A Review of Ranking Models in Data Envelopment Analysis <s> Some Other Ranking Techniques <s> Data envelopment analysis (DEA) is a methodology for identifying the efficient frontier of decision making units (DMUs). Context-dependent DEA refers to a DEA approach where a set of DMUs are evaluated against a particular evaluation context. Each evaluation context represents an efficient frontier composed by DMUs in a specific performance level. The context-dependent DEA measures (i) the attractiveness when DMUs exhibiting poorer performance are chosen as the evaluation context, and (ii) the progress when DMUs exhibiting better performance are chosen as the evaluation context. The current paper extends the context-dependent DEA by incorporating value judgment into the attractiveness and progress measures. The method is applied to measuring the attractiveness of 32 computer printers. It is shown that the attractive measure helps (i) customers to select the best option, and (ii) printer manufacturers to identify the potential competitors. <s> BIB001 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Some Other Ranking Techniques <s> In this paper a method, based on using gradient line, for ranking DMUs is proposed. The advantage of this method is its stability and robustness, where data have special structure. Some numerical examples are presented to show the results. <s> BIB002 </s> A Review of Ranking Models in Data Envelopment Analysis <s> Some Other Ranking Techniques <s> For ranking efficient DMUs some methods have been developed. These methods are not able to rank non-extreme efficient DMUs. In this paper, using Monte Carlo method, a method has been developed which is able to rank all (extreme and non-extreme) efficient DMUs. <s> BIB003
Seiford and Zhu BIB001 presented the context-dependent DEA method for ranking units. Let Journal of Applied Mathematics the set of decision-making units. Consider +1 = − in which = {DMU ∈ | * ( , ) = 1} where * ( , ) = 1 is the optimal value of following model: The previous model with = 1 is the original CCR model. Note that DMUs in 1 show the first level efficient frontier. = 2 indicates the second level efficient frontier when the first level efficient frontier is omitted. The following algorithm finds these efficient frontiers. Step 1. Set = 1 and evaluate the entire set of DMUs,  . In this way the first level efficient DMU, 1 , is identified. Step 2. Exclude the efficient DMUs from future DEA runs and set Step 3. Evaluate the new subset of "inefficient" DMUs, +1 , to obtain a new set of efficient DMUs, +1 . Step 4. Let l = l + 1. Go to Step 2. When +1 = ø, the algorithm stops. As the authors proved in this way it is possible to rank the DMUs in the first efficient frontier based upon their attractiveness scores and identify the best one. Jahanshahloo et al. BIB002 provided a paper for ranking units using gradient line. As the authors mentioned the advantage of this model is stability and robustness Note that ( * , − * ) is the gradient of hyperplane which supports oń, the obtained PPS by omitting the DMU under assessment in . As the authors proved a unit is efficient iff the optimal objective function of the following model is greater than zero. Consider Intersection of 0 and efficient surface of́is a half line where its equation is (− * ) + ( * ) = 0. To rank DMU the length of connecting arc DMU with intersection point of line and previous ellipse is calculated in ( , ) space. This intersection is as follows: * = ( Now, the length of connecting arc DMU to the point corresponding to * , * in ( , ) plan is calculated as follows: , where Jahanshahloo et al.  also provided a paper with the concept of advantage in data envelopment analysis. In their paper Jahanshahloo et al. BIB003 considering Monte Carlo method presented a new method of ranking. Step 1. Generate a uniformly distributed sequence of { }