Summary of Chapter 7
In this chapter we expanded the ability of DEA to deal with variables that are not under managerial control but nevertheless affect performances in ways that need to be taken into account when effecting evaluations. Non-discretionary and categorical variables represent two of the ways in which conditions beyond managerial control can be taken into account in a DEA analysis. Uses of upper or lower bounds constitute yet another approach and, of course, these approaches can be combined in a variety of ways. Finally, uses of Wilcoxon-Mann-Whitney statistics were introduced for testing results in a nonparametric manner when ranking can be employed.
Illustrative examples were supplied along with algorithms that can be used either separately or with the computer code DEA-Solver. We also showed how to extend DEA in order to deal with production possibility sets (there may be more than one) that are not convex. Finally we provided examples to show how new results can be secured when DEA is applied to such sets to test the efficiency of organization forms (and other types of activities) in ways that were not otherwise available.
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Notes
R.D. Banker and R. Morey (1986a) “Efficiency Analysis for Exogenously Fixed Inputs and Outputs,” Operations Research 34(4), pp.513–521
A. Charnes, W.W. Cooper, J.J. Rousseau and J. Semple (1987), “Data Envelopment Analysis and Axiomatic Notions of Efficiency and Reference Sets,” CCS Research Report 558 (Austin, Texas: University of Texas, Graduate School of Business, Center for Cybernetic Studies, Austin, Texas 78712).
E.F. Fama and M.C. Jensen (1983a) “Separation of Ownership and Control,” Journal of Law and Economics 26, pp.301–325. See also Fama and Jensen (1983b) “Agency Problems and Residual Claims,” Journal of Law and Economics 26, pp.327–349.
P.L. Brockett, W.W. Cooper, J.J. Rousseau and Y. Wang (1998) “DEA Evaluations of the Efficiency of Organizational Forms and Distribution Systems in the U.S. Property and Liability Insurance Industry,” International Journal of System Science 29, pp.1235–1247.
Solvency, defined as an ability to meet claims, for example, played a critically important role in Brockett et al. but not in the Fama-Jensen study. See P.L. Brockett, W.W. Cooper, L. Golden, J.J. Rousseau and Y. Wang “Evaluating Solvency and Efficiency Performances by U.S. Property-Liability Insurance Companies,” Journal of Risk and Insurance (submitted).
The Mann-Whitney statistic does not require equal sample size. See E.L. Lehman (1979) Nonparametrization: Statistical Methods Based on Ranks (New York: Holden-Day).
D.L. Adolphson, G.C. Cornia, L.C. Walters, “A Unified Framework for Classifying DEA Models,” Operational Research’ 90, edited by H.E. Bradley, Pergamon Press, pp.647–657 (1991).
K. Tone (1993), “On DEA Models,” (in Japanese) Communications of the Operations Research Society of Japan, 38, pp.34–40.
R.D. Banker and R.C. Morey (1986b), “The Use of Categorical Variables in Data Envelopment Analysis,” Management Science, 32(12), pp. 1613–1627.
W. A. Kamakura (1988) “A Note on The Use of Categorical Variables in Data Envelopment Analysis,” Management Science 34(10), pp.1273–1276.
J.J. Rousseau and J. Semple (1993) “Categorical Outputs in Data Envelopment Analysis,” Management Science 39(3), pp.384–386.
K. Tone (1997), “DEA with Controllable Category Levels,” in Proceedings of the 1997 Spring National Conference of the Operations Research Society of Japan, pp. 126–127.
K. Tone (1993), Data Envelopment Analysis (in Japanese) (Tokyo: JUSE Press, Ltd.).
A. Charnes, W.W. Cooper and E. Rhodes (1981) “Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through,” Management Science 27, pp.668–697.
P.L. Brockett and B. Golany (1996) “Using Rank Statistics for Determining Programmatic Efficiency Differences in Data Envelopment Analysis,” Management Science 42, pp.466–472.
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(2002). Discretionary, Non-discretionary and Categorical Variables. In: Data Envelopment Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47541-3_7
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DOI: https://doi.org/10.1007/0-306-47541-3_7
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