Islamic Azad University, Rasht Branch
Iranian Journal of Optimization
2008-5427
06
1
2010
09
01
A statistical test for outlier identification in data envelopment analysis
536
554
EN
Morteza
Khodabin
Islamic Azad University, Karaj Branch, Department of Mathematics P.O.Box 31485-313, Karaj, Iran.
m-kaodabin@kiau.ac.ir
Reza
Kazemi Matin
Islamic Azad University, Karaj Branch, Department of Mathematics P.O.Box 31485-313, Karaj, Iran.
In the use of peer group data to assess individual, typical or best practice performance, the effective detection of outliers is critical for achieving useful results. In these ‘‘deterministic’’ frontier models, statistical theory is now mostly available. This paper deals with the statistical pared sample method and its capability of detecting outliers in data envelopment analysis. In the presented method, each observation is deleted from the sample once and the resulting linear program is solved, leading to a distribution of efficiency estimates. Based on the achieved distribution, a pared test is designed to identify the potential outlier(s). We illustrate the method through a real data set. The method could be used in a first step, as an exploratory data analysis, before using any frontier estimation.
Data Envelopment Analysis (DEA),Outlier,Efficiency,Paired Sample Test
http://ijo.iaurasht.ac.ir/article_514143.html
http://ijo.iaurasht.ac.ir/article_514143_4f79709b7cf61f8410e7cadbb07134ea.pdf
Islamic Azad University, Rasht Branch
Iranian Journal of Optimization
2008-5427
06
1
2010
09
01
Obtaining a Unique Solution for the Cross Efficiency by Using the Lexicographic method
555
566
EN
G. R.
Jahanshahloo
epartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
R.
Fallahnejad
epartment of Mathematics, Khorram Abad Branch, Islamic Azad University, Khorram Abad, Iran
r.fallahnejad@gmail.com
Cross efficiency is a method with the idea of peer evaluation instead of self-evaluation, and is used for evaluation and ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA). Unlike most existing DEA ranking models which can only rank a subset of DMUs, for example non-efficient or extreme efficient DMUs, cross efficiency can rank all DMUs, even non-extreme ones. However, since DEA weights are generally not unique, cross-efficiency which uses optimal weights corresponding to evaluation of DMUs may not be unique either. This deficiency renders the cross efficiency method useless. However, the secondary goals proposed to deal with this deficiency of cross efficiency have such drawbacks themselves as well. In this paper we present a new secondary goal for cross efficiency method based on the lexicographic method. The main advantage of the proposed method is that with the possibility of existence of alternative optimal weights at the end of the secondary goal problem, the performance and the rank of DMUs will be constant, while the previous secondary goal methods don't offer any suggestions to deal with their alternative optimal weights.
Cross Efficiency,Data envelopment analysis,Lexicographic Method,Ranking
http://ijo.iaurasht.ac.ir/article_514144.html
http://ijo.iaurasht.ac.ir/article_514144_c0babd5ab89c5f1d7d18c6f5dd0bc94f.pdf
Islamic Azad University, Rasht Branch
Iranian Journal of Optimization
2008-5427
06
1
2010
09
01
Linear Programming, the Simplex Algorithm and Simple Polytopes
567
590
EN
Das
Sashi
Bhusan
Department of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, India
Biswal
Bagaban
Department of Mathematics F.M.Autonomous College, Balasore, Orissa, India
J.P
Tripathy
Department of Mathematics Gurukul Institute of Bhubaneswar,Orissa,India
jp_tripathy@yahoo.com
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
simplex algorithm,Randomized Pivot rule complexity combinational theory of simple polytopes
http://ijo.iaurasht.ac.ir/article_514145.html
http://ijo.iaurasht.ac.ir/article_514145_ea1a75142f8b8780dbdd391fe7c2a870.pdf
Islamic Azad University, Rasht Branch
Iranian Journal of Optimization
2008-5427
06
1
2010
09
01
A new method for ordering triangular fuzzy numbers
603
613
EN
S.H.
Nasseri
Department of Mathematical Sciences, Mazandaran University, Babolsar, Iran
nasseri@umz.ac.ir
S.
Mizuno
Department of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, Japan
Ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (CV index), distance between fuzzy sets, centroid point and original point, and also weighted mean value. In this paper, we introduce a new method for ranking triangular fuzzy number to overcome the shortcomings of the previous techniques. Finally, we compare our method with some convenient methods for ranking fuzzy numbers to illustrate the advantage our method.
Linear order,ranking fuzzy numbers,triangular fuzzy number
http://ijo.iaurasht.ac.ir/article_514147.html
http://ijo.iaurasht.ac.ir/article_514147_c6b92aaac83efba0eb5d155f24b46109.pdf