A well-defined efficiency measure for dealing with closest targets in DEA

The problem of deriving the closest projection to the efficient frontier has been one of the relevant issues in recent Data Envelopment Analysis (DEA) literature. One of the challenges related to this issue is to find a 'well-defined' efficiency measure. Overall, this means that the measure should satisfy a set of interesting properties from an economical and mathematical point of view. Regarding this point, an unsettled question so far is whether there exists a well-defined efficiency measure based on closest targets in DEA. Working on this problem, in this paper we show a solution for output-oriented models. In particular, we prove that, working with full dimensional efficient facets (FDEFs), a new Russell output measure of technical efficiency satisfies the general requirements that every well-defined efficiency measure should meet.

[1]  Jesús T. Pastor,et al.  An enhanced DEA Russell graph efficiency measure , 1999, Eur. J. Oper. Res..

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

[3]  W. Briec,et al.  Technical efficiency and distance to a reverse convex set , 1999, Eur. J. Oper. Res..

[4]  Eduardo González,et al.  From efficiency measurement to efficiency improvement: The choice of a relevant benchmark , 2001, Eur. J. Oper. Res..

[5]  Lawrence M. Seiford,et al.  Data envelopment analysis (DEA) - Thirty years on , 2009, Eur. J. Oper. Res..

[6]  J. Pastor,et al.  On how to properly calculate the Euclidean distance-based measure in DEA , 2014 .

[7]  Juan Aparicio,et al.  The relevance of DEA benchmarking information and the Least-Distance Measure: Comment , 2010, Math. Comput. Model..

[8]  Patrick T. Harker,et al.  Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA , 1999 .

[9]  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 .

[10]  Walter Briec,et al.  Hölder Distance Function and Measurement of Technical Efficiency , 1999 .

[11]  Olvi L. Mangasarian,et al.  Arbitrary-norm separating plane , 1999, Oper. Res. Lett..

[12]  Laurens Cherchye,et al.  A comment on multi-stage DEA methodology , 2001, Oper. Res. Lett..

[13]  Wade D. Cook,et al.  Efficiency bounds in Data Envelopment Analysis , 1996 .

[14]  Ole Bent Olesen,et al.  Indicators of ill-conditioned data sets and model misspecification in data envelopment analysis: an extended facet approach , 1996 .

[15]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[16]  Rolf Färe,et al.  Measuring the technical efficiency of production , 1978 .

[17]  A. Bessent,et al.  Efficiency Frontier Determination by Constrained Facet Analysis , 1988, Oper. Res..

[18]  Tim Coelli,et al.  A multi-stage methodology for the solution of orientated DEA models , 1998, Oper. Res. Lett..

[19]  Sebastián Lozano,et al.  Determining a sequence of targets in DEA , 2005, J. Oper. Res. Soc..

[20]  Emmanuel Thanassoulis,et al.  Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components , 2005, Eur. J. Oper. Res..

[21]  J. T. Pastor,et al.  A Quasi-Malmquist Productivity Index , 1998 .

[22]  Juan Aparicio,et al.  Closest targets and minimum distance to the Pareto-efficient frontier in DEA , 2007 .

[23]  Walter Briec,et al.  Metric Distance Function and Profit: Some Duality Results , 1999 .

[24]  Tarmo Räty.  Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification , 2002 .

[25]  A. Charnes,et al.  Classifying and characterizing efficiencies and inefficiencies in data development analysis , 1986 .

[26]  M. Farrell.  The Measurement of Productive Efficiency , 1957 .

[27]  R. Färe,et al.  The measurement of efficiency of production , 1985 .

[28]  Emmanuel Thanassoulis,et al.  Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies , 2003 .

[29]  Boaz Golany,et al.  Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions , 1985 .

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

[31]  Chulwoo Baek,et al.  The relevance of DEA benchmarking information and the Least-Distance Measure , 2009, Math. Comput. Model..

[32]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[33]  W. Cooper,et al.  RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA , 1999 .

[34]  Alireza Amirteimoori,et al.  A Euclidean distance-based measure of efficiency in data envelopment analysis , 2010 .