IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v312y2024i1p298-314.html
   My bibliography  Save this article

A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis

Author

Listed:
  • Halická, Margaréta
  • Trnovská, Mária
  • Černý, Aleš

Abstract

The paper analyses properties of a large class of “path-based” Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the directional distance function models, and even permits their generalisations. The modelling is not constrained to non-negative data and is flexible enough to accommodate variants of standard models over arbitrary data.

Suggested Citation

  • Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2024. "A unified approach to radial, hyperbolic, and directional efficiency measurement in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 312(1), pages 298-314.
    • Handle: RePEc:eee:ejores:v:312:y:2024:i:1:p:298-314
    DOI: 10.1016/j.ejor.2023.06.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723005118
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.06.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Tone, Kaoru & Chang, Tsung-Sheng & Wu, Chen-Hui, 2020. "Handling negative data in slacks-based measure data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 282(3), pages 926-935.
    2. M C A Silva Portela & E Thanassoulis & G Simpson, 2004. "Negative data in DEA: a directional distance approach applied to bank branches," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1111-1121, October.
    3. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    4. K Kerstens & I Van de Woestyne, 2011. "Negative data in DEA: a simple proportional distance function approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1413-1419, July.
    5. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    6. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    7. Rafael Cuesta & José Zofío, 2005. "Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks," Journal of Productivity Analysis, Springer, vol. 24(1), pages 31-48, September.
    8. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    9. W. Briec & J. B. Lesourd, 1999. "Metric Distance Function and Profit: Some Duality Results," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 15-33, April.
    10. William Cooper & Jesús Pastor & Fernando Borras & Juan Aparicio & Diego Pastor, 2011. "BAM: a bounded adjusted measure of efficiency for use with bounded additive models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 85-94, April.
    11. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The directional distance function and the translation invariance property," Omega, Elsevier, vol. 58(C), pages 1-3.
    12. 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.
    13. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    14. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, John Wiley & Sons, vol. 66(2), pages 294-318, October.
    15. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    16. Chambers, Robert G. & Fare, Rolf & Grosskopf, Shawna, 1996. "Productivity Growth in APEC Countries," Working Papers 197843, University of Maryland, Department of Agricultural and Resource Economics.
    17. Roshdi, Israfil & Hasannasab, Maryam & Margaritis, Dimitris & Rouse, Paul, 2018. "Generalised weak disposability and efficiency measurement in environmental technologies," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1000-1012.
    18. 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.
    19. Sahoo, Biresh K. & Mehdiloozad, Mahmood & Tone, Kaoru, 2014. "Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach," European Journal of Operational Research, Elsevier, vol. 237(3), pages 921-931.
    20. R. Robert Russell & William Schworm, 2018. "Technological inefficiency indexes: a binary taxonomy and a generic theorem," Journal of Productivity Analysis, Springer, vol. 49(1), pages 17-23, February.
    21. Cheng, Gang & Zervopoulos, Panagiotis & Qian, Zhenhua, 2013. "A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 225(1), pages 100-105.
    22. Hasannasab, Maryam & Margaritis, Dimitris & Roshdi, Israfil & Rouse, Paul, 2019. "Hyperbolic efficiency measurement: A conic programming approach," European Journal of Operational Research, Elsevier, vol. 278(2), pages 401-409.
    23. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
    24. Jean‐Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, John Wiley & Sons, vol. 66(2), pages 294-318, October.
    25. Färe, Rolf & Margaritis, Dimitris & Rouse, Paul & Roshdi, Israfil, 2016. "Estimating the hyperbolic distance function: A directional distance function approach," European Journal of Operational Research, Elsevier, vol. 254(1), pages 312-319.
    26. 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.
    27. A L Johnson & L F McGinnis, 2009. "The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1511-1517, November.
    28. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    29. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barbero, Javier & Zofío, José L., 2023. "The measurement of profit, profitability, cost and revenue efficiency through data envelopment analysis: A comparison of models using BenchmarkingEconomicEfficiency.jl," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    2. Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "A new measure of technical efficiency in data envelopment analysis based on the maximization of hypervolumes: Benchmarking, properties and computational aspects," European Journal of Operational Research, Elsevier, vol. 293(1), pages 263-275.
    3. Halická, Margaréta & Trnovská, Mária, 2021. "A unified approach to non-radial graph models in data envelopment analysis: common features, geometry, and duality," European Journal of Operational Research, Elsevier, vol. 289(2), pages 611-627.
    4. Pastor, Jesus T. & Zofío, José Luis & Aparicio, Juan & Pastor, D., 2023. "A general direct approach for decomposing profit inefficiency," Omega, Elsevier, vol. 119(C).
    5. Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    6. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    7. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The directional distance function and the translation invariance property," Omega, Elsevier, vol. 58(C), pages 1-3.
    8. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    9. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.
    10. Juan Aparicio & Jesus T. Pastor & Jose L. Sainz-Pardo & Fernando Vidal, 2020. "Estimating and decomposing overall inefficiency by determining the least distance to the strongly efficient frontier in data envelopment analysis," Operational Research, Springer, vol. 20(2), pages 747-770, June.
    11. Chambers, Robert G., 2024. "Numeraire choice, shadow profit, and inefficiency measurement," European Journal of Operational Research, Elsevier, vol. 319(2), pages 658-668.
    12. Aparicio, Juan & Kapelko, Magdalena, 2019. "Accounting for slacks to measure dynamic inefficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 278(2), pages 463-471.
    13. Juo, Jia-Ching & Fu, Tsu-Tan & Yu, Ming-Miin & Lin, Yu-Hui, 2016. "Non-radial profit performance: An application to Taiwanese banks," Omega, Elsevier, vol. 65(C), pages 111-121.
    14. Aparicio, Juan & Garcia-Nove, Eva M. & Kapelko, Magdalena & Pastor, Jesus T., 2017. "Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis," Omega, Elsevier, vol. 72(C), pages 1-14.
    15. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    16. Camanho, Ana Santos & Silva, Maria Conceicao & Piran, Fabio Sartori & Lacerda, Daniel Pacheco, 2024. "A literature review of economic efficiency assessments using Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 315(1), pages 1-18.
    17. Rafael Benítez & Vicente Coll-Serrano & Vicente J. Bolós, 2021. "deaR-Shiny: An Interactive Web App for Data Envelopment Analysis," Sustainability, MDPI, vol. 13(12), pages 1-19, June.
    18. Cova-Alonso, David José & Díaz-Hernández, Juan José & Martínez-Budría, Eduardo, 2021. "A strong efficiency measure for CCR/BCC models," European Journal of Operational Research, Elsevier, vol. 291(1), pages 284-295.
    19. Tianqun Xu & Ping Gao & Qian Yu & Debin Fang, 2017. "An Improved Eco-Efficiency Analysis Framework Based on Slacks-Based Measure Method," Sustainability, MDPI, vol. 9(6), pages 1-21, June.
    20. Pastor, Jesus T. & Lovell, C.A. Knox & Aparicio, Juan, 2020. "Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index," European Journal of Operational Research, Elsevier, vol. 281(1), pages 222-230.

    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:ejores:v:312:y:2024:i:1:p:298-314. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.