IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v90y2020ics0305048318304304.html
   My bibliography  Save this article

Ranking using η-efficiency and relative size measures based on DEA

Author

Listed:
  • Kanematsu, Simon Y.
  • Carvalho, Ney P.
  • Martinhon, Carlos A.
  • Almeida, Mariana R.

Abstract

In this paper, we propose a new way to define the size of organizations or Decision Making Units (DMUs) based on Data Envelopment Analysis (DEA). A great number of managerial decisions, social and economic activities, political analysis and engineering process include in their analysis some information about the size of corporations. Usually, organizations consider particular attributes such as revenues, employees, number of clients, profit and so forth to evaluate their sizes, which could result on an incomplete and/or partial size evaluation. Here, we investigate this question more deeply and propose a non-parametric approach for ranking size. To address this issue, we first construct a DEA super-efficiency target vector defined over an extended Technology set and find a common set of weights to determine new efficiencies and sizes, possibly greater than one. After, we define rotation and translation of DMUs and show how to construct a range area, associated to η-efficiencies and relative sizes that are less than or equal to one. Additionally, based on managerial decisions, we show how to use these ideas to achieve new η-efficiency and relative size goals for one or more DMUs in the set. We consider an empirical application to illustrate our approach on a dataset of international airlines and conclude the paper with some final remarks and future directions.

Suggested Citation

  • Kanematsu, Simon Y. & Carvalho, Ney P. & Martinhon, Carlos A. & Almeida, Mariana R., 2020. "Ranking using η-efficiency and relative size measures based on DEA," Omega, Elsevier, vol. 90(C).
    • Handle: RePEc:eee:jomega:v:90:y:2020:i:c:s0305048318304304
    DOI: 10.1016/j.omega.2018.10.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048318304304
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2018.10.014?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. 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. Paolo Angelini & Andrea Generale, 2008. "On the Evolution of Firm Size Distributions," American Economic Review, American Economic Association, vol. 98(1), pages 426-438, March.
    3. 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.
    4. Evans, David S, 1987. "The Relationship between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 567-581, June.
    5. Chen, Yao & Du, Juan & Huo, Jiazhen, 2013. "Super-efficiency based on a modified directional distance function," Omega, Elsevier, vol. 41(3), pages 621-625.
    6. Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.
    7. Torben Schubert & Guoliang Yang, 2016. "Institutional change and the optimal size of universities," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(3), pages 1129-1153, September.
    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. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    10. 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.
    11. Chih-Hai Yang & Ku-Hsieh Chen, 2009. "Are small firms less efficient?," Small Business Economics, Springer, vol. 32(4), pages 375-395, April.
    12. Friedman, Lea & Sinuany-Stern, Zilla, 1997. "Scaling units via the canonical correlation analysis in the DEA context," European Journal of Operational Research, Elsevier, vol. 100(3), pages 629-637, August.
    13. Zoltan J. Acs & David B. Audretsch, 2008. "Innovation in Large and Small Firms: An Empirical Analysis," Chapters, in: Entrepreneurship, Growth and Public Policy, chapter 1, pages 3-15, Edward Elgar Publishing.
    14. Roll, Y & Golany, B., 1993. "Alternate methods of treating factor weights in DEA," Omega, Elsevier, vol. 21(1), pages 99-109, January.
    15. 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.
    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. 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.
    18. S C Ray, 2008. "The directional distance function and measurement of super-efficiency: an application to airlines data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 788-797, June.
    19. Ruiyue Lin & Zhiping Chen, 2017. "A directional distance based super-efficiency DEA model handling negative data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1312-1322, November.
    20. Baumann, Julian & Kritikos, Alexander S., 2016. "The link between R&D, innovation and productivity: Are micro firms different?," Research Policy, Elsevier, vol. 45(6), pages 1263-1274.
    21. Li, Yongjun & Xie, Jianhui & Wang, Meiqiang & Liang, Liang, 2016. "Super efficiency evaluation using a common platform on a cooperative game," European Journal of Operational Research, Elsevier, vol. 255(3), pages 884-892.
    22. Doyle, John R., 1995. "Multiattribute Choice for the Lazy Decision Maker: Let the Alternatives Decide!," Organizational Behavior and Human Decision Processes, Elsevier, vol. 62(1), pages 87-100, April.
    23. Afsharian, Mohsen & Ahn, Heinz & Thanassoulis, Emmanuel, 2017. "A DEA-based incentives system for centrally managed multi-unit organisations," European Journal of Operational Research, Elsevier, vol. 259(2), pages 587-598.
    24. Siegfried Schaible, 1977. "A note on the sum of a linear and linear‐fractional function," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(4), pages 691-693, December.
    25. Suzuki, Soushi & Nijkamp, Peter, 2016. "An evaluation of energy-environment-economic efficiency for EU, APEC and ASEAN countries: Design of a Target-Oriented DFM model with fixed factors in Data Envelopment Analysis," Energy Policy, Elsevier, vol. 88(C), pages 100-112.
    26. Tone, Kaoru, 2002. "A slacks-based measure of super-efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 143(1), pages 32-41, November.
    27. Hall, Bronwyn H, 1987. "The Relationship between Firm Size and Firm Growth in the U.S. Manufacturing Sector," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 583-606, June.
    28. Guo, I-Lung & Lee, Hsuan-Shih & Lee, Dan, 2017. "An integrated model for slack-based measure of super-efficiency in additive DEA," Omega, Elsevier, vol. 67(C), pages 160-167.
    29. Kottas, Angelos T. & Madas, Michael A., 2018. "Comparative efficiency analysis of major international airlines using Data Envelopment Analysis: Exploring effects of alliance membership and other operational efficiency determinants," Journal of Air Transport Management, Elsevier, vol. 70(C), pages 1-17.
    30. Alvarez, Roberto & Crespi, Gustavo, 2003. "Determinants of Technical Efficiency in Small Firms," Small Business Economics, Springer, vol. 20(3), pages 233-244, May.
    31. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    32. Takehiko Yasuda, 2005. "Firm Growth, Size, Age and Behavior in Japanese Manufacturing," Small Business Economics, Springer, vol. 24(1), pages 1-15, December.
    33. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    34. Yu, Ming-Miin & Chen, Li-Hsueh & Chiang, Hui, 2017. "The effects of alliances and size on airlines’ dynamic operational performance," Transportation Research Part A: Policy and Practice, Elsevier, vol. 106(C), pages 197-214.
    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. Kiani Mavi, Reza & Kiani Mavi, Neda & Farzipoor Saen, Reza & Goh, Mark, 2022. "Common weights analysis of renewable energy efficiency of OECD countries," Technological Forecasting and Social Change, Elsevier, vol. 185(C).

