Showing papers by "William W. Cooper published in 1987"

Data Envelopment Analysis and Axiomatic Notions of Efficiency and Reference Sets.

Abstract: : Serious mathematical and computational errors and misstatements culminating in erroneous characterizations of Data Envelopment Analysis (DEA) models and methods and their relationship to the axiomatic production models of Shepard type by Fare, Hunsaker and others are corrected together with new exposition and contrast of current DEA methodology with the Shepard axiomatic modelling types. The stochastic base of DEA is shown to be uncertainty, not risk. A new computationally effective extended additive (EA) model is developed to handle processes with input thresholds and output ceilings and thereby not subsumable under Shepard axiomatics. Keywords: CCR Ratio model; Multi-objective programming.

Explicit Construction and Analysis of Some Efficient Empirical Production Functions in Data Envelopment Analysis.

Abstract: : In contrast to classical econometric work which only tests data for consistency with a special class of production functions, new theory and explicit construction by Data Envelopment Analysis of the empirical Pareto-Koopmans efficient production function is developed for data sets which satisfy two conditions met in all previous real applications of DEA known to the authors The construction requires no additional computation beyond that of the DEA tests In section 2, we bring forth the differences in key preoccupations of research in economic production theory with those of DEA by references to papers of Hanoch and Rothschild (1972), of Diewert and Parkan (1983) and, in still another direction by Fare, Grosskopf and Lovell (1985) and Debreu (1951) In section 3, we develop basic concepts of and theorems for geometric elucidation and analysis of the empirical efficient production functions of DEA including a new lemma on optimal solutions to the general linear programming problem (for arbitrary ordered fields of scalars) Then, restricting ourselves to two conditions on empirical data which have held in every DEA application we have made, we show that the mathematical structure of the efficient empirical function is so simplified that it is available immediately in analytic form without further computational work on top of the DEA tests The efficient empirical production is then, moreover, piece-wise linear and continuous from piece to piece