IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v323y2025i3p975-987.html
   My bibliography  Save this article

Measuring technical efficiency under variable returns to scale using Debreu's loss function

Author

Listed:
  • Díaz-Hernández, Juan José
  • Cova-Alonso, David-José
  • Martínez-Budría, Eduardo

Abstract

This paper proposes a model that makes two contributions to the measurement of technical efficiency under a technology with variable returns to scale. First, the criteria for identifying an optimal benchmark are not limited to technical dominance and Pareto efficiency, but also include maximum average productivity, defined as the ratio between a weighted linear aggregate of outputs and inputs.

Suggested Citation

  • Díaz-Hernández, Juan José & Cova-Alonso, David-José & Martínez-Budría, Eduardo, 2025. "Measuring technical efficiency under variable returns to scale using Debreu's loss function," European Journal of Operational Research, Elsevier, vol. 323(3), pages 975-987.
  • Handle: RePEc:eee:ejores:v:323:y:2025:i:3:p:975-987
    DOI: 10.1016/j.ejor.2024.12.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724009895
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2024.12.050?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Coelli, Tim & Grifell-Tatje, Emili & Perelman, Sergio, 2002. "Capacity utilisation and profitability: A decomposition of short-run profit efficiency," International Journal of Production Economics, Elsevier, vol. 79(3), pages 261-278, October.
    2. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    3. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    5. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    6. 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.
    7. 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.
    8. Cooper, W.W. & Pastor, Jesus T. & Aparicio, Juan & Borras, Fernando, 2011. "Decomposing profit inefficiency in DEA through the weighted additive model," European Journal of Operational Research, Elsevier, vol. 212(2), pages 411-416, July.
    9. Golany, Boaz & Yu, Gang, 1997. "Estimating returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 103(1), pages 28-37, November.
    10. Dan Rosen & Claire Schaffnit & Joseph Paradi, 1998. "Marginal Rates and Two-dimensional Level Curves in DEA," Journal of Productivity Analysis, Springer, vol. 9(3), pages 205-232, March.
    11. Juan Aparicio & Fernando Borras & Jesus T. Pastor & Jose L. Zofio, 2016. "Loss Distance Functions and Profit Function: General Duality Results," International Series in Operations Research & Management Science, in: Juan Aparicio & C. A. Knox Lovell & Jesus T. Pastor (ed.), Advances in Efficiency and Productivity, chapter 0, pages 71-96, Springer.
    12. 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.
    13. 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.
    14. 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.
    15. Walter Briec & Audrey Dumas & Kristiaan Kerstens & Agathe Stenger, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," Post-Print hal-03702639, HAL.
    16. 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.
    17. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    18. 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.
    19. 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. 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.
    2. 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.
    3. Chambers, Robert G., 2024. "Numeraire choice, shadow profit, and inefficiency measurement," European Journal of Operational Research, Elsevier, vol. 319(2), pages 658-668.
    4. Taleb, Mushtaq & Khalid, Ruzelan & Ramli, Razamin & Ghasemi, Mohammad Reza & Ignatius, Joshua, 2022. "An integrated bi-objective data envelopment analysis model for measuring returns to scale," European Journal of Operational Research, Elsevier, vol. 296(3), pages 967-979.
    5. Halická, Margaréta & Trnovská, Mária & Černý, Aleš, 2025. "On indication, strict monotonicity, and efficiency of projections in a general class of path-based data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 320(1), pages 175-187.
    6. Aparicio, Juan & Ortiz, Lidia & Pastor, Jesus T., 2017. "Measuring and decomposing profit inefficiency through the Slacks-Based Measure," European Journal of Operational Research, Elsevier, vol. 260(2), pages 650-654.
    7. Walheer, Barnabé, 2018. "Scale efficiency for multi-output cost minimizing producers: The case of the US electricity plants," Energy Economics, Elsevier, vol. 70(C), pages 26-36.
    8. 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.
    9. 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.
    10. Mehdiloo, Mahmood & Podinovski, Victor V., 2019. "Selective strong and weak disposability in efficiency analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1154-1169.
    11. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    12. Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    13. 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.
    14. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
    15. Zarepisheh, M. & Soleimani-damaneh, M., 2009. "A dual simplex-based method for determination of the right and left returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 194(2), pages 585-591, April.
    16. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.
    17. Kao, Chiang, 2022. "A maximum slacks-based measure of efficiency for closed series production systems," Omega, Elsevier, vol. 106(C).
    18. Kao, Chiang, 2022. "Closest targets in the slacks-based measure of efficiency for production units with multi-period data," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1042-1054.
    19. Ioannis E. Tsolas, 2020. "Financial Performance Assessment of Construction Firms by Means of RAM-Based Composite Indicators," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    20. Zelenyuk, Valentin, 2013. "A scale elasticity measure for directional distance function and its dual: Theory and DEA estimation," European Journal of Operational Research, Elsevier, vol. 228(3), pages 592-600.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:ejores:v:323:y:2025:i:3:p:975-987. 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.