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Abraham Charnes

Bio: Abraham Charnes is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Linear programming & Data envelopment analysis. The author has an hindex of 57, co-authored 222 publications receiving 63459 citations. Previous affiliations of Abraham Charnes include Carnegie Institution for Science & Northwestern University.


Papers
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ReportDOI
01 Jul 1965
TL;DR: The general n-period expectation- objective model of chance-constrained programming is presented and certain necessary conditions are established for decision rules to be optimal for such a model.
Abstract: : The first five sections of this paper contain an introduction to the topic of chance-constrained programming. Then the general n-period expectation- objective model of chance-constrained programming is presented and certain necessary conditions are established for decision rules to be optimal for such a model. The question of the consistency of the constraints and the finiteness of the optimal value of the objective function for such problems is discussed and several methods of resolving these questions are presented. The simplification that results when the chance-constrained problem is treated as a problem of linear programming under uncertainty is also discussed. The paper is concluded by solving two two-stage problems.

24 citations

Journal ArticleDOI
TL;DR: It is shown that the modular design problem can be transformed into a problem of minimizing a separable convex function subject to linear equality constraints and nonnegativities by using a generalized inverse of the constraint matrix.
Abstract: It is shown that the modular design problem \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{array}{[email protected]{\quad}[email protected]{\quad}l}\mbox{minimize} & \sum^{i=m}_{i=1}y_{i} \sum^{j=n}_{j=1} z_{j},\\ \mbox{subject to} & y_{i}z_{j}\geq r_{ij},\\ & y_{i}z_{j} > 0, & i=1, \ldots, m,\ j=1, \ldots, n\end{array}$$ \end{document} can be transformed into a problem of minimizing a separable convex function subject to linear equality constraints and nonnegativities. This transformation is effected by using a generalized inverse of the constraint matrix. Moreover the nature of the functional and the constraints of the separable problem are such that a good starting point for its solution can be obtained by solving a particular transportation problem. Several possible methods for solving the separable problem are discussed, and the results of our computational experience with these methods are given. It is also shown that the modular design problem can be viewed as a special case of a large class of general engineering design problems that have been discussed in the literature.

24 citations

Journal ArticleDOI
TL;DR: This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination, and generalization of the classical distribution problem makes the model more versatile from a theoretical standpoint and more usable from an applications viewpoint.
Abstract: This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination. Our problem differs from the classical distribution model in which the node shipping amounts are, by contrast, specified exactly. This generalization of the classical distribution problem not only makes the model more versatile from a theoretical standpoint but also makes the model more usable from an applications viewpoint.

23 citations

Book ChapterDOI
01 Jan 1976
TL;DR: In this paper, an absolute value formulation of objectives and a numerical illustration with differing weights for each of the indicated classes of objectives are briefly discussed, along with different approaches to problems of validation and, subsequently, implementation in a U.S. Navy context.
Abstract: Previous manpower planning models — e.g., in the OCMM series — have utilized multi-period Markoff processes embedded in goal programming (multiple objective) models. These are here extended to Equal Employment Opportunity plans directed to changing the mix of employees over time. At each point in the planning interval, the organization is taken as given, e.g., in terms of the probabilities for promotion, transfer, etc., When formulating manpower programs. Over time, however, these organization processes are submitted to planned changes which alter the probabilities of occurrence for these events. The Merit Promotion System is preserved and other controls are also imposed explicitly for the exercise of managerial discretion. The focus here is on an ordinary (absolute value) formulation of objectives and a numerical illustration is supplied with differing weights for each of the indicated classes of objectives. Other types of objectives are briefly discussed, along with different approaches to problems of validation and, subsequently, implementation in a U.S. Navy context.

23 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