Skip to main content
SpringerLink
Log in

The data envelopment analysis model with intersection form production possibility set

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

The data envelopment analysis (DEA) model is used to evaluate the relative economic efficiency of a given set of decision making units (DMUs). In this paper, the DEA production possibility set is transferred from the conventional sum form into the intersection form which is represented by a linear inequality system. Although it is time consuming to obtain the intersection form of the production possibility set, it suggests a new angle to investigate the properties of DMUs and to extend the DEA research further beyond the efficiency measurement. Following the intersection form, the analytical formula of the efficiency indicator and projection is given. Various aspects of technical efficiency, returns to scale and evidence of congestion of the DMUs are studied. The relationship between the weak DEA efficiency and the weak Pareto solution is discussed. Finally, a procedure for DMU grouping is proposed to help the decision makers for better resource reallocation and strategy adjustment.

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

References

  1. M. J. Farrell, The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A, 1957, 120: 253–281.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. R. Färe and S. Grosskopf, A nonparametric cost approach to scale efficiency, Scand. Journal of Economics, 1985, 87: 594–604.

    Article  MATH  Google Scholar 

  5. L. M. Seiford and R. M. Thrall, Recent developments in DEA, the mathematical programming approach to frontier analysis, Journal of Econometrics, 1990, 46: 7–38.

    Article  MATH  MathSciNet  Google Scholar 

  6. Q. L. Wei and H. Yan, A method of transferring polyhedron between the intersection-form and the sum-form, Computers and Mathematics with Application, 2001, 41: 1327–1142.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Yan and Q. L. Wei, A method of transferring cones of intersection-form to cones of sum-form and its applications in DEA models, International Journal of Systems Science, 2000, 31(5): 629–638.

    Article  MATH  Google Scholar 

  8. Q. L. Wei and H. Yan, Congestion and returns to scale in Data Envelopment Analysis, European Journal of Operational Research, 2004, 153: 641–660.

    Article  MATH  MathSciNet  Google Scholar 

  9. Q. L. Wei, G. Yu, and J. S. Lu, Necessary and sufficient conditions for return-to-scale properties in generalized data envelopment analysis models, Chinese Science, 2002, 45(5): 503–517.

    Article  MATH  Google Scholar 

  10. D. Day, A. Y. Lewin, H. Li, and R. Salazar, Strategic Leaders in the US Brewing Industry: A Longitudinal Analysis of Outliers, Data Envelopment Analysis, edited by Charnes et al., Kluwer Academic Publishers, Boston, Dordrecht and London, 1994.

    Google Scholar 

  11. M. S. Hunt, Competition in the major house appliance industry 1960–1970, Doctoral Dissertation, Harvard University, 1972.

  12. A. Boussofiane, R. G. Dyson, and E. Thanassoulis, Invited review: Applied data envelopment analysis, European Journal of Operational Research, 1991, 52: 1–15.

    Article  Google Scholar 

  13. A. Charnes, W. W. Cooper, A. Y. Lewin, and L. M. Seiford, Data Envelopment Analysis, Kluwer Academic Pulisher, Boston, 1994.

    MATH  Google Scholar 

  14. R. D. Banker and R. M. Thrall, Estimation of returns to scale using data envelopment analysis, European Journal of Operational Research, 1992, 62(2): 74–84.

    Article  MATH  MathSciNet  Google Scholar 

  15. Q. L. Wei and G. Yu, Analyzing the properties of K-cone in generalized data envelopment analysis model, Journal of Economics, 1997, 80: 63–84.

    MATH  MathSciNet  Google Scholar 

  16. G. Yu, Q. L. Wei, P. Brockett, and L. Zhou, Construction of all DEA efficient surfaces of the production possibility set under the generalized surfaces of the production possibility set under the generalized DEA model, European Journal of Operational Research, 1996, 95: 491–510.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Operations Research and Mathematical Economics, Renmin University of China, Beijing, 100872, China

    Quanling Wei

  2. Department of Logistics, The Hongkong Polytechnic University, Hongkong, China

    Hong Yan

Authors
  1. Quanling Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research is supported by the National Natural Science Foundation of China under Grant Nos. 70531040, 70871114, and the 985 Research Grant of Renmin University of China, and the Hong Kong CERG Research Fund PolyU5457/06H and PolyU 5485/09H.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wei, Q., Yan, H. The data envelopment analysis model with intersection form production possibility set. J Syst Sci Complex 23, 1086–1101 (2010). https://doi.org/10.1007/s11424-010-9218-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-010-9218-y

Key words

Search

Navigation