IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v314y2024i1p308-322.html
   My bibliography  Save this article

A new multiple criteria data envelopment analysis with variable return to scale: Applying bi-dimensional representation and super-efficiency analysis

Author

Listed:
  • da Silva, Aneirson Francisco
  • Miranda, Rafael de Carvalho
  • Marins, Fernando Augusto Silva
  • Dias, Erica Ximenes

Abstract

It is known that, in general, in practical real-world problems, when the number of Decision- Making Units (DMUs) is not large enough compared to the total number of input and output parameters, the traditional DEA models with Constant Return to Scale – CRS and with Variable Return to Scale – VRS have a weak power of discrimination, producing solutions that identify many DMUs as being efficient, in addition to obtaining unrealistic weight distributions. In this context, it is recommended to work with Multiple Criteria Data Envelopment Analysis - MCDEA models. So far, all MCDEA models available in the literature adopt CRS approach. This paper proposes a New Multiple Criteria Data Envelopment Analysis (NMCDEA) – VRS model, as well as performs a super-efficiency analysis for this model. Furthermore, through bi- dimensional graphic representations, a geometric demonstration is provided, showing that, in fact, the proposed model is a good representation of situations in which it is interesting to consider a VRS behavior. The results obtained through the optimization of instances available in the literature, for real instances, as well as the sensitivity analysis carried out, indicated that the NMCDEA-VRS has a much greater power of discrimination compared to the classic DEA–VRS model.

Suggested Citation

  • da Silva, Aneirson Francisco & Miranda, Rafael de Carvalho & Marins, Fernando Augusto Silva & Dias, Erica Ximenes, 2024. "A new multiple criteria data envelopment analysis with variable return to scale: Applying bi-dimensional representation and super-efficiency analysis," European Journal of Operational Research, Elsevier, vol. 314(1), pages 308-322.
    • Handle: RePEc:eee:ejores:v:314:y:2024:i:1:p:308-322
    DOI: 10.1016/j.ejor.2023.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723007142
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.09.008?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. 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.
    2. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    3. Mehdi Toloo & Mona Barat & Atefeh Masoumzadeh, 2015. "Selective measures in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 623-642, March.
    4. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
    5. 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.
    6. Hadi Moheb-Alizadeh & Robert Handfield, 2018. "An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation," International Journal of Production Research, Taylor & Francis Journals, vol. 56(21), pages 6890-6916, November.
    7. Suzuki, Soushi & Nijkamp, Peter & Rietveld, Piet & Pels, Eric, 2010. "A distance friction minimization approach in data envelopment analysis: A comparative study on airport efficiency," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1104-1115, December.
    8. 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.
    9. Bana e Costa, Carlos A. & Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia, 2016. "A new approach to the bi-dimensional representation of the DEA efficient frontier with multiple inputs and outputs," European Journal of Operational Research, Elsevier, vol. 255(1), pages 175-186.
    10. Aneirson Francisco Silva & Fernando Augusto S. Marins & Erica Ximenes Dias, 2020. "Improving the discrimination power with a new multi-criteria data envelopment model," Annals of Operations Research, Springer, vol. 287(1), pages 127-159, April.
    11. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    12. Ghasemi, Mohammad Reza & Ignatius, Joshua & Rezaee, Babak, 2019. "Improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 442-447.
    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. Rubem, Ana Paula dos Santos & Soares de Mello, João Carlos C.B. & Angulo Meza, Lidia, 2017. "A goal programming approach to solve the multiple criteria DEA model," European Journal of Operational Research, Elsevier, vol. 260(1), pages 134-139.
    15. Yongbo Li & Amir-Reza Abtahi & Mahya Seyedan, 2019. "Supply chain performance evaluation using fuzzy network data envelopment analysis: a case study in automotive industry," Annals of Operations Research, Springer, vol. 275(2), pages 461-484, April.
    16. Ghasemi, M.-R. & Ignatius, Joshua & Emrouznejad, Ali, 2014. "A bi-objective weighted model for improving the discrimination power in MCDEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 640-650.
    17. Dariush Khezrimotlagh & Wade D. Cook & Joe Zhu, 2021. "Number of performance measures versus number of decision making units in DEA," Annals of Operations Research, Springer, vol. 303(1), pages 529-562, August.
    18. Seiford, Lawrence M. & Zhu, Joe, 1999. "An investigation of returns to scale in data envelopment analysis," Omega, Elsevier, vol. 27(1), pages 1-11, February.
    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. Ebrahimi, Bohlool & Dhamotharan, Lalitha & Ghasemi, Mohammad Reza & Charles, Vincent, 2022. "A cross-inefficiency approach based on the deviation variables framework," Omega, Elsevier, vol. 111(C).
    2. Aneirson Francisco Silva & Fernando Augusto S. Marins & Erica Ximenes Dias, 2020. "Improving the discrimination power with a new multi-criteria data envelopment model," Annals of Operations Research, Springer, vol. 287(1), pages 127-159, April.
    3. 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.
    4. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2017. "Global and local scale characteristics in convex and nonconvex nonparametric technologies: A first empirical exploration," European Journal of Operational Research, Elsevier, vol. 259(2), pages 576-586.
    5. Ghasemi, Mohammad Reza & Ignatius, Joshua & Rezaee, Babak, 2019. "Improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 442-447.
    6. Mostafa Omidi & Mohsen Rostamy-Malkhalifeh & Ali Payan & Farhad Hosseinzadeh Lotfi, 2019. "Estimation of Overall Returns to Scale (RTS) of a Frontier Unit Using the Left and Right RTS," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 633-655, February.
    7. Kristof Witte & Rui Marques, 2011. "Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies," Journal of Productivity Analysis, Springer, vol. 35(3), pages 213-226, June.
    8. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    9. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 168(2), pages 425-449, January.
    10. Mahdiloo, Mahdi & Lim, Sungmook & Duong, Thach-Thao & Harvie, Charles, 2021. "Some comments on improving discriminating power in data envelopment models based on deviation variables framework," European Journal of Operational Research, Elsevier, vol. 295(1), pages 394-397.
    11. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.
    12. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    13. Matthias Klumpp & Dominic Loske, 2021. "Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency," Sustainability, MDPI, vol. 13(10), pages 1-20, May.
    14. Kaoru Tone, 2001. "On Returns to Scale under Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 16(1), pages 31-47, July.
    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. Wang, Ying-Ming & Lan, Yi-Xin, 2013. "Estimating most productive scale size with double frontiers data envelopment analysis," Economic Modelling, Elsevier, vol. 33(C), pages 182-186.
    17. Subhash C. Ray, 2014. "Data Envelopment Analysis: An Overview," Working papers 2014-33, University of Connecticut, Department of Economics.
    18. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    19. Shuji Yao & Zhongwei Han & Dan Luo, 2010. "Performance of the Chinese Insurance Industry under Economic Reforms," Books, Edward Elgar Publishing, number 12788.
    20. Fang, Tao & Fang, Debin & Yu, Bolin, 2022. "Carbon emission efficiency of thermal power generation in China: Empirical evidence from the micro-perspective of power plants," Energy Policy, Elsevier, vol. 165(C).

    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:314:y:2024:i:1:p:308-322. 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.