IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v63y2025i1d10.1007_s11123-024-00734-2.html
   My bibliography  Save this article

Constant returns-to-scale production technologies with fixed ratio inputs and outputs

Author

Listed:
  • Ole Bent Olesen

    (The University of Southern Denmark)

  • Grammatoula Papaioannou

    (Loughborough University)

  • Victor V. Podinovski

    (Loughborough University)

Abstract

In practical applications of data envelopment analysis, inputs and outputs are often stated as ratio measures, including various percentages and proportions characterizing the production process. Such ratio measures are inconsistent with the basic assumptions of convexity and scalability required by the conventional variable and constant returns-to-scale (VRS and CRS) models. This issue has been addressed by the development of the Ratio-VRS (R-VRS) and Ratio-CRS (R-CRS) models of technology, both of which can incorporate volume and ratio inputs and outputs. In this paper, we provide a detailed standalone development of the special case of the R-CRS technology, referred to as the F-CRS technology, in which all ratio inputs and outputs are of the fixed type. Such ratio measures can be used to represent environmental and quality characteristics of the production process that stay constant while simultaneously allowing the scaling of the volume of production. We illustrate the use of the F-CRS technology by an application in the context of school education.

Suggested Citation

  • Ole Bent Olesen & Grammatoula Papaioannou & Victor V. Podinovski, 2025. "Constant returns-to-scale production technologies with fixed ratio inputs and outputs," Journal of Productivity Analysis, Springer, vol. 63(1), pages 37-48, February.
    • Handle: RePEc:kap:jproda:v:63:y:2025:i:1:d:10.1007_s11123-024-00734-2
    DOI: 10.1007/s11123-024-00734-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11123-024-00734-2
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11123-024-00734-2?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. V V Podinovski, 2004. "Production trade-offs and weight restrictions in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1311-1322, December.
    2. 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.
    3. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
    4. Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2015. "Efficiency analysis with ratio measures," European Journal of Operational Research, Elsevier, vol. 245(2), pages 446-462.
    5. 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.
    6. Podinovski, Victor V. & Wu, Junlin & Argyris, Nikolaos, 2024. "Production trade-offs in models of data envelopment analysis with ratio inputs and outputs: An application to schools in England," European Journal of Operational Research, Elsevier, vol. 313(1), pages 359-372.
    7. Lifen Wu, 2019. "Linear fractional radial graph measure of efficiency of production," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(11), pages 2004-2018, November.
    8. Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2017. "Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 261(2), pages 640-655.
    9. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    10. 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.
    11. 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.
    12. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Production technologies with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1164-1178.
    13. 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.
    14. Fare, Rolf & Grosskopf, Shawna & Logan, James, 1983. "The relative efficiency of Illinois electric utilities," Resources and Energy, Elsevier, vol. 5(4), pages 349-367, December.
    15. Ruggiero, John, 1996. "On the measurement of technical efficiency in the public sector," European Journal of Operational Research, Elsevier, vol. 90(3), pages 553-565, 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. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Production technologies with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1164-1178.
    2. Mehdiloo, Mahmood & Papaioannou, Grammatoula & Podinovski, Victor V., 2024. "Efficient targets and reference sets in selectively convex technologies," Omega, Elsevier, vol. 129(C).
    3. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs," Annals of Operations Research, Springer, vol. 318(1), pages 383-423, November.
    4. Podinovski, Victor V. & Wu, Junlin & Argyris, Nikolaos, 2024. "Production trade-offs in models of data envelopment analysis with ratio inputs and outputs: An application to schools in England," European Journal of Operational Research, Elsevier, vol. 313(1), pages 359-372.
    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. Mehdiloozad, Mahmood & Podinovski, Victor V., 2018. "Nonparametric production technologies with weakly disposable inputs," European Journal of Operational Research, Elsevier, vol. 266(1), pages 247-258.
    7. Mehdiloo, Mahmood & Podinovski, Victor V., 2021. "Strong, weak and Farrell efficient frontiers of technologies satisfying different production assumptions," European Journal of Operational Research, Elsevier, vol. 294(1), pages 295-311.
    8. Cherchye, L. & Post, G.T., 2001. "Methodological Advances in Dea," ERIM Report Series Research in Management ERS-2001-53-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    9. Bolós, V.J. & Benítez, R. & Coll-Serrano, V., 2024. "Chance constrained directional models in stochastic data envelopment analysis," Operations Research Perspectives, Elsevier, vol. 12(C).
    10. Papaioannou, Grammatoula & Podinovski, Victor V., 2023. "Multicomponent production technologies with restricted allocations of shared inputs and outputs," European Journal of Operational Research, Elsevier, vol. 308(1), pages 274-289.
    11. Ole Bent Olesen & Niels Christian Petersen & Victor V. Podinovski, 2022. "The structure of production technologies with ratio inputs and outputs," Journal of Productivity Analysis, Springer, vol. 57(3), pages 255-267, June.
    12. Kuosmanen, Timo, 2001. "DEA with efficiency classification preserving conditional convexity," European Journal of Operational Research, Elsevier, vol. 132(2), pages 326-342, July.
    13. Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2017. "Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs," European Journal of Operational Research, Elsevier, vol. 261(2), pages 640-655.
    14. Victor V. Podinovski & Ole Bent Olesen & Cláudia S. Sarrico, 2018. "Nonparametric Production Technologies with Multiple Component Processes," Operations Research, INFORMS, vol. 66(1), pages 282-300, January.
    15. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    16. 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.
    17. Asmild, Mette & Pastor, Jesús T., 2010. "Slack free MEA and RDM with comprehensive efficiency measures," Omega, Elsevier, vol. 38(6), pages 475-483, December.
    18. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    19. Victoria Wojcik & Harald Dyckhoff & Marcel Clermont, 2019. "Is data envelopment analysis a suitable tool for performance measurement and benchmarking in non-production contexts?," Business Research, Springer;German Academic Association for Business Research, vol. 12(2), pages 559-595, December.
    20. 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.

    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:kap:jproda:v:63:y:2025:i:1:d:10.1007_s11123-024-00734-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.