Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.

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

[2]  Emmanuel Thanassoulis,et al.  Applied data envelopment analysis , 1991 .

[3]  Da Ruan,et al.  Data envelopment analysis based decision model for optimal operator allocation in CMS , 2005, Eur. J. Oper. Res..

[4]  A. Charnes,et al.  Data Envelopment Analysis Theory, Methodology and Applications , 1995 .

[5]  Patrizia Beraldi,et al.  Probabilistically constrained models for efficiency and dominance in DEA , 2009 .

[6]  Ram Rachamadugu,et al.  A closer look at the use of data envelopment analysis for technology selection , 1997 .

[7]  Jie Wu,et al.  Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method , 2009, Eur. J. Oper. Res..

[8]  W. Cook,et al.  Preference voting and project ranking using DEA and cross-evaluation , 1996 .

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

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

[11]  Dimitris K. Despotis,et al.  Improving the discriminating power of DEA: focus on globally efficient units , 2002, J. Oper. Res. Soc..

[12]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[13]  Srinivas Talluri,et al.  A cone-ratio DEA approach for AMT justification , 2000 .

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

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

[16]  F. Liu,et al.  DEA Malmquist productivity measure: Taiwanese semiconductor companies , 2008 .

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

[18]  Nuria Ramón,et al.  A multiplier bound approach to assess relative efficiency in DEA without slacks , 2010, Eur. J. Oper. Res..

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

[20]  Gholam R. Amin,et al.  An Assurance Interval for the Non-Archimedean Epsilon in DEA Models , 2000, Oper. Res..

[21]  Emmanuel Thanassoulis,et al.  Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions , 1997, Ann. Oper. Res..

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

[23]  Barton A. Smith,et al.  Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas , 1986 .

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

[25]  Ling Liu-yi,et al.  Ranking all decision making units based on their elementary differences , 2012 .

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

[27]  Gerhard Reichmann,et al.  University library benchmarking: An international comparison using DEA , 2006 .

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

[29]  John E. Beasley,et al.  Restricting Weight Flexibility in Data Envelopment Analysis , 1990 .

[30]  A. Charnes,et al.  Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks , 1990 .

[31]  William W. Cooper,et al.  Selecting non-zero weights to evaluate effectiveness of basketball players with DEA , 2009, Eur. J. Oper. Res..

[32]  F. Hosseinzadeh Lotfi,et al.  A cross-efficiency model based on super-efficiency for ranking units through the TOPSIS approach and its extension to the interval case , 2011, Math. Comput. Model..

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

[34]  R. Dyson,et al.  Reducing Weight Flexibility in Data Envelopment Analysis , 1988 .

[35]  Hasan Bal,et al.  A New Approach To Cross Efficiency In Data Envelopment Analysis and Performance Evaluation of Turkey Cities , 2012 .

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

[37]  Sebastián Lozano,et al.  Application of centralised DEA approach to capital budgeting in Spanish ports , 2011, Comput. Ind. Eng..

[38]  Toshiyuki Sueyoshi,et al.  A unified framework for the selection of a Flexible Manufacturing System , 1995 .

[39]  Jun Liu,et al.  An integrated AHP-DEA methodology for bridge risk assessment , 2008, Comput. Ind. Eng..

[40]  Jie Wu,et al.  Olympics ranking and benchmarking based on cross efficiency evaluation method and cluster analysis: the case of Sydney 2000 , 2008 .