    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. 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.
    2. Helmi Hammami & Thanh Ngo & David Tripe & Dinh-Tri Vo, 2022. "Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking sector," Annals of Operations Research, Springer, vol. 311(2), pages 675-694, April.
    3. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    4. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2021. "A review of DEA approaches applying a common set of weights: The perspective of centralized management," European Journal of Operational Research, Elsevier, vol. 294(1), pages 3-15.
    5. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    6. Kao, Chiang, 2010. "Malmquist productivity index based on common-weights DEA: The case of Taiwan forests after reorganization," Omega, Elsevier, vol. 38(6), pages 484-491, December.
    7. Mai, Nhat Chi, 2015. "Efficiency of the banking system in Vietnam under financial liberalization," OSF Preprints qsf6d, Center for Open Science.
    8. Ghosh, Santosh & Yadav, Vinod Kumar & Mukherjee, Vivekananda, 2018. "Evaluation of cumulative impact of partial shading and aerosols on different PV array topologies through combined Shannon's entropy and DEA," Energy, Elsevier, vol. 144(C), pages 765-775.
    9. 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.
    10. Seyed Rakhshan & Ali Kamyad & Sohrab Effati, 2015. "Ranking decision-making units by using combination of analytical hierarchical process method and Tchebycheff model in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 505-525, March.
    11. Shih-Heng Yu & Chia-Wei Hsu, 2020. "A unified extension of super-efficiency in additive data envelopment analysis with integer-valued inputs and outputs: an application to a municipal bus system," Annals of Operations Research, Springer, vol. 287(1), pages 515-535, April.
    12. Ramanathan, Ramakrishnan & Ramanathan, Usha & Bentley, Yongmei, 2018. "The debate on flexibility of environmental regulations, innovation capabilities and financial performance – A novel use of DEA," Omega, Elsevier, vol. 75(C), pages 131-138.
    13. Vicente J. Bolós & Rafael Benítez & Vicente Coll-Serrano, 2023. "Continuous models combining slacks-based measures of efficiency and super-efficiency," 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. 31(2), pages 363-391, June.
    14. Yung-ho Chiu & Chin-wei Huang & Chung-te Ting, 2012. "A non-radial measure of different systems for Taiwanese tourist hotels’ efficiency assessment," 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. 20(1), pages 45-63, March.
    15. Tran, Trung Hieu & Mao, Yong & Nathanail, Paul & Siebers, Peer-Olaf & Robinson, Darren, 2019. "Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis," Omega, Elsevier, vol. 85(C), pages 156-165.
    16. Lin, Ruiyue & Liu, Yue, 2019. "Super-efficiency based on the directional distance function in the presence of negative data," Omega, Elsevier, vol. 85(C), pages 26-34.
    17. Guo-Ya Gan & Hsuan-Shih Lee, 2021. "Resolving the infeasibility of the super-efficiency DEA based on DDF," Annals of Operations Research, Springer, vol. 307(1), pages 139-152, December.
    18. Dimitrov Stanko, 2014. "Comparing Data Envelopment Analysis and Human Decision Making Unit Rankings: A Survey Approach," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 129-141, December.
    19. Soltanifar, Mehdi & Shahghobadi, Saeid, 2013. "Selecting a benevolent secondary goal model in data envelopment analysis cross-efficiency evaluation by a voting model," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 65-74.
    20. Adler, Nicole & Yazhemsky, Ekaterina, 2010. "Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction," European Journal of Operational Research, Elsevier, vol. 202(1), pages 273-284, April.

    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:jomega:v:90:y:2020:i:c:s0305048318304304. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.