Skip to main content
SpringerLink
Log in

Determining radial efficiency with a large data set by solving small-size linear programs

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

Abstract

This paper presents a new algorithm for determining radial efficiency with a large data set by using small-size linear programs (LPs). Instead of trying to “reduce” the size of individual LPs, the proposed algorithm attempts to “control” the size of individual LPs, e.g., no more than 100 data points each time while maintaining the solution quality. The algorithm is specifically designed to address the problem of LP size limitation. From the empirical results, we conclude that the proposed algorithm can converge within a reasonable number of iterations without incurring extra computation time and has savings of up to 60 % of the benchmarks when the data set contains 15,000 points.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. The data set is publicly available at http://nirvana.iem.nctu.edu.tw/wenchih/DEAdata.

References

  • Ali, A. I. (1993). Streamlined computation for data envelopment analysis. European Journal of Operational Research, 64, 61–67.

    Article  Google Scholar 

  • Ali, A. I. (1994). Computational aspects of DEA. In A. Charnes, W. W. Cooper, A. Lewin, & L. M. Seiford (Eds.), Data envelopment analysis. Methodology and applications: Theory (pp. 63–88). Netherlands: Springer.

  • Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 30(9), 1078–1092.

    Article  Google Scholar 

  • Barr, R. S., & Durchholz, M. L. (1997). Parallel and hierarchical decomposition approaches for solving large-scale data envelopment analysis models. Annals of Operations Research, 73, 339–372.

    Article  Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 428–444.

    Article  Google Scholar 

  • Chen, Y., & Ali, A. I. (2002). Output–input ratio analysis and DEA frontier. European Journal of Operational Research, 142, 476–479.

    Article  Google Scholar 

  • Chen, W.-C., & Cho, W.-J. (2009). A procedure for large-scale DEA computations. Computers & Operations Research, 36(6), 1813–1824.

    Article  Google Scholar 

  • Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. New York, NY: Springer.

    Google Scholar 

  • Dulá, J. H., & Thrall, R. M. (2001). A computational framework for accelerating DEA. Journal of Productivity Analysis, 16, 63–78.

    Article  Google Scholar 

  • Dulá, J. H. (2002). Computations in DEA. Pesquisa Operacional, 22, 165–182.

    Article  Google Scholar 

  • Dulá, J. H. (2008). A computational study of DEA with massive data sets. Computers & Operations Research, 35, 1191–1203.

    Article  Google Scholar 

  • Dulá, J. H., & López, F. J. (2009). Preprocessing DEA. Computers & Operations Research, 36, 1204–1220.

    Article  Google Scholar 

  • Dulá, J. H. (2011). An algorithm for data envelopment analysis. INFORMS Journal on Computing, 23(2), 284–296.

    Article  Google Scholar 

  • Färe, R. F., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontier. Cambridge: Cambridge University Press.

    Google Scholar 

  • Farrell, M. J. (1957). The measurement of productive efficiency of production. Journal of the Royal Statistical Society, Series A, 120((III)), 253–281.

    Article  Google Scholar 

  • Korhonen, P. J., & Siitari, P.-A. (2009). A dimensional decomposition approach to identifying efficient units in large-scale DEA models. Computers & Operations Research, 36, 234–244.

    Article  Google Scholar 

  • López, F. J. (2011). Generalizing cross redundancy in data envelopment analysis. European Journal of Operational Research, 214(3), 716–721.

    Article  Google Scholar 

  • Olesen, O. B., & Petersen, N. C. (1996). Indicators of ill-conditioned data sets and model misspecification in data envelopment analysis: An extended facet approach. Management Science, 42(2), 205–219.

    Article  Google Scholar 

  • Sueyoshi, T., & Chang, Y.-L. (1989). Efficient algorithm for additive and multiplicative models in data envelopment analysis. Operations Research Letters, 8(4), 205–213.

    Article  Google Scholar 

  • Wilson, P. W. (2008). FEAR 1.0: A software package for frontier efficiency analysis with R. Socio-Economic Planning Sciences, 42, 247–254.

    Article  Google Scholar 

Download references

Acknowledgments

This research is partially supported by grants from the Ministry of Science and Technology, Taiwan (NSC 100-2628-E-009-005 and 101-2628-E-009-009-MY3). We thank the editor and anonymous referees for their thoughtful suggestions; any errors remaining in the paper are our own. We thank Professor Jose Dulá for providing the banking data set for computational testing.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, 1001 Ta Hsueh Rd., Hsinchu, Taiwan

    Wen-Chih Chen & Sheng-Yung Lai

Authors
  1. Wen-Chih Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-Yung Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen-Chih Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, WC., Lai, SY. Determining radial efficiency with a large data set by solving small-size linear programs. Ann Oper Res 250, 147–166 (2017). https://doi.org/10.1007/s10479-015-1968-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-015-1968-4

Keywords

Search

Navigation