Advertisement

Several Algorithms to Determine Multipliers for Use in Cone-Ratio Envelopment Approaches to Efficiency Evaluations in DEA

  • Kaoru Tone
Part of the Advances in Computational Economics book series (AICE, volume 6)

Abstract

In this paper, we will discuss subjects related to virtual multipliers in the cone-ratio model in DEA. Usually, there exists ambiguity in the virtual multipliers in the polyhedral cone-ratio method when some exemplary efficient DMUs’ multipliers are employed as the admissible directions of the cone. We will propose three practical methods for resolving this ambiguity, along with an example. Then, we will discuss possible applications of vertex enumeration software, based on the Double Description Method.

Keywords

Data Envelopment Analysis Data Envelopment Analysis Model Convex Polyhedron Fractional Program Polyhedral Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Charnes, A., W.W. Cooper, Z.M. Huang, and D.B. Sun, 1990, ‘Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks’, Journal of Econometrics 46, 73–91.CrossRefGoogle Scholar
  2. Charnes, A., W.W. Cooper, and E. Rhodes, 1978, ‘Measuring the efficiency of cecision making units’, European Journal of Operational Research 2, 429–444.CrossRefGoogle Scholar
  3. Charnes, A., W.W. Cooper, and R.M. Thrall, 1991, ‘A structure for classifying and characterizing efficiency and inefficiency in data envelopment analysis’, The Journal of Productivity Analysis 2, 197–237.CrossRefGoogle Scholar
  4. Charnes, A., W.W. Cooper, Q.L. Wei, and Z.M. Huang, 1989, ‘Cone ratio data envelopment analysis and multi-objective programming’, International Journal of System Sciences 20, 1099–1118.CrossRefGoogle Scholar
  5. Choi, I.C., C.L. Monmma, and D.F. Shanno, 1990, ‘Further development of a primal-dual interior point method’, ORSA Journal on Computing 2, 304–311.CrossRefGoogle Scholar
  6. Fukuda, K., 1993, ‘cdd.c: C-implementation of the double description method for computing all vertices and extremal rays of a convex polyhedron given by a system of linear inequalities’, Department of Mathematics, Swiss Federal Institute of Technology, Lausanne, Switzerland.Google Scholar
  7. Kojima, M., S. Mizuno, and A. Yoshise, 1989, ‘A primal-dual interior point method for linear programming’, in Progress in Mathematical Programming: Interior-Point and Related Methods, N. Megiddo (Ed.), New York: Springer-Verlag, pp. 29–48.Google Scholar
  8. McShane K.A., C.L. Monma, and D.F. Shanno, 1989, ‘An implementation of a primal-dual interior point method for linear programming’, ORSA Journal on Computing 1, 70–83.CrossRefGoogle Scholar
  9. Motzkin, T.S., H. Raiffa, G.L. Thompson, and M.R. Thrall, 1958, ‘The double description method’, in Contribution to the Theory of Games, Vol. 2, H.W. Kuhn and A.W. Tucker (Eds), Annals of Mathematics Studies, No. 28, Princeton: Princeton University Press, pp. 81–103.Google Scholar
  10. Roll, Y. and B. Golany, 1993, ‘Alternate methods of treating factor weights in DEA’, OMEGA International Journal of Management Science 21, 99–109.CrossRefGoogle Scholar
  11. Sun, D.B., 1987, ‘Evaluation of managerial performance of large commercial banks by data envelopment analysis’, Unpublished Ph.D. dissertation (Graduate School of Business, University of Texas, Austin, Texas).Google Scholar
  12. Thompson, R.G., P.S. Dharmapala, L.J. Rothenberg, and R.M. Tharll, 1994, ‘DEA ARs and CRs applied to worldwide major oil companies’, Journal of Productivity Analysis 5, 181–203.CrossRefGoogle Scholar
  13. Thompson, R.G., L.N. Langemeier, C.-T. Lee, E. Lee, and R.M. Thrall, 1990, ‘The role of multiplier bounds in efficiency analysis with application to Kansas farming’, Journal of Econometrics 46, 93–108.CrossRefGoogle Scholar
  14. Thompson, R.G., F.D. Singleton, Jr., R.M. Thrall, and B.A. Smith, 1986, ‘Comparative site evaluations for locating a high-energy physics lab in Texas’, Interfaces 16, 35–49.CrossRefGoogle Scholar
  15. Thompson, R.G., E.A. Waltz, D.S. Dharmapala, and R.M. Thrall, 1995, ‘DEA/AR measures and Malmquist indexes applied to ten OECD nations’, Working Paper No. 115, Jesse H. Jones Graduate School of Administration, Rice University, Houston, Texas 77251.Google Scholar
  16. Thompson, R.G. and R.M. Thrall, 1995, ‘Assurance region and cone ratio’, Paper presented at the First International Conference of the Society on Computational Economics, May 21–24, 1995, Austin, Texas.Google Scholar
  17. Tone, K., 1993, ‘An s-free DEA and a new measure of efficiency’, Journal of the Operations Research Society of Japan 36, 167–174.Google Scholar
  18. Yamashita, H., 1992, revised 1994, ‘A globally convergent primal-dual interior point method for constrained optimization’, Technical Report, Mathematical Systems Institute Inc., Tokyo, Japan.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Kaoru Tone

There are no affiliations available

Personalised recommendations