Skip to main content
SpringerLink
Log in

A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs

  • Original Paper
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Data Envelopment Analysis (DEA) is a non-parametric technique for evaluating a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs. Various DEA methods have been proposed to rank all the DMUs or to select a single efficient DMU with a single constant input and multiple outputs [i.e., without explicit inputs (WEI)] as well as multiple inputs and a single constant output [i.e., without explicit outputs (WEO)]. However, the majority of these methods are computationally complex and difficult to use. This study proposes an efficient method for finding a single efficient DMU, known as the most efficient DMU, under WEI and WEO conditions. Two compact forms are introduced to determine the most efficient DMU without solving an optimization model under the DEA-WEI and DEA-WEO conditions. A comparative analysis shows a significant reduction in the computational complexity of the proposed method over previous studies. Four numerical examples from different contexts are presented to demonstrate the applicability and exhibit the effectiveness of the proposed compact forms.

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

Similar content being viewed by others

Notes

  1. The number of international papers indexed by the Science Citation Index.

  2. The number of full-time research staff.

  3. Total research expenditures.

  4. The number of high quality papers published in top research journals.

  5. The external research funding obtained.

  6. The number of graduate students enrolled.

References

  • Adler, N., Friedman, L., & Stern, Z. S. (2002). Review of ranking methods in data envelopment analysis context. European Journal of Operational Research, 140, 249–265.

    Article  Google Scholar 

  • Amin, G. R. (2009). Optimal solution of technology selection model: A computational efficient form. International Journal of Advance Manufacturing Technology, 42, 1046–1050.

    Article  Google Scholar 

  • Amin, G. R., Gattoufi, S., & Rezaee Seraji, E. (2011). A maximum discrimination DEA method for ranking association rules in data mining. International Journal of Computer Mathematics, 88(11), 2233–2245.

    Article  Google Scholar 

  • Amin, G. R., Toloo, M., & Sohrabi, B. (2006). An improved MCDM DEA model for technology selection. International Journal of Production Research, 44(13), 2681–2686.

    Article  Google Scholar 

  • Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39(10), 1261–1264.

    Article  Google Scholar 

  • Asmild, M., Hougaard, J. L., & Kronborg, D. (2013). Do efficiency scores depend on input mix? A statistical test and empirical illustration. Annals of Operations Research, 211, 37–48.

    Article  Google Scholar 

  • Asmild, M., Paradi, J. C., & Pastor, J. T. (2012). DEA-based models for reallocations of police personnel. OR Spectrum, 34, 921–941.

    Article  Google Scholar 

  • Baker, P. C., & Talluri, S. (1997). A closer look at the use of data envelopment analysis for technology selection. Computers and Industrial Engineering, 32, 101–108.

    Article  Google Scholar 

  • Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2010). Linear programming and network flows (4th ed.). New York: Wiley.

    Google Scholar 

  • Chen, Y. (2004). Ranking efficient units in DEA. Omega, 32, 213–219.

    Article  Google Scholar 

  • Chen, Z., & Lin, R. (2006). Mutual fund performance evaluation using data envelopment analysis with new risk measures. OR Spectrum, 28, 375–398.

    Article  Google Scholar 

  • Cook, W. D., Kress, M., & Seiford, L. M. (1996). Data envelopment analysis in the presence of both quantitative and qualitative factors. Journal of Operational Research Society, 47, 945–953.

    Article  Google Scholar 

  • Cook, W. D., & Zhu, J. (2005). Rank order data in DEA: A general framework. European Journal of Operational Research, 174, 1021–1038.

    Article  Google Scholar 

  • Despotis, D. K. (2005). Measuring human development via data envelopment analysis: The case of Asia and the Pacific. Omega, 33, 385–390.

    Article  Google Scholar 

  • Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: Convexity consideration. Applied Mathematical Modelling, 33(1), 486–498.

    Article  Google Scholar 

  • Farzipoor Saen, R. (2007). Suppliers selection in the presence of both cardinal and ordinal data. European Journal of Operational Research, 183, 741–747.

    Article  Google Scholar 

  • Farzipoor Saen, R. (2011). Media selection in the presence of flexible factors and imprecise data. Journal of the Operational Research Society, 62, 1695–1703.

    Article  Google Scholar 

  • Fernandez-Castro, A., & Smith, P. (1994). Towards a general non-parametric model of corporate performance. Omega, 22(3), 237–49.

    Article  Google Scholar 

  • Foroughi, A. A. (2011). A note on “A new method for ranking discovered rules from data mining by DEA”, and a full ranking approach. Expert Systems with Applications, 38, 12913–12916.

    Article  Google Scholar 

  • Green, R. H., Doyle, J. R., & Cook, W. D. (1996). Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research, 90, 461–472.

