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William W. Cooper

Bio: William W. Cooper is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Data envelopment analysis & Linear programming. The author has an hindex of 79, co-authored 254 publications receiving 76641 citations. Previous affiliations of William W. Cooper include Harvard University & Carnegie Mellon University.


Papers
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Posted Content
01 Jan 2007

1,195 citations

Journal ArticleDOI
TL;DR: It will be shown how the methods of linear programming may be used to obtain estimates of parameters when more usual methods, such as “least squares,” are difficult or impossible to apply.
Abstract: Linear programming, as an optimizing method for handling a mass of interacting variables, has received considerable attention in applications to such problems as production scheduling, logistics, and mobilization studies. But linear programming may also be used in a variety of other ways. This paper is concerned with one such alternative use. It will be shown how, by appropriate adaptations, the methods of linear programming may be used to obtain estimates of parameters when more usual methods, such as “least squares,” are difficult or impossible to apply.

1,058 citations

Journal ArticleDOI
TL;DR: In this paper, the existence of deterministic equivalents for a general class of linear decision rules under the following three classes of objectives 1 maximum expected value (E model), 2 minimum variance (V model), and 3 maximum probability (P model) was established.
Abstract: Chance constrained programming admits random data variations and permits constraint violations up to specified probability limits. Different kinds of decision rules and optimizing objectives may be used so that, under certain conditions, a programming problem not necessarily linear can be achieved that is deterministic---in that all random elements have been eliminated. Existence of such “deterministic equivalents” in the form of specified convex programming problems is here established for a general class of linear decision rules under the following 3 classes of objectives 1 maximum expected value “E model”, 2 minimum variance “V model”, and 3 maximum probability “P model”. Various explanations and interpretations of these results are supplied along with other aspects of chance constrained programming. For example, the “P model” is interpreted so that H. A. Simon's suggestions for “satisficing” can be studied relative to more traditional optimizing objectives associated with “E” and “V model” variants.

987 citations

Book
16 Nov 2005
TL;DR: The basic CCR Model and Production Correspondence and Alternative Dea Models are described, as well as alternative models with Restricted Multipliers and Super-Efficiency Models, which are described below.
Abstract: General Discussion.- The Basic CCR Model.- The CCR Model and Production Correspondence.- Alternative Dea Models.- Returns To Scale.- Models with Restricted Multipliers.- Discretionary, non-Discretionary and Categorical Variables.- Allocation Models.- Data Variations.- Super-Efficiency Models.

974 citations


Cited by
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Journal ArticleDOI
TL;DR: 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 and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.

25,433 citations

Journal ArticleDOI
TL;DR: The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs as mentioned in this paper.
Abstract: In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."

14,941 citations

Book
31 Jul 1985
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

7,877 citations

Journal ArticleDOI
01 May 1981
TL;DR: This chapter discusses Detecting Influential Observations and Outliers, a method for assessing Collinearity, and its applications in medicine and science.
Abstract: 1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

4,948 citations

Book
30 Nov 1999
TL;DR: In this article, the basic CCR model and DEA models with restricted multipliers are discussed. But they do not consider the effect of non-discretionary and categorical variables.
Abstract: List of Tables. List of Figures. Preface. 1. General Discussion. 2. The Basic CCR Model. 3. The CCR Model and Production Correspondence. 4. Alternative DEA Models. 5. Returns to Scale. 6. Models with Restricted Multipliers. 7. Discretionary, Non-Discretionary and Categorical Variables. 8. Allocation Models. 9. Data Variations. Appendices. Index.

4,395 citations