BIB003 </s> A Review of Ranking Models in Data Envelopment Analysis <s> =1 <s> Abstract The motivation of this study is to propose an equitable method for ranking decision making units (DMUs) based on the data envelopment analysis (DEA) concept. For this purpose, first, the minimum and maximum efficiency values of each DMU are computed under the assumption that the sum of efficiency values of all DMUs is equal to unity. Then, the rank of each DMU is determined in proportion to a combination of its minimum and maximum efficiency values. <s> BIB004 </s> A Review of Ranking Models in Data Envelopment Analysis <s> =1 <s> In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method. <s> BIB005
on(0, 1). Step 2. Random numbers should be classified into pairs like ( 1 , 1 ) , . . . , ( , ) in a way that each number is used just one time. Step 3. Compute = + ( − ) and ( ) > . Step 4. Estimate the integral by = ( − )( / ). Now consider DMU as an efficient unit measure those units that are dominated DMU . As for dome DMUs this would be unbounded, thus the authors, for each unit, bounded the region. Then, for DMU if (− , ) ≥ (− , ), then (− , ) is in the RED of DMU . Now by using = * ( / ) all the hits (the above condition) can be counted, where * is the measure of the whole region. Jahanshahloo and Afzalinejad BIB001 presented a method based on distance of the unit under evaluation to the full inefficient frontier. They presented two models, radian and nonradial  Amirteimoori BIB002 based on the same idea considered both efficient and antiefficient frontiers for efficiency analysis and ranking units. Kao BIB003 mentioned that determining the weights of individual criteria in multiple criteria decision analysis in a way that all alternatives can be compared according to the aggregate performance of all criteria is of great importance. As Kao noted this problem relates to search for alternatives with a shorter and longer distance, respectively, to the ideal and anti-ideal units. He proposed a measure that considered the calculation of the relative position of an alternative between the ideal and anti-ideal for finding an appropriate rankings. Khodabakhshi and Aryavash BIB004 presented a method for ranking all units using DEA concept. First, Compute the minimum and maximum efficiency values of each DMU in regard to this assumption that the sum of efficiency values of all DMUs equals to 1. Second, determine the rank of each DMU in relation to a combination of its minimum and maximum efficiency values. Zerafat Angiz et al. BIB005 proposed a technique in order to aggregate the opinions of experts in voting system. As the authors mentioned the presented method uses fuzzy concept, and it is computationally efficient and can fully rank alternatives. At first, number of votes given to a rank position was grouped to construct fuzzy numbers, and then the artificial ideal alternative introduced. Furthermore, by performing DEA the efficiency measure of alternatives was obtained considering artificial ideal alternative compared by each of the alternatives pair by pair. Thus alternatives are ranked in accordance with their efficiency scores. If this method cannot completely rank alternatives, weight restrictions based on fuzzy concept are imposed into the analysis.