Abstract
In this chapter, we introduced the assurance region and cone-ratio methods for combining subjective and expert evaluations with the more objective methods of DEA.
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Usually expressed in the form of lower and upper bounds, the assurance region method puts constraints on the ratio of input (output) weights or multiplier values. This helps to get rid of zero weights which frequently appear in solution to DEA models. The thus evaluated efficiency score generally drops from its initial (unconstrained) value. Careful choice of the lower and upper bounds is recommended.
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Not covered in this chapter is the topic of “linked constraints” in which conditions on input and output multipliers are linked. See Problem 6.3.
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The cone-ratio method confines the feasible region of virtual multipliers v, u, to a convex cone generated by admissible directions. Formulated as a “cone ratio envelopment” this method can be regarded as a generalization of the assurance region approach.
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Example applications were used to illustrate uses of both of the “assurance region” and “cone ratio envelopment” approaches.
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Notes
R.G. Thompson, 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, pp. 35–49. See also R.G. Dyson and E.Thanassoulis (1988), “Reducing Weight Flexibility in Data Envelopment Analysis,” Journal of the Operational Research Society, 39, pp. 563–576. Finally, see Notes and Selected Bibliography in Section 6.9 of this chapter for references on uses of DEA for site selection.
A. Charnes, 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, pp. 73–91. For a treatment that studies this approach as an alternative to the more rigid approach to risk evaluation under the “Basel Agreement” for controlling risks in bank portfolios see P.L. Brockett, A. Charnes, W.W. Cooper, Z.M. Huang and D.B. Sun, “Data Transformations in DEA Cone-Ratio Approaches for Monitoring Bank Performance,” European Journal of Operational Research, 98, 1997, pp. 250–268.
Y. Roll, W.D. Cook and B. Golany (1991), “Controlling Factor Weights in Data Envelopment Analysis,” IIE Transactions 23, pp. 2–9.
R. Allen, A. Athanassopoulos, R.G. Dyson and E. Thanassoulis (1997), “Weights restrictions and value judgements in data envelopment analysis,” Annals of Operations Research 73, pp.13–34.
P.L. Brockett, A. Charnes, W.W. Cooper, Z. Huang and D.B. Sun (1997), “Data Transformations in DEA Cone Ratio Envelopment Approaches for Monitoring Bank Performance,” European Journal of Operational Research 98, pp.250–268.
For detailed discussions see the references cited in A. Charnes, W.W. Cooper, Z. Huang and D.B. Sun (1997), “Data Transformations in DEA Cone Ratio Envelopment Approaches for Monitoring Bank Performance,” European Journal of Operational Research 98, pp.250–268 Brockett et al. (1997).
In response to this trend, Barr, Seiford, and Siems with the Federal Reserve Bank of Dallas developed a bank failure prediction model based on DEA which outperforms all other failure prediction models in the banking literature. See R.S. Barr, L.M. Seiford and T.F. Siems (1994), “Forcasting Bank Failure: A Non-Parametric Frontier Estimation Approach,” Recherches Economiques de Louvain 60, pp.417–429 and R.S. Barr, L.M. Seiford and T.F. Siems (1993), “An Envelopment-Analysis Approach to Measuring the Managerial Efficiency of Banks,” Annals of Operations Research, 45, pp.1–19 for details.
See the definition and discussion of “Reserve (=Allowance) for Bad Debts” on page 433 in Kohler’s Dictionary for Accountants, 6th Edition (Englewood Cliffs, N.J., Prentice-Hall Inc., 1983.)
R.M. Nun (1989), “Bank Failure: The Management Factor” (Austin, TX., Texas Department of Banking).
See A. Ben Israel and T.N. Greville, Generalized Inverses (New York, John Wiley & Sons Inc., 1974).
Y. Takamura and K. Tone (2003), “A Comparative Site Evaluation Study for Relocating Japanese Government Agencies out of Tokyo,” Socio-Economic Planning Sciences 37, pp.85–102.
AHP (Analytic Hierarchy Process) was invented by T.L. Saaty (1980), Analytic Hierarchy Process, New York: McGraw-Hill. See also K. Tone (1989), “A Comparative Study on AHP and DEA,” International Journal of Policy and Information 13, pp.57–63.
See J.A. Dewar and J.A. Friel (2001), “Delphi Method,” in S.I. Gass and CM. Harris, eds., Encyclopedia of Operations Research and Management Science (Norwell, Mass., Kluwer Academic Publishers) pp.208–209.
Y. Yamada, T. Matsui and M. Sugiyama (1994), “An Inefficiency Measurement Method for Management Systems,” Journal of the Operations Research Society of Japan 37,2, pp.158–167.
See the 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, pp. 35–49 Note 1 reference.
R.G. Thompson, L.N Langemeir, C. 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, pp.93–108.
Y. Roll and B. Golany (1993), “Alternate Methods of Treating Factor Weights in DEA,” OMEGA 21, pp.99–109.
R.G. Dyson and E. Thanassoulis (1988), “Reducing Weight Flexibility in Data Envelopment Analysis,” Journal of the Operational Research Society 39, pp.563–576.
A.D. Athanassopoulos and J.E. Storbeck (1995), “Non-Parametric Models for Spatial Efficiency,” The Journal of Productivity Analysis 6, pp.225–245.
A. Desai, K. Haynes and J.E. Storbeck “A Spatial Efficiency Framework for the Support of Locational Decisions,” in Data Envelopment Analysis: Theory, Methodology, and Applications, A. Charnes, W. W. Cooper, Arie Y. Lewin, and Lawrence M. Seiford (editors), Kluwer Academic Publishers, Boston, 1994.
D.B. Sun (1988), “Evaluation of Managerial Performance in Large Commercial Banks by Data Envelopment Analysis,” Ph.D. dissertation, Graduate School of Business, University of Texas, Austin, TX.
A. Charnes, W.W. Cooper, Q.L. Wei and Z.M. Huang (1989), “Cone Ratio Data Envelopment Analysis and Multi-objective Programming,” International Journal of Systems Science 20, pp.1099–1118.
See the 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, pp.73–91 Note 2 reference.
See the A. Charnes, W.W. Cooper, Z. Huang and D.B. Sun (1997), “Data Transformations in DEA Cone Ratio Envelopment Approaches for Monitoring Bank Performance,” European Journal of Operational Research 98, pp.250–268 Note 8 reference.
K. Tone (2001), “On Returns to Scale under Weight Restrictions in Data Envelopment Analysis,” Journal of Productivity Analysis 16, pp.31–47.
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Cooper, W.W., Seiford, L.M., Tone, K. (2007). Models with Restricted Multipliers. In: Data Envelopment Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-45283-8_6
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