    Article  Google Scholar 

  • Karsak, E. E., & Ahiska, S. S. (2005). Practical common weight multi-criteria decision making approach with an improved discriminating power for technology selection. International Journal of Production Research, 43(8), 1537–1554.

    Article  Google Scholar 

  • Karsak, E. E., & Ahiska, S. S. (2008). Improved common weight MCDM model for technology selection. International Journal of Production Research, 46(24), 6933–6944.

    Article  Google Scholar 

  • Lee, H. S., & Zhu, J. (2012). Super-efficiency infeasibility and zero data in DEA. European Journal of Operational Research, 2012, 429–33.

    Article  Google Scholar 

  • Liu, W. B., Zhang, D. Q., Meng, W., Li, X. X., & Xu, F. (2011). A study of DEA models without explicit inputs. Omega, 39, 472–480.

    Article  Google Scholar 

  • Lovell, C. A. K., & Pastor, J. T. (1999). Radial DEA models without inputs or without outputs. European Journal of Operational Research, 188, 46–51.

    Article  Google Scholar 

  • Lozano, S., Iribarren, D., Moreira, M. T., & Feijoo, G. (2009). The link between operational efficiency and environmental impacts: A joint application of life cycle assessment and data envelopment analysis. Science of the Total Environment, 407, 1744–1754.

    Article  Google Scholar 

  • Moreno, P., & Lozano, S. (2014). A network DEA assessment of team efficiency in the NBA. Annals of Operations Research, 214(1), 99–124.

    Article  Google Scholar 

  • Ramón, N., Ruiz, J. L., & Sirvent, I. (2012). Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players. Expert Systems with Applications, 39, 4882–4889.

    Article  Google Scholar 

  • Seiford, L. M., & Zhu, J. (2003). Context-dependent data envelopment analysis–Measuring attractiveness and progress. Omega, 31, 397–408.

    Article  Google Scholar 

  • Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation, 32, 73–105.

    Article  Google Scholar 

  • Shokouhi, A. H., Shahriari, H., Agrell, P. J., & Hatami-Marbini, A. (2014). Consistent and robust ranking in imprecise data envelopment analysis under perturbations of random subsets of data. OR Spectrum, 36, 133–160.

    Article  Google Scholar 

  • Thompson, R. G., Singleton, F. D, Jr., Thrall, R. M., & Smith, B. A. (1986). Comparative site evaluations for locating a high-energy physics lab in Texas. Interfaces, 16(6), 35–49.

    Article  Google Scholar 

  • Toloo, M. (2012). On finding the most BCC-efficient DMU: A new integrated MIP-DEA model. Applied Mathematical Modelling, 36(11), 5515–5520.

    Article  Google Scholar 

  • Toloo, M. (2013). The most efficient unit without explicit inputs: An extended MILP-DEA model. Measurement, 46, 3628–3634.

    Article  Google Scholar 

  • Toloo, M. (2014). Selecting and full ranking suppliers with imprecise data: A new DEA method. International Journal of Advanced Manufacturing Technology, 74(5–8), 1141–1148.

    Article  Google Scholar 

  • Toloo, M. (2016). A cost efficiency approach for strategic vendor selection problem under certain input prices assumption. Measurement, 85, 175–183.

    Article  Google Scholar 

  • Toloo, M., & Ertay, T. (2014). The most cost efficient automotive vendor with price uncertainty: A new DEA approach. Measurement, 52, 135–144.

    Article  Google Scholar 

  • Toloo, M., & Kresta, A. (2014). Finding the best asset financing alternative: A DEA-WEO approach. Measurement, 55, 288–294.

    Article  Google Scholar 

  • Wang, Y.-M., & Jiang, P. (2012). Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis. Computers and Industrial Engineering, 62, 546–553.

  • Zhu, J. (2003). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research, 144, 513–529.

    Article  Google Scholar 

  • Zhu, J. (2004). Imprecise DEA via standard linear DEA models with a revisit to a Korean mobile telecommunication company. Operations Research, 52, 323–329.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions. The research was supported by the European Social Fund within the project CZ.1.07/2.3.00/20.0296 and the Czech Science Foundation through project No. 16-17810S. All support is greatly acknowledged.

Author information

Authors and Affiliations

  1. Department of Systems Engineering, Faculty of Economics, Technical University of Ostrava, Ostrava, Czech Republic

    Mehdi Toloo

  2. Business Systems and Analytics Department, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

Authors
  1. Mehdi Toloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madjid Tavana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Madjid Tavana.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Toloo, M., Tavana, M. A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs. Ann Oper Res 253, 657–681 (2017). https://doi.org/10.1007/s10479-016-2375-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-016-2375-1

Keywords

Search

Navigation