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Notes
In the linear programming literature this is called the “complementary slackness” condition. This terminology is given by 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 Appendix A.6 for a detailed development.
K. Tone “An Extension of the Two Phase Process in the CCR Model,” in Proceedings of the 1999 Fall National Conference of the Operations Research Society of Japan.
T. Coelli (1998) “A Multi-stage Methodology for the Solution of Oriented DEA Models,” Operations Research Letters, 22, pp. 143–149.
“Aborts” were treated as reciprocals so that an increase in their output would reduce the value of the numerator in the (FP0) 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 “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 ICQ 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).
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(2002). The CCR Model and Production Correspondence. In: Data Envelopment Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47541-3_3
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