×

zbMATH — the first resource for mathematics

Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. (English) Zbl 0582.90007
The construction and analysis of Pareto-efficient frontier production functions by a new data envelopment analysis method is presented in the context of new theoretical characterizations of the inherent structure and capabilities of such empirical production functions. Contrasts and connections with other developments, including solutions of some remaining problems, are made regarding aspects such as informatics, economies of scale, isotonicity and non-concavity, discretionary and non- discretionary inputs, piecewise linearity, partial derivatives and Cobb- Douglas properties of the functions. Non-Archimedean constructs are not required.

MSC:
91B38 Production theory, theory of the firm
62P20 Applications of statistics to economics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Afriat, S., Efficiency estimation of production functions, International economic review, 13, 568-598, (1972) · Zbl 0264.90022
[2] Aigner, D.J.; Lovell, C.A.K.; Schmidt, P.J., Formulation and estimation of stochastic frontier production function models, Journal of econometrics, 6, 21-37, (1977) · Zbl 0366.90026
[3] Banker, R., Estimating most productive scale size using data envelopment analysis, European journal of operational research, 17, 35-44, (1984) · Zbl 0538.90030
[4] Banker, R.; Charnes, A.; Cooper, W.W., Models for estimating technical and scale efficiencies in data envelopment analysis, Management science, 30, 1078-1092, (1984) · Zbl 0552.90055
[5] Banker, R., W. Bowlin, A. Charnes and W.W. Cooper, in process, Mix inefficiencies and synergies in data envelopment analysis, CCS report (Center for Cybernetic Studies, The University of Texas, Austin, TX).
[6] Ben-Israel, A.; Ben-Tal, A.; Charnes, A., Necessary and sufficient conditions for a Pareto optimum in convex programming, Econometrica, 45, 811-820, (1977) · Zbl 0367.90093
[7] Bessent, A.; Bessent, W.; Charnes, A.; Cooper, W.W.; Thorogood, N., Evaluation of educational program proposals by means of DEA, Educational administration quarterly, 19, 82-107, (1983)
[8] Charnes, A.; Cooper, W.W.; Charnes, A.; Cooper, W.W., Programming with linear fractional functionals, Naval research logistics quarterly, Naval research logistics quarterly, 9, no. 4, (1962) · Zbl 0122.15302
[9] Charnes, A.; Cooper, W.W., Goal programming and multiple objective optimizations, European journal of operational research, 1, no. 1, (1977) · Zbl 0375.90079
[10] Charnes, A.; Cooper, W.W., Management models and industrial applications of linear programming, (1961), Wiley New York · Zbl 0107.37004
[11] Charnes, A.; Cooper, W.W., Auditing and accounting for program efficiency in not-for-profit entities, Accounting, organizations and society, 5, 87-107, (1980)
[12] Charnes, A. and W.W. Cooper, forthcoming, Preface to topics in data envelopment analysis, Annals of Operations Research.
[13] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision-making units, European journal of operations research, 2, 429-444, (1978) · Zbl 0416.90080
[14] Charnes, A.; Cooper, W.W.; Rhodes, E., Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through, Management science, 27, 668-687, (1981)
[15] Charnes, A.; Cooper, W.W.; Schinnar, A., Transforms and approximations in cost and production function relations, Omega, 10, 207-211, (1982)
[16] Charnes, A., W.W. Cooper and D. Sherman, in process, A comparative study of DEA with ratio and regression approaches to efficiency evaluations, CCS report (Center for Cybernetic Studies, The University of Texas, Austin, TX).
[17] Charnes, A.; Cooper, W.W.; Seiford, L.; Stutz, J., A multiplicative model for efficiency analysis, Socio-economic planning sciences, 6, 223-224, (1982)
[18] Charnes, A.; Cooper, W.W.; Seiford, L.; Stutz, J., A units invariant multiplicative measure, Operations research letters, (1983) · Zbl 0521.90066
[19] Charnes, A., W.W. Cooper, A. Lewin, R. Morey and J. Rousseau, forthcoming, An approach to positivity and stability analysis in DEA, Annals of Operations Research.
[20] Färe, R.; Lovell, C.A.K., Measuring the technical efficiency of production, Journal of economic theory, 19, 150-162, (1978) · Zbl 0398.90012
[21] Farrell, M.J., The measurement of productive efficiency, Journal of royal statistical society, A 120, 253-281, (1957)
[22] Fenchel, W., Convex sets, cones and functions, (1953), Princeton University Press Princeton, NJ · Zbl 0053.12203
[23] Försund, F.; Hjalmarsson, L., Generalized farrell measures of efficiency: an application to milk processing in swedish dairy plants, Economic journal, 89, 294-315, (1979)
[24] Frisch, R., The principles of substitution: an example of its application in the chocolate industry, Nordisk tidsskrift for teknisk ekonomi, 1, 12-27, (1935)
[25] Rockfellar, T., Convex analysis, (1970), Princeton University Press Princeton, NJ
[26] Shephard, R.W., Cost and production functions, (1953), Princeton University Press Princeton, NJ · Zbl 0052.15901
[27] Shephard, R.W., Theory of cost and production functions, (1970), Princeton University Press Princeton, NJ · Zbl 0052.15901
[28] Schaible, S., Parameter-free convex equivalent and dual programs of fractional programming problems, Zeitschift für operations research, 18, 187-196, (1974) · Zbl 0291.90067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.