Document Type : Research Paper

Authors

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

The science of Data Envelopment Analysis (DEA) evaluates the effectiveness of decision making units. But, one of the problems of Data Envelopment Analysis (DEA) is that, if the number of units with the same efficiency equal to one was more than one, then we couldn’t select the best between them. It means that, we can’t rank them. Therefore, the need for ranking these units is considered by the managers. Different methods were proposed in this context. Most of these methods are modeled by DEA models. Due to the variety of ranking methods in DEA, this paper will describe ranking methods which are based on super-efficiency. More precisely, we introduced methods that rank using elimination (removing) of decision making units under the evaluation of observations(set). These methods have some advantages and disadvantages such as, model feasibility or infeasibility, stability or instability, being linear or nonlinear, being radial or non-radial, existence or non- existence of bounded optimal solution in objective function, existence or non- existence of multiple optimal solution, non-extreme efficient units ranking, complexity or simplicity of computational processes, that in this paper, Super Efficiency methods are compared with these eight properties.

Keywords

Main Subjects

[1]     Jahanshahloo et al. (1387). Data Envelopment Analysis and its applications. Islamic Azad University. Science & Research Branch.
[2]       Adler,N., Friedman,L., Sinuany-Stern,Z.,2002.Review of ranking method in the data envelopment analysis context. European Journal of operational research.140,249-265.
[3]      Amirteimoori,A.,Jahanshahloo,G.R., Kordrostami,S.,2005. Ranking of decision making units in data envelopment analysis: A distance-based approach.Applied Mathematics and Computation 171.122-135.
[4]  Andaerson,P., Petersen,N.C.1993(A Procedure for ranking efficient units in data envelopment Analysis, management science 39.1261-1264.)
[5]  Banker, R.D., Charnes,A.,Cooper, W.W.,1984. Some method for estimating technical and scale inefficiencies in data envelopment analysis, management science,30(9).1078-1092.
 
 
[6]  Charnes,A.,Cooper, W.W., Rhodes, E.,1978. Measuring efficiency of decision making units, Uroupean Journal of Operational Research.
[7]  Jahanshahloo, G.R., Afzalinejad,M,2006b. A ranking method based on a full-inefficient frontier. Applied Mathemstical Modeling.30,248-260.
[8]  Jahanshahloo, G.R., Hosseinzadeh Lotfi, F, Bagherzadeh Valami(2008). Ranking units using by cotext-dependent data envelopment analysis. applied mathematics Journal.
[9]     Jahanshahloo, G.R., HosseinZadeh Lotfi,F,Junior,H.V., Akbarian,D,2006a. A new DEA rnking system based on changing the reference set. European Journal of operational research.
[10]         Jahanshahloo, G.R., HosseinZadeh Lotfi,F, Rezai,H,Akbarian,D.,2004c. Ranking efficient DMUs using tchebycheff norm. working paper.
[11]        Jahanshahloo, G.R., HosseinZadeh Lotfi,F, Shoja,N, Tohidi,G, Razavian,S,2004a. Ranking using 𝐿1 norm data envelopment analysis. Applied mathematic and computation.153(1),215-224.
[12]   Jahanshahloo, G.R., HosseinZadeh Lotfi,F, Zhiani Rezaei,F, Rezaei Balf,F.2005. Using Monte carlo method for ranking efficient DMUs. Applied mathematic and computation.162.371-379.
[13]      Jahanshahloo, G.R., Sanei,M, HosseinZadeh Lotfi,F ,Shoja,N,2004e. using the gradiant line for ranking DMUs in DEA. Applied mathematic and computation.151(1),209-217.
[14]       Jahanshahloo, G.R., Sanei,M, Shoja,N,2004b. Modified ranking models, using the cocept of advantagein data envelopment analysis. Article in press.
[15]   Jahanshahloo, G.R., Pourkarimi,L., Zarepishe,M.,2006c.Modified MAJ model for ranking of decision making unite in data envelopment analysis. Applied Mathmatics and computation.174.1054-1059.
[16]   Khodabakhshi,M,2007.A super-efficiency model based on improved outputs in data envelopment analysis. Applied mathematic and computation,184,695-703.
[17]        Li,Sh, Jahanshahloo, G.R., Khodabakhshi,M,2007. A super- efficiency model for ranking efficient units in data envelopment analysis. . Applied mathematics and computation.