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.

Continuous Optimization A simulation study of DEA and parametric frontier models in the presence of heteroscedasticity

Abstract: This paper studies the effects of heteroscedasticity on the following five types of estimators: (1) Data Envelopment Analysis (DEA) per se as well as DEA joined to regression forms, (2) Corrected Ordinary Least Squares based on maximum residual (COLS-R), (3) Corrected Ordinary Least Squares based on moments of residuals (COLS-M), (4) Maximum Likelihood Estimation (MLE), and (5) Goal Programming with one-sided deviations as in Aigner and Chu (A&C). This is accomplished with simulated data in an experiment designed around a single output–single input production function which is piecewise Cobb–Douglas. Robustness of results is confirmed with another experiment employing a shifted smooth Cobb–Douglas production function. The model has a composed error term consisting of two components––one for measurement error and the other for inefficiency. The simulation results indicate that heteroscedasticity does not have an adverse impact on DEA-based estimators and that DEA-based estimators are the best estimators of efficient output even under heteroscedasticity. 2003 Elsevier B.V. All rights reserved.

Structural sensitivity analysis in linear programming and an exact product from left inverse

Abstract: : This paper shows how to obtain an exact inverse in the form of a product modification to a given inverse when the matrix has been altered additively by a matrix of a certain class. Explicit formulae are derived for sensitivity analyses, e.g., in linear programming, wherein the elements of the structural matrix are to be varied.

Note on an Application of a Goal Programming Model for Media Planning

Abstract: An illustrative example is developed from an actual application of goal programming to media planning over a period of time. These goals involve distributions of frequencies by demographic and other characteristics as well as budget and other constraining limitations.

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

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."

Fuzzy Set Theory - and Its Applications

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.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

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.

Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software

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.