Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306120100901A statistical test for outlier identification in data envelopment analysis536554514143ENMorteza KhodabinIslamic Azad University, Karaj Branch, Department of Mathematics P.O.Box 31485-313, Karaj, Iran.Reza Kazemi MatinIslamic Azad University, Karaj Branch, Department of Mathematics P.O.Box 31485-313, Karaj, Iran.Journal Article20100830<span>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 </span><span>results. In these ‘‘deterministic’’ frontier models, statistical theory is now mostly </span><span>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. </span>Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306120100901Obtaining a Unique Solution for the Cross Efficiency by Using the Lexicographic method555566514144ENG. R. Jahanshahlooepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranR. Fallahnejadepartment of Mathematics, Khorram Abad Branch, Islamic Azad University, Khorram Abad, IranJournal Article20100730<span>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. </span>Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306120100901Linear Programming, the Simplex Algorithm and Simple Polytopes567590514145ENDas SashiBhusanDepartment of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, IndiaBiswal BagabanDepartment of Mathematics F.M.Autonomous College, Balasore, Orissa, IndiaJ.P TripathyDepartment of Mathematics Gurukul Institute of Bhubaneswar,Orissa,IndiaJournal Article20100730<span>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. </span>Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306120100901A new method for ordering triangular fuzzy numbers603613514147ENS.H. NasseriDepartment of Mathematical Sciences, Mazandaran University, Babolsar, IranS. MizunoDepartment of Industrial Engineering and Management, Tokyo Institute of Technology, Tokyo, JapanJournal Article20100730<span>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. </span>