Maximum appreciative cross-efficiency in DEA: A new ranking method

Suggests a cross-efficiency based ranking method in DEA.Uses individual appreciativeness to generate maximum appreciative cross-efficiency.Combines maximum cross-efficiency, preference voting, and OWA operator, to provide a full ranking.Illustrates an application of the proposed method in ranking 15 baseball players. Ranking decision making units (DMUs) is one of the most important applications of data envelopment analysis (DEA). In this paper, we exploit the power of individual appreciativeness in developing a methodology that combines cross-evaluation, preference voting and ordered weighted averaging (OWA). We show that each stage of the proposed methodology enhances discrimination among DMUs while offering more flexibility to the decision process. Our approach is illustrated through an example involving 15 baseball players.

[1]  Nie Jia-jia.  Cross Efficiency Evaluation Method Based on Maximizing Deviations , 2012 .

[2]  José L. Ruiz,et al.  On the choice of weights profiles in cross-efficiency evaluations , 2010, Eur. J. Oper. Res..

[3]  Wen-Min Lu,et al.  A Cross-Efficiency Profiling For Increasing Discrimination in Data Envelopment Analysis , 2005 .

[4]  Zilla Sinuany-Stern,et al.  Review of ranking methods in the data envelopment analysis context , 2002, Eur. J. Oper. Res..

[5]  Ying Luo,et al.  Cross-efficiency evaluation based on ideal and anti-ideal decision making units , 2011, Expert Syst. Appl..

[6]  Ali Emrouznejad,et al.  Improving minimax disparity model to determine the OWA operator weights , 2010, Inf. Sci..

[7]  W. Cooper,et al.  Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software , 1999 .

[8]  Adli Mustafa,et al.  Cross-ranking of Decision Making Units in Data Envelopment Analysis , 2013 .

[9]  I. Contreras,et al.  Optimizing the rank position of the DMU as secondary goal in DEA cross-evaluation , 2012 .

[10]  William W. Cooper,et al.  Data Envelopment Analysis: History, Models, and Interpretations , 2011 .

[11]  Desheng Dash Wu,et al.  Performance evaluation: An integrated method using data envelopment analysis and fuzzy preference relations , 2009, Eur. J. Oper. Res..

[12]  Satoshi Washio,et al.  Expansion of the cross-efficiency evaluation by using the equations forming the efficient frontier in DEA , 2013, Optim. Methods Softw..

[13]  Jie Wu,et al.  Determination of cross-efficiency under the principle of rank priority in cross-evaluation , 2009, Expert Syst. Appl..

[14]  Kim Fung Lam,et al.  In the determination of weight sets to compute cross-efficiency ratios in DEA , 2010, J. Oper. Res. Soc..

[15]  Jie Wu,et al.  Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game , 2009, Expert Syst. Appl..

[16]  Jie Wu,et al.  Alternative secondary goals in DEA cross-efficiency evaluation , 2008 .

[17]  Kwai-Sang Chin,et al.  A neutral DEA model for cross-efficiency evaluation and its extension , 2010, Expert Syst. Appl..

[18]  Ali Emrouznejad,et al.  An extended minimax disparity to determine the OWA operator weights , 2006, Comput. Ind. Eng..

[19]  Hong Yan,et al.  Bargaining game model in the evaluation of decision making units , 2009, Expert Syst. Appl..

[20]  K. Chin,et al.  The use of OWA operator weights for cross-efficiency aggregation , 2011 .

[21]  José L. Ruiz,et al.  On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations , 2012, Eur. J. Oper. Res..

[22]  K. Chin,et al.  Some alternative models for DEA cross-efficiency evaluation , 2010 .

[23]  Chris Tofallis,et al.  Input efficiency profiling: An application to airlines , 1997, Comput. Oper. Res..

[24]  P. Andersen,et al.  A procedure for ranking efficient units in data envelopment analysis , 1993 .

[25]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[26]  John S. Liu,et al.  Data envelopment analysis 1978-2010: A citation-based literature survey , 2013 .

[27]  W. Cook,et al.  A data envelopment model for aggregating preference rankings , 1990 .

[28]  F. Hosseinzadeh Lotfi,et al.  Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation , 2011 .

[29]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[30]  Byungho Jeong,et al.  A New Ranking Approach with a modified Cross Evaluation Matrix , 2013, Asia Pac. J. Oper. Res..

[31]  Jie Wu,et al.  Cross efficiency evaluation method based on weight-balanced data envelopment analysis model , 2012, Comput. Ind. Eng..

[32]  William W. Cooper,et al.  Choosing weights from alternative optimal solutions of dual multiplier models in DEA , 2007, Eur. J. Oper. Res..

[33]  Ying-Ming Wang,et al.  A minimax disparity approach for obtaining OWA operator weights , 2005, Inf. Sci..

[34]  Peng Jiang,et al.  Weight determination in the cross-efficiency evaluation , 2011, Comput. Ind. Eng..

[35]  Ronald R. Yager,et al.  On the dispersion measure of OWA operators , 2009, Inf. Sci..

[36]  Nuria Ramón,et al.  Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation , 2011 .

[37]  T. Sexton,et al.  Data Envelopment Analysis: Critique and Extensions , 1986 .

[38]  Muhittin Oral,et al.  A methodology for collective evaluation and selection of industrial R&D projects , 1991 .

[39]  Wilhelm Rödder,et al.  A consensual peer-based DEA-model with optimized cross-efficiencies - Input allocation instead of radial reduction , 2011, Eur. J. Oper. Res..

[40]  T. Anderson,et al.  The Fixed Weighting Nature of A Cross-Evaluation Model , 2002 .

[41]  Jie Wu,et al.  Determination of weights for ultimate cross efficiency using Shannon entropy , 2011, Expert Syst. Appl..

[42]  篠原 正明,et al.  William W.Cooper,Lawrence M.Seiford,Kaoru Tone 著, DATA ENVELOPMENT ANALYSIS : A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Kluwer Academic Publishers, 2000年, 318頁 , 2002 .

[43]  Liang Liang,et al.  DEA game cross-efficiency approach to Olympic rankings , 2009 .

[44]  Stanko Dimitrov,et al.  Promoting symmetric weight selection in data envelopment analysis: A penalty function approach , 2010, Eur. J. Oper. Res..

[45]  Sungmook Lim,et al.  Minimax and maximin formulations of cross-efficiency in DEA , 2012, Comput. Ind. Eng..

[46]  Rodney H. Green,et al.  Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses , 1994 .

[47]  A. U.S.,et al.  Measuring the efficiency of decision making units , 2003 .

[48]  Amar Oukil,et al.  The appreciative democratic voice of DEA: A case of faculty academic performance evaluation , 2014 .

[49]  Jie Wu,et al.  The DEA Game Cross-Efficiency Model and Its Nash Equilibrium , 2008, Oper. Res..

[50]  C. Tofallis,et al.  Improving Discernment in DEA Using Profiling , 1996 .

[51]  Hasan Bal,et al.  Goal programming approaches for data envelopment analysis cross efficiency evaluation , 2011, Appl. Math. Comput..

[52]  Satoshi Washio,et al.  Evaluation method based on ranking in data envelopment analysis , 2013, Expert Syst. Appl..