Measuring the efficiency of decision making units. (English) Zbl 0416.90080

Summary: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.


90C90 Applications of mathematical programming
90B50 Management decision making, including multiple objectives
91B06 Decision theory
Full Text: DOI


[1] Aigner, D.J.; Ameiya, T.; Poirier, P.J., On the estimation of production frontiers: maximum likelihood estimation of the parameters of a discontinuous density function, Internat. econ. rev., XVII, 2, 377-396, (1976) · Zbl 0339.62083
[2] Aigner, D.J.; Chu, S.F., On estimating the industry production function, American economic review, LVIII, 826-839, (1968)
[3] Alioto, R.F.; Jungherr, J.A., Operational PPBS for education, (1971), Harper and Row New York
[4] Arrow, K.J.; Hahn, F.H., General competitive analysis, (1971), Holden-Day San Francisco · Zbl 0311.90001
[5] Bector, C.R., Duality in linear fractional programming, Utilitas Mathematica, 4, 155-168, (1973) · Zbl 0271.90048
[6] Carlson, S., A study on the pure theory of production, (1956), Kelley and Millman, Inc New York
[7] Charnes, A.; Cooper, W.W., An explicit general solution in linear fractional programming, Naval research logistics quarterly, 20, 3, (1973) · Zbl 0267.90087
[8] Charnes, A.; Cooper, W.W., Management models and industrial applications of linear programming, (1961), Wiley New York · Zbl 0107.37004
[9] A. Chames and W.W. Cooper, Managerial economics — past, present, future, Journal of Enterprise Management (forthcoming).
[10] Charnes, A.; Cooper, W.W., Programming with linear fractional functionals, Naval res. logist. quart., 9, 3, 4, 181-185, (1962) · Zbl 0127.36901
[11] Charnes, A.; Cooper, W.W.; Rhodes, E., Expositions, interpretations, and extensions of farrell efficiency measures, () · Zbl 0416.90080
[12] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units with some new production functions and estimation methods, () · Zbl 0416.90080
[13] Charnes, A.; Cooper, W.W.; Schinnar, A., Transforms and approximations in cost and production function relations, () · Zbl 0339.90029
[14] (), 352-353
[15] Farrell, M.J., The measurement of productive efficiency, J. roy. statist. soc. ser. A, III, 253-290, (1957)
[16] Farrell, M.J.; Fieldhouse, M., Estimating efficient production functions under increasing returns to scale, J. roy. statist. soc. ser. A, II, 252-267, (1962)
[17] ()
[18] Jaganathan, R., Duality for nonlinear fractional programs, (), 1-3 · Zbl 0249.90064
[19] Johnston, J., Statistical cost analysis, (1960), McGraw-Hill New York
[20] Lancaster, K., Consumer demand, (), 40
[21] Rhodes, E., Data envelopment analysis and related approaches for measuring the efficiency of decision making units with an application to program follow through in U.S. education, ()
[22] Robinson, A., Non-standard analysis, (1966), North-Holland Amsterdam · Zbl 0151.00803
[23] Samuelson, P.A., Prices of factors and goods in general equilibrium, Rev. econom. stud., 21, 1-20, (1953-1954)
[24] Sato, K., Production functions and aggregation, (1975), North-Holland Amsterdam · Zbl 0344.90011
[25] Schaible, S., Parameter-free convex equivalent and dual programs of fractional programming problems, Z. operations res., 18, 187-196, (1974) · Zbl 0291.90067
[26] Shephard, R.W., Cost and production functions, (1953), Princeton University Press Princeton · Zbl 0052.15901
[27] Shephard, R.W., The theory of cost and production functions, (1970), Princeton University Press Princeton · Zbl 0381.90031
[28] Sitgler, G.J., The xistence of X-efficiency, Am. econom. rev., 213-216, (March 1976)
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