Skip to main content
SpringerLink
Log in

Comparison of Different Methods for Estimation of Returns to Scale in Nonradial Data Envelopment Analysis Models

  • OPTIMIZATION, SYSTEM ANALYSIS, OPERATIONS RESEARCH
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The data envelopment analysis (DEA) approach has been actively developed in recent years and is used to analyze the activities of complex production units (regions, financial institutions, industrial enterprises, etc.). An important role in such an analysis is played by the calculation of various indicators of the activity of units: returns to scale, efficiency scores, marginal rates of substitution, transformations, etc. Dependences between variables in the DEA models are not explicitly specified; therefore, special optimization models are used to calculate these indicators. Much attention is given in the scientific literature to the estimation of returns to scale. This paper describes and compares some of the best known methods for calculating returns to scale. Computational experiments show that under certain conditions, the approach proposed by the authors has advantages over other methods.

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.

Similar content being viewed by others

REFERENCES

  1. Charnes, A., Cooper, W.W., and Rhodes, E., Measuring the efficiency of decision making units, Eur. J. Oper. Res., 1978, vol. 2, no. 6, pp. 429–444. https://doi.org/10.1016/0377-2217(78)90138-8

    Article  MathSciNet  MATH  Google Scholar 

  2. Banker, R.D., Charnes, A., and Cooper, W.W., Some models for estimating technical and scale efficiency in data envelopment analysis, Manage. Sci., 1984, vol. 30, no. 9, pp. 1078–1092. https://doi.org/10.1287/mnsc.30.9.1078

    Article  MATH  Google Scholar 

  3. Hanoch, G., Homotheticity in joint production, J. Econ. Theor., 1970, vol. 2, no. 4, pp. 432–426. https://doi.org/10.1016/0022-0531(70)90024-4

    Article  MathSciNet  Google Scholar 

  4. Panzar, J.C. and Willig, R.D., Economies of scale in multi-output production, Q. J. Econ., 1977, vol. 91, no. 3, pp. 481–493. https://doi.org/10.2307/1885979

    Article  MATH  Google Scholar 

  5. Starrett, D.A., Measuring returns to scale in the aggregate, and scale effect of public goods, Econometrica, 1977, vol. 45, no. 6, pp. 1439–1455. https://doi.org/10.2307/1912310

    Article  MathSciNet  MATH  Google Scholar 

  6. Shepard, R.W., Theory of Cost and Production Functions, New Jersey: Princeton Univ. Press, 1970.

    Google Scholar 

  7. Afanasiev, A.P., Krivonozhko, V.E., Lychev, A.V., and Sukhoroslov, O.V., Multidimensional frontier visualization based on optimization methods using parallel computations, J. Global. Optim., 2020, vol. 76, pp. 563–574. https://doi.org/10.1007/s10898-019-00812-y

    Article  MathSciNet  MATH  Google Scholar 

  8. Banker, R.D. and Thrall, R.M., Estimation of returns to scale using data envelopment analysis, Eur. J. Oper. Res., 1992, vol. 62, no. 1, pp. 74–84. https://doi.org/10.1016/0377-2217(92)90178-C

    Article  MATH  Google Scholar 

  9. Førsund, F.R., On the calculation of the scale elasticity in DEA models, J. Prod. Anal., 1996, vol. 7, nos. 2–3, pp. 283–302. https://doi.org/10.1007/BF00157045

  10. Cooper, W.W., Seiford, L.M., and Tone, K., Data Envelopment Analysis. A Comprehensive Text with Models, Applications, References and DEA-Solver Software, New York: Springer Sci. Bus. Media, 2007, 2nd ed. https://doi.org/10.1007/978-0-387-45283-8

  11. Tone, K., A simple characterization of returns to scale in DEA, J. Oper. Res. Soc. Jpn., 1996, vol. 39, no. 4, pp. 604–613.

