IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v71y2017icp1-10.html
   My bibliography  Save this article

The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects

Author

Listed:
  • Aparicio, Juan
  • Cordero, Jose M.
  • Pastor, Jesus T.

Abstract

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniques have been proposed in order to implement the new paradigm. A group of these techniques is based on identifyiexit3b2tex.batng all the efficient faces of the polyhedral production possibility set and, therefore, is associated with the resolution of a NP-hard problem. In contrast, a second group proposes different models and particular algorithms to solve the problem avoiding the explicit identification of all these faces. These techniques have been applied more or less successfully. Nonetheless, the new paradigm is still unsatisfactory and incomplete to a certain extent. One of these challenges is that related to measuring technical inefficiency in the context of oriented models, i.e., models that aim at changing inputs or outputs but not both. In this paper, we show that existing specific techniques for determining the least distance without identifying explicitly the frontier structure for graph measures, which change inputs and outputs at the same time, do not work for oriented models. Consequently, a new methodology for satisfactorily implementing these situations is proposed. Finally, the new approach is empirically checked by using a recent PISA database consisting of 902 schools.

Suggested Citation

  • Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
  • Handle: RePEc:eee:jomega:v:71:y:2017:i:c:p:1-10
    DOI: 10.1016/j.omega.2016.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316301803
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Angel Prieto & José ZofIo, 2001. "Evaluating Effectiveness in Public Provision of Infrastructure and Equipment: The Case of Spanish Municipalities," Journal of Productivity Analysis, Springer, vol. 15(1), pages 41-58, January.
    2. Tommaso Agasisti & Pablo Zoido, 2015. "The Efficiency of Secondary Schools in an International Perspective: Preliminary Results from PISA 2012," OECD Education Working Papers 117, OECD Publishing.
    3. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    4. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    5. Walter Briec & Hervé Leleu, 2003. "Dual Representations of Non-Parametric Technologies and Measurement of Technical Efficiency," Journal of Productivity Analysis, Springer, vol. 20(1), pages 71-96, July.
    6. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    7. Kristof de Witte & Laura López-Torres, 2015. "Efficiency in Education. A Review of Literature and a Way Forward," Working Papers 1501, Departament Empresa, Universitat Autònoma de Barcelona, revised Apr 2015.
    8. J L Ruiz & I Sirvent, 2011. "A DEA approach to derive individual lower and upper bounds for the technical and allocative components of the overall profit efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1907-1916, November.
    9. Frances Frei & Patrick Harker, 1999. "Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA," Journal of Productivity Analysis, Springer, vol. 11(3), pages 275-300, June.
    10. Gonzalez, Eduardo & Alvarez, Antonio, 2001. "From efficiency measurement to efficiency improvement: The choice of a relevant benchmark," European Journal of Operational Research, Elsevier, vol. 133(3), pages 512-520, September.
    11. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    12. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    13. Eva Crespo-Cebada & Francisco Pedraja-Chaparro & Daniel Santín, 2014. "Does school ownership matter? An unbiased efficiency comparison for regions of Spain," Journal of Productivity Analysis, Springer, vol. 41(1), pages 153-172, February.
    14. Hirofumi Fukuyama & Hiroya Masaki & Kazuyuki Sekitani & Jianming Shi, 2014. "Distance optimization approach to ratio-form efficiency measures in data envelopment analysis," Journal of Productivity Analysis, Springer, vol. 42(2), pages 175-186, October.
    15. Hirofumi Fukuyama & Jens Leth Hougaard & Kazuyuki Sekitani & Jianming Shi, 2016. "Efficiency measurement with a non-convex free disposal hull technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(1), pages 9-19, January.
    16. Wu, Desheng Dash, 2010. "BiLevel programming Data Envelopment Analysis with constrained resource," European Journal of Operational Research, Elsevier, vol. 207(2), pages 856-864, December.
    17. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    18. Briec, W. & Lemaire, B., 1999. "Technical efficiency and distance to a reverse convex set," European Journal of Operational Research, Elsevier, vol. 114(1), pages 178-187, April.
