A Review of Ranking Models in Data Envelopment Analysis

Abstract

In the course of improving various abilities of data envelopment analysis (DEA) models, many investigations have been carried out for ranking decision-making units (DMUs). This is an important issue both in theory and practice. There exist a variety of papers which apply different ranking methods to a real data set. Here the ranking methods are divided into seven groups. As each of the existing methods can be viewed from different aspects, it is possible that somewhat these groups have an overlapping with the others. The first group conducts the evaluation by a cross-efficiency matrix where the units are self-and peer-evaluated. In the second one, the ranking units are based on the optimal weights obtained from multiplier model of DEA technique. In the third group, superefficiency methods are dealt with which are based on the idea of excluding the unit under evaluation and analyzing the changes of frontier. The fourth group involves methods based on benchmarking, which adopts the idea of being a useful target for the inefficient units. The fourth group uses the multivariate statistical techniques, usually applied after conducting the DEA classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The sixth approach involves multiple-criteria decision methodologies with the DEA technique. In the last group, some different methods of ranking units are mentioned.

A novel holistic approach for solving the multi-criteria transshipment problem for infectious waste management

“…The frontier approach was described by Farrel in 1957 (Farrell, 1957), but a mathematical model for measuring relative efficiency was first introduced as the DEA-CCR model by Charnes et al (1978). The DEA technique defines the relative efficiency of a group of homogeneous DMUs on the basis of various input-output variables, using mathematical model (Hosseinzadeh Lotfi et al, 2013). Generally, a DMU will be efficient if it obtains the maximum score of 1; otherwise DMUs are inefficient.…”

Ranking of petrochemical companies using preferential voting at unequal levels of voting power through data envelopment analysis

“…Therefore, several methods have been introduced for ranking efficient DMUs. Hosseinzadeh et al [27] (4)…”

“…In the data envelopment analysis technique, there are numerous methods available, to rank the efficient DMUs. Hosseinzadeh et al [27] reviewed some of the models. In utilizing each of the ranking models, different ranks were attained for the decision-making units.…”

“…In utilizing each of the ranking models, different ranks were attained for the decision-making units. The ranking models (RM) discussed by Hosseinzadeh et al [27] Ranking the efficient petrochemical companies 1, 2, 3, 4, 7 and 8 by the above-mentioned models, the results are displayed in Table 5. For example, Column (3) demonstrates the fact that DMU2 has ranked first for eleven times and similarly has ranked third once, as well as ranked second thrice.…”

“…Hosseinzadeh et al [27] defined seven properties for ranking models. These properties are as follows:…”