Skip to main content
SpringerLink
Log in

On the importance of perspective and flexibility for efficiency measurement: effects on the ranking of decision-making units

  • Published:
Journal of the Operational Research Society

Abstract

The efficiency of a firm can be assessed from several perspectives and using a variety of methodologies. Data envelopment analysis (DEA) is one of the most commonly used methodologies. Conventional DEA analyses or models allow one to classify decision-making units (DMUs) into efficient and inefficient ones based on their efficiency scores, which could also be used for ranking DMUs; however, such rankings generally show many ties. Super-efficiency DEA analyses have been proposed to address the tie issue. On the other hand, conventional DEA analyses only take account of a single perspective in estimating efficiency scores. Cross-efficiency DEA analyses provide an alternative that takes account of the perspectives or perceptions of different DMUs. Conventional DEA analyses designed for handling crisp data have also been extended to deal with fuzzy data. In this paper, we propose a fuzzy version of cross-efficiency DEA analysis along with a method for ranking DMUs. We illustrate our proposal with a real example from the Spanish banking sector. In order to assess the robustness of our proposal, we compared our results with those obtained with three different approaches based on the perspective from which efficiency aims to be evaluated: a fuzzy DEA approach, a cross-efficiency-based approach and a TOPSIS-based approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2

Similar content being viewed by others

Notes

  1. Although we have used indicator Y, according to Proposition 1, for our study, indicators Y, CM and S are coincident.

References

  • Adler N, Friedman L and Sinuany-Stern Z (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research 140(2):249–265.

    Article  Google Scholar 

  • AEB (2014). Anuario Estadístico de la Banca en España 2014. http://www.aebanca.es/cs/groups/public/documents/publicaciones/22-201502366.Pdf.

  • Andersen P and Petersen NC (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science 39(10):1261–1264.

    Article  Google Scholar 

  • Banker R, Charnes A and Cooper W (1984). Some models for estimating technical and scale efficiencies in Data Envelopment Analysis. Management Science 30(9):1078–1092.

    Article  Google Scholar 

  • Boscá JE, Liern V, Sala R and Martínez A (2011). Ranking decision making units by means soft computing DEA models. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19(1):115–134.

    Article  Google Scholar 

  • Calvo C, Ivorra C and Liern V (2016). Fuzzy portfolio selection with non-financial goals: Exploring the efficient frontier. Annals of Operations Research 245(1):31–46.

    Article  Google Scholar 

  • Campos L and Muñoz A (1989). A subjective approach for ranking fuzzy numbers. Fuzzy Sets and Systems 29(2):145–153.

    Article  Google Scholar 

  • Charnes A, Cooper WW and Rhodes E (1978). Measuring the efficiency of decision making units. European Journal of Operational Research 2(6):429–444.

    Article  Google Scholar 

  • Chen CB and Klein CM (1997). An efficient approach to solving fuzzy MADM problems. Fuzzy Sets and Systems 88(1):51–67.

    Article  Google Scholar 

  • Cooper WW, Seiford LM and Tone K (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software (2nd ed.). New York: Springer.

    Google Scholar 

  • Doyle J and Green R (1995). Cross-evaluation in DEA: Improving discrimination among DMUs. INFOR 33(3):205–222.

    Google Scholar 

  • Doyle J and Green R (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operations Research Society 45(5):567–578.

    Article  Google Scholar 

  • Emrouznejad A, Parker BR and Tavares G (2008). Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA. Socio-Economic Planning Sciences 42(3):151–157.

    Article  Google Scholar 

  • Green RH, Doyle JR and Cook WD (1996). Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research 90(3):461–472.

    Article  Google Scholar 

  • Hwang CL and Yoon K (1981). Multiple Attribute Decision Making Methods and Applications. Berlin: Springer.

    Book  Google Scholar 

  • Jahanshahloo GR, Hosseinzadeh Lotfi F and Izadikhah M (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation 175(2):1375–1384.

    Article  Google Scholar 

  • Kao C and Liu ST (2000). Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems 113(3):427–437.

    Article  Google Scholar 

  • Kaufmann A and Gil-Aluja J (1987). Técnica operativas de gestión para el tratamiento de la incertidumbre. Barcelona: Hispano-europea.

    Google Scholar 

  • Lamata MT, Liern V and Pérez-Gladish B (2016). Doing good by doing well: A MCDM framework for evaluating corporate social responsibility attractiveness. Annals of Operations Research. doi:10.1007/s10479-016-2271-8.

    Google Scholar 

  • León T, Liern V, Ruiz J and Sirvent I (2003). A possibilistic programming approach to the assessment of efficiency with DEA models. Fuzzy Sets and Systems 139(2):407–419.