    MathSciNet  MATH  Google Scholar 

  12. Banker, R.D., Cooper, W.W., Seiford, L.M., et al., Returns to scale in different DEA models, Eur. J. Oper. Res., 2004, vol. 154, pp. 345–362. https://doi.org/10.1016/S0377-2217(03)00174-7

    Article  MathSciNet  MATH  Google Scholar 

  13. Sueyoshi, T. and Sekitani, K., Measurement of returns to scale using a non-radial DEA model: a range-adjusted measure approach, Eur. J. Oper. Res., 2007, vol. 176, pp. 1918–1946. https://doi.org/10.1016/j.ejor.2005.10.043

    Article  MATH  Google Scholar 

  14. Sueyoshi, T. and Sekitani, K., An occurrence of multiple projections in DEA-based measurement of technical efficiency: theoretical comparison among DEA models from desirable properties, Eur. J. Oper. Res., 2009, vol. 196, pp. 764–794. https://doi.org/10.1016/j.ejor.2008.01.045

    Article  MathSciNet  MATH  Google Scholar 

  15. Krivonozhko, V.E., Førsund, F.R., and Lychev, A.V., Measurement of returns to scale using non-radial DEA models, Eur. J. Oper. Res., 2014, vol. 232, no. 3, pp. 664–670. https://doi.org/10.1016/j.ejor.2013.06.046

  16. Mehdiloozad, M., Mirdehghan, S.M., Sahoo, B.K., et al., On the identification of the global reference set in data envelopment analysis, Eur. J. Oper. Res., 2015, vol. 245, no. 3, pp. 779–788. https://doi.org/10.1016/j.ejor.2015.03.029

    Article  MathSciNet  MATH  Google Scholar 

  17. Krivonozhko, V.E., Førsund, F.R., and Lychev, A.V., Returns-to-scale properties in DEA models: the fundamental role of interior points, J. Prod. Anal., 2012, vol. 38, pp. 121–130. https://doi.org/10.1007/s11123-011-0253-z

  18. Krivonozhko, V.E., Førsund, F.R., and Lychev, A.V., Methods for determination of multiple reference sets in the DEA models, Dokl. Math., 2012, vol. 85, pp. 134–138.

  19. Krivonozhko, V.E., Lychev, A.V., and Førsund, F.R., Measurement of returns to scale in radial DEA models, Comput. Math. Math. Phys., 2017, vol. 57, no. 1, pp. 83–93.

  20. Førsund, F.R., Hjalmarsson, L., Krivonozhko, V.E., et al., Calculation of scale elasticities in DEA models: direct and indirect approaches, J. Prod. Anal., 2007, vol. 28, pp. 45–56. https://doi.org/10.1007/s11123-007-0047-5

  21. Bertsimas, D. and Tsitsiklis, J.N., Introduction to Linear Optimization, Belmont, MA: Athena Sci., 1997.

    Google Scholar 

  22. Mehdiloozad, M. and Sahoo, B.K., Identifying the global reference set in DEA: an application to the determination of returns to scale, in Handbook of Operations Analytics Using Data Envelopment Analysis, Hwang, S.-N., Lee, H.-S., and Zhu, J., Eds., Boston, MA: Springer US, 2016, pp. 299–330. https://doi.org/10.1007/978-1-4899-7705-2_12

  23. Mehdiloozad, M., Identifying the global reference set in DEA: a mixed 0-1 LP formulation with an equivalent LP relaxation, Oper. Res. Int. J., 2017, vol. 17, pp. 205–211. https://doi.org/10.1007/s12351-015-0222-9

    Article  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 17-11-01353.

Author information

Authors and Affiliations

  1. National University of Science and Technology “MISiS”, Moscow, 119049, Russia

    V. E. Krivonozhko & A. V. Lychev

  2. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051, Russia

    A. P. Afanasiev

  3. RUDN University, Moscow, 117198, Russia

    A. P. Afanasiev

  4. University of Oslo, Oslo, 0316, Norway

    F. R. Førsund

Authors
  1. V. E. Krivonozhko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Afanasiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. R. Førsund
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. V. Lychev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. E. Krivonozhko, A. P. Afanasiev, F. R. Førsund or A. V. Lychev.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krivonozhko, V.E., Afanasiev, A.P., Førsund, F.R. et al. Comparison of Different Methods for Estimation of Returns to Scale in Nonradial Data Envelopment Analysis Models. Autom Remote Control 83, 1136–1148 (2022). https://doi.org/10.1134/S0005117922070098

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117922070098

Keywords

Search

Navigation