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.
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References
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.
Charnes, A., W.W. Cooper, and E. Rhodes, 1978, ‘Measuring the efficiency of cecision making units’, European Journal of Operational Research 2, 429–444.
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.
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.
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.
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.
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.
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.
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.
Roll, Y. and B. Golany, 1993, ‘Alternate methods of treating factor weights in DEA’, OMEGA International Journal of Management Science 21, 99–109.
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).
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.
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.
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.
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.
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.
Tone, K., 1993, ‘An s-free DEA and a new measure of efficiency’, Journal of the Operations Research Society of Japan 36, 167–174.
Yamashita, H., 1992, revised 1994, ‘A globally convergent primal-dual interior point method for constrained optimization’, Technical Report, Mathematical Systems Institute Inc., Tokyo, Japan.
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Tone, K. (1997). Several Algorithms to Determine Multipliers for Use in Cone-Ratio Envelopment Approaches to Efficiency Evaluations in DEA. In: Amman, H., Rustem, B., Whinston, A. (eds) Computational Approaches to Economic Problems. Advances in Computational Economics, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2644-2_7
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DOI: https://doi.org/10.1007/978-1-4757-2644-2_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4770-3
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