    Article  Google Scholar 

  • León T, Ramón N, Ruiz JL and Sirvent I (2014). Using induced ordered weighted averaging (IOWA) operators for aggregation in cross-efficiency evaluations. International Journal of Intelligent Systems 29(12):1100–1116.

    Article  Google Scholar 

  • Liu JS, Lu LYY, Lu WM and Lin BJY (2013). Data envelopment analysis 1978–2010: A citation-based literature survey. Omega 41(1):3–15.

    Article  Google Scholar 

  • Liu JS, Lu LYY and Lu WM (2016). Research fronts in data envelopment analysis. Omega 58(1):33–45.

    Article  Google Scholar 

  • Lu WM and Lo SF (2007). A closer look at the economic-environmental disparities for regional development in China. European Journal of Operational Research 183(2):882–894.

    Article  Google Scholar 

  • Maudos J (2015). Post-restructuring challenges for the Spanish banking sector. Spanish Economic and Financial Outlook 4(6):15–29.

    Google Scholar 

  • Opricovic S and Tzeng GH (2004). The Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research 156(2):445–455.

    Article  Google Scholar 

  • Oral M, Kettani O and Lang P (1991). A methodology for collective evaluation and selection of industrial R&D projects. Management Science 7:871–883.

    Article  Google Scholar 

  • Paradi JC and Zhu H (2013). A survey on bank branch efficiency and performance research with data envelopment analysis. Omega 41(1):61–79.

    Article  Google Scholar 

  • Ramón N, Ruiz JL and Sirvent I (2010). On the choice of weights profiles in cross-efficiency evaluations. European Journal of Operational Research 207(3):1564–1572.

    Article  Google Scholar 

  • Ruiz JL and Sirvent I (2017). Fuzzy cross-efficiency evaluation: A possibility approach. Fuzzy Optimization and Decision Making 16(1):111–126.

    Article  Google Scholar 

  • Sexton TR, Silkman RH and Hogan AJ (1986). Data envelopment analysis: Critique and extensions. In Measuring Efficiency: An Assessment of Data Envelopment Analysis, ed. Silkman RH. San Francisco: Jossey-Bass.

    Google Scholar 

  • Shang J and Sueyoshi T (1995). A unified framework for the selection of a flexible manufacturing system. European Journal of Operational Research 85(2):297–315.

    Article  Google Scholar 

  • Sherman HD and Gold F (1985). Bank branch operating efficiency. Banking and Finances 9(2):297–315.

    Google Scholar 

  • Talluri S and Sarkis J (1997). Extensions in measurement of alternative machine component grouping solutions via data envelopment analysis. IEEE Transactions on engineering Management 44(3):299–304.

    Article  Google Scholar 

  • Tanaka, K. (1997). An Introduction to Fuzzy Logic for Practical Applications. New York: Springer.

    Google Scholar 

  • Wang X and Kerre E (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems 118(3):375–385.

    Article  Google Scholar 

  • Yager RR (1981). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences 24(2):143–161.

    Article  Google Scholar 

  • Yang F, Ang S, Xia Q and Yang C (2012). Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis. European Journal of Operational Research 223(2):483–488.

    Article  Google Scholar 

  • Yu PL (1973). Bank branch operating efficiency. Banking and Finances 9(2):297–315.

    Google Scholar 

  • Zadeh LA (1965). Fuzzy sets. Information and Control 8(3):338–353.

    Article  Google Scholar 

  • Zeleny M (1982). Multiple Criteria Decision Making. New York: Mc Graw-Hill.

  • Zerafat Angib M and Askari Sajedi M (2012). Improving cross-efficiency evaluation using fuzzy concepts. World Applied Sciences Journal 16(10):1352–1359.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep. Matemática Aplicada, Universitat Politècnica de València, Valencia, Spain

    Mª Leonor Plá

  2. Dep. Matemàtica per a l’Economia i l’Empresa, Universitat de València, Valencia, Spain

    Trinidad Casasús & Vicente Liern

  3. I.E.S. Andreu Sempere, Alcoi, Spain

    Juan Carlos Pérez

Authors
  1. Mª Leonor Plá
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Trinidad Casasús
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vicente Liern
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juan Carlos Pérez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vicente Liern.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Plá, M.L., Casasús, T., Liern, V. et al. On the importance of perspective and flexibility for efficiency measurement: effects on the ranking of decision-making units. J Oper Res Soc (2017). https://doi.org/10.1057/s41274-017-0250-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1057/s41274-017-0250-3

Keywords

Search

Navigation