Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Abstract Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.

[1]  Adel Hatami-Marbini,et al.  General and multiplicative non-parametric corporate performance models with interval ratio data , 2012 .

[2]  Tomoe Entani,et al.  Dual models of interval DEA and its extension to interval data , 2002, Eur. J. Oper. Res..

[3]  Jie Wu,et al.  DEA based resource allocation considering environmental factors , 2013, Math. Comput. Model..

[4]  R. Hämäläinen,et al.  Preference programming through approximate ratio comparisons , 1995 .

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

[6]  Ying Luo,et al.  DEA efficiency assessment using ideal and anti-ideal decision making units , 2006, Appl. Math. Comput..

[7]  M. Asmild,et al.  Using DEA and Worst Practice DEA in Credit Risk Evaluation , 2004 .

[8]  William W. Cooper,et al.  IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units) , 2001, J. Oper. Res. Soc..

[9]  Kwai-Sang Chin,et al.  A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers , 2009 .

[10]  Alireza Amirteimoori.  DEA efficiency analysis: Efficient and anti-efficient frontier , 2007, Appl. Math. Comput..

[11]  Joe Zhu,et al.  Rank order data in DEA: A general framework , 2006, Eur. J. Oper. Res..

[12]  Jian-Bo Yang,et al.  Interval efficiency assessment using data envelopment analysis , 2005, Fuzzy Sets Syst..

[13]  Soung Hie Kim,et al.  An application of data envelopment analysis in telephone offices evaluation with partial data , 1999, Comput. Oper. Res..

[14]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[15]  Kaoru Tone,et al.  A slacks-based measure of super-efficiency in data envelopment analysis , 2001, Eur. J. Oper. Res..

[16]  Kwai-Sang Chin,et al.  Fuzzy data envelopment analysis: A fuzzy expected value approach , 2011, Expert Syst. Appl..

[17]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[18]  Cheng-Li Chen,et al.  The worst-practice DEA model with slack-based measurement , 2009, Comput. Ind. Eng..

[19]  Sebastián Lozano,et al.  Network DEA approach to airports performance assessment considering undesirable outputs , 2013 .

[20]  Ying Luo,et al.  Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises , 2009, Expert Syst. Appl..

[21]  Alireza Amirteimoori,et al.  An improvement to the cost efficiency interval: A DEA-based approach , 2006, Appl. Math. Comput..

[22]  Ying-Ming Wang,et al.  Measuring Malmquist productivity index: A new approach based on double frontiers data envelopment analysis , 2011, Math. Comput. Model..

[23]  Chiang Kao,et al.  Fuzzy efficiency measures in data envelopment analysis , 2000, Fuzzy Sets Syst..

[24]  Ying-Ming Wang,et al.  Estimating most productive scale size with double frontiers data envelopment analysis , 2013 .

[25]  Ying-Ming Wang,et al.  Measuring the performances of decision-making units using interval efficiencies , 2007 .

[26]  Wei Wang,et al.  Evaluating the performances of decision-making units based on interval efficiencies , 2008 .

[27]  Chiang Kao,et al.  Interval efficiency measures in data envelopment analysis with imprecise data , 2006, Eur. J. Oper. Res..

[28]  Gang Yu,et al.  An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company , 2001, Oper. Res..

[29]  Hossein Azizi,et al.  A note on data envelopment analysis with missing values: an interval DEA approach , 2013 .

[30]  Gq Huang,et al.  Computers & Industrial Engineering , 2015 .

[31]  Ana S. Camanho,et al.  The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs , 2010, Eur. J. Oper. Res..

[32]  Alireza Amirteimoori,et al.  Data envelopment analysis in dynamic framework , 2006, Appl. Math. Comput..

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

[34]  Yao Chen,et al.  Ranking efficient units in DEA , 2004 .

[35]  Lei Fang,et al.  Duality and efficiency computations in the cost efficiency model with price uncertainty , 2013, Comput. Oper. Res..

[36]  Alireza Amirteimoori,et al.  Multi-component efficiency measurement with imprecise data , 2005, Appl. Math. Comput..

[37]  K. S. Park,et al.  Efficiency bounds and efficiency classifications in DEA with imprecise data , 2007, J. Oper. Res. Soc..

[38]  Jian-Bo Yang,et al.  Measuring the performances of decision-making units using geometric average efficiency , 2007, J. Oper. Res. Soc..

[39]  Hossein Azizi,et al.  Measurement of overall performances of decision-making units using ideal and anti-ideal decision-making units , 2010, Comput. Ind. Eng..

[40]  Alireza Amirteimoori,et al.  Resource allocation and target setting in data envelopment analysis , 2010, Expert Syst. Appl..

[41]  Hossein Azizi,et al.  DEA efficiency analysis: A DEA approach with double frontiers , 2014, Int. J. Syst. Sci..

[42]  Kaoru Tone,et al.  A slacks-based measure of efficiency in data envelopment analysis , 1997, Eur. J. Oper. Res..

[43]  C. Kao,et al.  Predicting bank performance with financial forecasts: A case of Taiwan commercial banks , 2004 .

[44]  Ying-Ming Wang,et al.  Improved DEA models for measuring interval efficiencies of decision-making units , 2013 .

[45]  Peng Song,et al.  A two-grade approach to ranking interval data , 2012, Knowl. Based Syst..

[46]  Hossein Azizi.  A note on “Supplier selection by the new AR-IDEA model” , 2014 .

[47]  Chiang Kao,et al.  Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan , 2008, Eur. J. Oper. Res..

[48]  G. Jahanshahloo.  Data Envelopment Analysis with Imprecise Data , 2011 .

[49]  Gholam Reza Jahanshahloo,et al.  A ranking method based on a full-inefficient frontier , 2006 .

[50]  Hossein Azizi.  A note on “A decision model for ranking suppliers in the presence of cardinal and ordinal data, weight restrictions, and nondiscriminatory factors” , 2013, Ann. Oper. Res..

[51]  WangYing-Ming,et al.  Interval efficiency assessment using data envelopment analysis , 2005 .

[52]  Soung Hie Kim,et al.  Identification of inefficiencies in an additive model based IDEA (imprecise data envelopment analysis) , 2002, Comput. Oper. Res..

[53]  Hossein Azizi,et al.  Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data , 2011 .

[54]  F. Hosseinzadeh Lotfi,et al.  Classification of Decision Making Units with Interval Data Using SBM Model , 2007 .

[55]  Hossein Azizi,et al.  Improved data envelopment analysis models for evaluating interval efficiencies of decision-making units , 2011, Comput. Ind. Eng..

[56]  Jian-Bo Yang,et al.  A preference aggregation method through the estimation of utility intervals , 2005, Comput. Oper. Res..

[57]  Joe Zhu,et al.  Imprecise data envelopment analysis (IDEA): A review and improvement with an application , 2003, Eur. J. Oper. Res..

[58]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[59]  Dimitris K. Despotis,et al.  Data envelopment analysis with missing values: An interval DEA approach , 2006, Appl. Math. Comput..

[60]  Reza Farzipoor Saen,et al.  Supplier selection by the new AR-IDEA model , 2008 .

[61]  Alireza Amirteimoori,et al.  Measuring the multi-component efficiency with shared inputs and outputs in data envelopment analysis , 2004, Appl. Math. Comput..

[62]  Jian-Bo Yang,et al.  Interval weight generation approaches based on consistency test and interval comparison matrices , 2005, Appl. Math. Comput..

[63]  Hossein Azizi,et al.  The interval efficiency based on the optimistic and pessimistic points of view , 2011 .

[64]  Ramon E. Moore,et al.  Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.) , 1979 .