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Keywords
- Data Envelopment Analysis
- Efficiency Score
- Efficient Frontier
- Fractional Programming
- Complementary Slackness
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Notes
See Appendix A.4.
See Appendix A.4.
Farrell also restricted his treatments to the single output case. See M.J. Farrell (1957) “The Measurement of Production Efficiency,” Journal of the Royal Statistical Society A, 120, pp.253–281.
In the linear programming literature this is called the “complementary slackness” condition. This terminology is due to A.W. Tucker who is responsible for formulating and proving this. See E.D. Nering and A.W. Tucker Linear Programs and Related Problems, (Harcourt Brace, 1993). See our Appendix A.6 for a detailed development.
See Appendix A.8.
See Appendix A.4.
We notice that OQ and OA are measured by some “distance measure.” If we employ the “Euclidian measure” — also called the “l 2 metric” — we have \( \frac{{d(OQ)}} {{d(OA)}} = \frac{{\sqrt {3.428^2 + 2.571^2 } }} {{\sqrt {4^2 + 3^2 } }} = \frac{{\surd 18.36}} {{\sqrt {25} }} = 8.57. \) However, the measure is not restricted to Euclidian measure. Any l k measure gives the same result. See Appendix A in Charnes and Cooper, Management Models and Industrial Applications of Linear Programming (New York, John Wiley, Inc., 1961). See also W.W. Cooper, L.M. Seiford, K. Tone and J. Zhu “DEA: Past Accomplishments and Future Prospects,” Journal of Productivity Analysis (submitted, 2005).
“Aborts” were treated as reciprocals so that an increase in their output would reduce the value of the numerator in the (FP o) objective represented in (2.3). They could also have been subtracted from a dominatingly large positive constant. See A. Charnes, T. Clark, W.W. Cooper and B. Golany “A Development Study of Data Envelopment Analysis in Measuring the Efficiency of Maintenance Units in the U.S. Air Forces,” Annals of Operational Research 2, 1985, pp.59–94.
R.D. Banker and R.C. Morey (1986), “Efficiency Analysis for Exogenously Fixed Inputs and Outputs,” Operations Research 34, 1986, pp.513–521. See also Chapter 10 in R. Färe, S. Grosskopf and C.A. Knox Lovell Production Frontiers (Cambridge University Press, 1994) where this is referred to as “sub-vector optimizations.”
I.R. Bardhan (1995), “DEA and Stochastic Frontier Regression Approaches Applied to Evaluating Performances of Public Secondary Schools in Texas,” Ph.D. Thesis. Austin Texas: Graduate School of Business, the University of Texas at Austin. Also available from University Microfilms, Inc. in Ann Arbor, Michigan.
V.L. Arnold, I.R. Bardhan and W.W. Cooper “A Two-Stage DEA Approach for Identifying and Rewarding Efficiency in Texas Secondary Schools” in W.W. Cooper, S. Thore, D. Gibson and F. Phillips, eds., IMPACT: How IC 2 Research Affects Public Policy and Business Practices (Westport, Conn.: Quorum Books, 1997)
See Arnold et al. (1997) for further suggestions and discussions.
See Governmental Accounting Standards Board (GASB) Research Report: “Service Efforts and Accomplishments Reporting: Its Time Has Come,” H.P. Hatry, J.M. Sullivan, J.M. Fountain and L. Kremer, eds. (Norwell, Conn., 1990).
C.A.K. Lovell, L.C. Walters and Lisa Wood, “Stratified Models of Education Production Using Modified DEA and Regression Analysis,” in A. Charnes, W.W. Cooper, A.Y. Lewin and L.M. Seiford, eds., Data Envelopment Analysis: Theory, Methodology and Applications (Norwell, Mass.: Kluwer Academic Publishers, 1994).
W.W. Cooper (2005), “Origin, Uses of and Relations Between Goal Programming and DEA (Data Envelopment Analysis)” Journal of Multiple Criteria Decision Analysis (to appear).
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(2006). The CCR Model and Production Correspondence. In: Introduction to Data Envelopment Analysis and Its Uses. Springer, Boston, MA. https://doi.org/10.1007/0-387-29122-9_3
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