Three-Dimensional Visualization for Multidimensional Analysis and Performance Management of Socio-Economic Systems

Data Envelopment Analysis (DEA) models and Free Disposal Hull (FDH) models were proposed almost simultaneously in the scientific literature. In DEA models, the constraints generate a convex set. For this reason, optimization methods and software are widely used for modeling and computations for these models. Non-convexity of production possibility set of FDH models refrained significantly the development of these models. In this paper, two methods are proposed for two-and three-dimensional frontier visualization for DEA and FDH models. Computational experiments using real-life datasets documented reliability and effectiveness of proposed methods.

[1]  Henry Tulkens,et al.  On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit , 1993 .

[2]  A. V. Lychev,et al.  Measurement of returns to scale in radial DEA models , 2017 .

[4]  Lennart Hjalmarsson,et al.  Calculation of scale elasticities in DEA models: direct and indirect approaches , 2007 .

[5]  Jan Schoenfelder,et al.  The use of Data Envelopment Analysis (DEA) in healthcare with a focus on hospitals , 2019, Health care management science.

[6]  Finn R. Førsund,et al.  A note on imposing strong complementary slackness conditions in DEA , 2012, Eur. J. Oper. Res..

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

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

[9]  Antonio Jurado,et al.  Construction and Evolution of a Multidimensional Well-Being Index for the Spanish Regions , 2012 .

[10]  S. Greco,et al.  On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness , 2019 .

[11]  A. V. Volodin,et al.  About the structure of boundary points in DEA , 2005, J. Oper. Res. Soc..

[12]  Kristiaan Kerstens,et al.  Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit , 1999, Eur. J. Oper. Res..

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

[14]  Vladimir E. Krivonozhko,et al.  On some generalization of the DEA models , 2009, J. Oper. Res. Soc..

[15]  Dominique Deprins,et al.  Measuring Labor-Efficiency in Post Offices , 2006 .

[16]  V. Krivonozhko,et al.  Construction of rating function using DEA models , 2009 .

[17]  Kristiaan Kerstens,et al.  Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration , 2017, Eur. J. Oper. Res..

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

[19]  V. V. Podinovski.  Local and global returns to scale in performance measurement , 2004, J. Oper. Res. Soc..

[20]  Kristof De Witte,et al.  Efficiency in education: a review of literature and a way forward , 2017, J. Oper. Res. Soc..

[21]  Kristiaan Kerstens,et al.  Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity , 2004 .

[22]  E H Feroz,et al.  Financial statement analysis: A data envelopment analysis approach , 2003, J. Oper. Res. Soc..

[23]  A. V. Volodin,et al.  Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods , 2004, J. Oper. Res. Soc..

[24]  A. V. Lychev,et al.  Frontier visualization for nonconvex models with the use of purposeful enumeration methods , 2017 .

[25]  A. V. Lychev,et al.  Frontier Visualization and Estimation of Returns to Scale in Free Disposal Hull Models , 2019, Computational Mathematics and Mathematical Physics.

[26]  Ali Emrouznejad,et al.  DEA models for ratio data:convexity consideration , 2009 .

[27]  Kristiaan Kerstens,et al.  Solution Methods for nonconvex Free disposal Hull Models: a Review and some Critical Comments , 2014, Asia Pac. J. Oper. Res..