    19. E. Grifell-Tatjé & C. Lovell & J. Pastor, 1998. "A Quasi-Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 10(1), pages 7-20, July.
    20. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    21. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    22. Ruiz, José L. & Segura, José V. & Sirvent, Inmaculada, 2015. "Benchmarking and target setting with expert preferences: An application to the evaluation of educational performance of Spanish universities," European Journal of Operational Research, Elsevier, vol. 242(2), pages 594-605.
    23. Daniel Santín & Gabriela Sicilia, 2015. "Measuring the efficiency of public schools in Uruguay: main drivers and policy implications," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 24(1), pages 1-28, December.
    24. Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
    25. Fukuyama, Hirofumi & Maeda, Yasunobu & Sekitani, Kazuyuki & Shi, Jianming, 2014. "Input–output substitutability and strongly monotonic p-norm least distance DEA measures," European Journal of Operational Research, Elsevier, vol. 237(3), pages 997-1007.
    26. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Juan Aparicio & Magdalena Kapelko & Bernhard Mahlberg & Jose L. Sainz-Pardo, 2017. "Measuring input-specific productivity change based on the principle of least action," Journal of Productivity Analysis, Springer, vol. 47(1), pages 17-31, February.
    2. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2019. "Extending the bargaining approach to DEA target setting," Omega, Elsevier, vol. 85(C), pages 94-102.
    3. Olkis, Christopher & Brandani, Stefano & Santori, Giulio, 2019. "Design and experimental study of a small scale adsorption desalinator," Applied Energy, Elsevier, vol. 253(C), pages 1-1.
    4. Atwood, Joseph & Shaik, Saleem, 2020. "Theory and statistical properties of Quantile Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 286(2), pages 649-661.
    5. Cordero, Jose M. & Polo, Cristina & Santín, Daniel & Simancas, Rosa, 2018. "Efficiency measurement and cross-country differences among schools: A robust conditional nonparametric analysis," Economic Modelling, Elsevier, vol. 74(C), pages 45-60.
    6. Cook, Wade D. & Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada & Zhu, Joe, 2019. "DEA-based benchmarking for performance evaluation in pay-for-performance incentive plans," Omega, Elsevier, vol. 84(C), pages 45-54.
    7. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    8. Aparicio, Juan & Cordero, Jose M. & Ortiz, Lidia, 2019. "Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    9. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    10. Lozano, Sebastián & Calzada-Infante, Laura, 2018. "Computing gradient-based stepwise benchmarking paths," Omega, Elsevier, vol. 81(C), pages 195-207.
    11. Aparicio, Juan & Cordero, Jose M. & Gonzalez, Martin & Lopez-Espin, Jose J., 2018. "Using non-radial DEA to assess school efficiency in a cross-country perspective: An empirical analysis of OECD countries," Omega, Elsevier, vol. 79(C), pages 9-20.
    12. De Clercq, Djavan & Wen, Zongguo & Caicedo, Luis & Cao, Xin & Fan, Fei & Xu, Ruifei, 2017. "Application of DEA and statistical inference to model the determinants of biomethane production efficiency: A case study in south China," Applied Energy, Elsevier, vol. 205(C), pages 1231-1243.
    13. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2020. "Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA," Omega, Elsevier, vol. 92(C).
    14. Debora Di Caprio & Ali Ebrahimnejad & Mojtaba Ghiyasi & Francisco J. Santos-Arteaga, 2020. "Integrating fuzzy goal programming and data envelopment analysis to incorporate preferred decision-maker targets in efficiency measurement," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 673-690, December.
    15. Ando, Kazutoshi & Minamide, Masato & Sekitani, Kazuyuki & Shi, Jianming, 2017. "Monotonicity of minimum distance inefficiency measures for Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 260(1), pages 232-243.
    16. Fangqing Wei & Junfei Chu & Jiayun Song & Feng Yang, 2019. "A cross-bargaining game approach for direction selection in the directional distance function," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 787-807, September.
    17. Seyed Ali Rakhshan, 2017. "Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(8), pages 906-918, August.

    More about this item

    Keywords

    Data Envelopment Analysis; least distance; oriented models;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • H52 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Education

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:71:y:2017:i:c:p:1-10. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.