IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v386y2020ics0096300320304550.html
   My bibliography  Save this article

Finding efficient surfaces in DEA-R models

Author

Listed:
  • Mozaffari, Mohammad Reza
  • Dadkhah, Fatemeh
  • Jablonsky, Josef
  • Wanke, Peter Fernandes

Abstract

Finding efficient surfaces is quite an important task in data envelopment analysis (DEA) because scale efficiency, returns to scale, and other characteristics of decision making units (DMUs) may easily be derived using them. Traditional DEA models assume that the inputs and outputs are given as non-ratio characteristics. In cases where only a ratio of inputs to outputs (or vice versa) is available for our DMUs, the decision maker is forced to make use of ratio data envelopment analysis (DEA-R) models for efficiency and performance evaluation. This paper deals with identification of efficient surfaces in DEA-R models. The axioms for specifying the production possibility set in constant returns to scale technology for DEA-R are discussed, and, finally an original algorithm for identification of efficient surfaces in this class of models is proposed. In the following, we will find the efficient hyper planes for the 10 bank branches under study. To expand the present study, a comparison was made between the BCC models in DEA and DEA-R, and DEA-R-efficient surfaces were calculated under CRS and VRS assumptions in a simple numerical example.

Suggested Citation

  • Mozaffari, Mohammad Reza & Dadkhah, Fatemeh & Jablonsky, Josef & Wanke, Peter Fernandes, 2020. "Finding efficient surfaces in DEA-R models," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304550
    DOI: 10.1016/j.amc.2020.125497
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304550
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125497?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. Liu, W.B. & Zhang, D.Q. & Meng, W. & Li, X.X. & Xu, F., 2011. "A study of DEA models without explicit inputs," Omega, Elsevier, vol. 39(5), pages 472-480, October.
    2. repec:bla:scandj:v:87:y:1985:i:4:p:594-604 is not listed on IDEAS
    3. M. Mozaffari & J. Gerami & J. Jablonsky, 2014. "Relationship between DEA models without explicit inputs and DEA-R models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 1-12, March.
    4. Jahanshahloo, G.R. & Hosseinzadeh Lotfi, F. & Zhiani Rezai, H. & Rezai Balf, F., 2007. "Finding strong defining hyperplanes of Production Possibility Set," European Journal of Operational Research, Elsevier, vol. 177(1), pages 42-54, February.
    5. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Ozren Despić & Mladen Despić & Joseph Paradi, 2007. "DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications," Journal of Productivity Analysis, Springer, vol. 28(1), pages 33-44, October.
    11. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    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. Dariush Akbarian, 2021. "Network DEA based on DEA-ratio," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.

    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. Javad Gerami & Reza Kiani Mavi & Reza Farzipoor Saen & Neda Kiani Mavi, 2023. "A novel network DEA-R model for evaluating hospital services supply chain performance," Annals of Operations Research, Springer, vol. 324(1), pages 1041-1066, May.
    2. Dariush Akbarian, 2021. "Network DEA based on DEA-ratio," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.
    3. A. Ghazi & F. Hosseinzadeh Lotfi, 2023. "Marginal rates in DEA using defining hyperplanes of PPS with CRS technology," Operational Research, Springer, vol. 23(1), pages 1-37, March.
    4. Javad Gerami & Mohammad Reza Mozaffari & P. F. Wanke & Henrique Correa, 2022. "A novel slacks-based model for efficiency and super-efficiency in DEA-R," Operational Research, Springer, vol. 22(4), pages 3373-3410, September.
    5. 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.
    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. M. Mozaffari & J. Gerami & J. Jablonsky, 2014. "Relationship between DEA models without explicit inputs and DEA-R models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 1-12, March.
    8. 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.
    9. Po, Rung-Wei & Guh, Yuh-Yuan & Yang, Miin-Shen, 2009. "A new clustering approach using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 199(1), pages 276-284, November.
    10. 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.
    11. 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.
    12. Amineh Ghazi & Farhad Hosseinzadeh Lotfı & Masoud Sanei, 2022. "Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming," Operational Research, Springer, vol. 22(1), pages 165-198, March.
    13. 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.
    14. 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.
    15. Chenini Hajer & Jarboui Anis, 2018. "Analysis of the Impact of Governance on Bank Performance: Case of Commercial Tunisian Banks," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 9(3), pages 871-895, September.
    16. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    17. Noel Uri, 2003. "The Effect of Incentive Regulation in Telecommunications in the United States," Quality & Quantity: International Journal of Methodology, Springer, vol. 37(2), pages 169-191, May.
    18. Silvia Saravia-Matus & T. S. Amjath-Babu & Sreejith Aravindakshan & Stefan Sieber & Jimmy A. Saravia & Sergio Gomez y Paloma, 2021. "Can Enhancing Efficiency Promote the Economic Viability of Smallholder Farmers? A Case of Sierra Leone," Sustainability, MDPI, vol. 13(8), pages 1-17, April.
    19. 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.
    20. María Victoria Uribe‐Bohorquez & Jennifer Martínez‐Ferrero & Isabel‐María García‐Sánchez, 2019. "Women on boards and efficiency in a business‐orientated environment," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 26(1), pages 82-96, January.

    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:apmaco:v:386:y:2020:i:c:s0096300320304550. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.