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.

Critical Path Analyses Via Chance Constrained and Stochastic Programming

Abstract: Chance-constrained programming methods are applied to examine some statistical properties of PERT networks. Using duality, the PERT method is shown to be equivalent to use of the crudest linear decision rule and the confidence or lack thereof in meeting constraints is explicitly presented. The distribution of completion times = Tintner's stochastic programming follows easily and may often be multimodal, contrasting with erroneous central limit theorem usages in the literature. Possible extensions and developments of PERT using more adequate chance-constrained models and techniques are suggested and will be presented elsewhere.

Efficiency characterizations in different DEA models

Abstract: Relations of efficiency and non-efficiency for the same sets of DMUs (Decision Making Units) are developed for the Charnes, Cooper and Rhodes (CCR) and Barker, Charnes, Cooper (BCC) ratio models, as well as DEA Additive and Multiplicative Models Surprisingly, additively efficient DMUs are not necessarily multiplicatively efficient A geometric “stretching” phenomenon is identified for the latter case

Inter-Temporal Analysis and Optimization of Bank Portfolios

Abstract: This paper is concerned with formulating, exploring and interpreting the uses and constructs which may be derived from a mathematical model of programming type which expresses more realistically than past efforts the actual conditions of current operations. It is an attempt to provide a means of attaining thereby an objective understanding of the implications of actual Federal Reserve liquidity policy on the actions and opportunities of banking institutions. The model presented corresponds to the problem of determining an optimal portfolio for an individual bank over several time periods in accordance with requirements laid down by bank examiners which are interpreted as defining limits within which the level of risk associated with the return on the portfolio is an acceptable one. The problem is transformed into an equivalent one offering advantages of analysis and of computation. Some methods of effective computation are explored.

A Goal Programming Model for Media Planning

Abstract: A goal programming model for selecting media is presented which alters the objective and extends previous media models by accounting for cumulative duplicating audiences over a variety of time periods. This permits detailed control of the distribution of message frequencies directed at each of numerous marketing targets over a sequence of interrelated periods. This is accomplished via a new logarithmic non-reach device and a continuous lognormal generation of the discrete message frequencies.

A Comparison of DEA and Translog Estimates of Production Frontiers Using Simulated Observations from a Known Technology

Abstract: Data envelopment analysis (DEA), introduced in Charnes, Cooper, and Rhodes (1978), provides a new approach to the estimation of relative efficiencies of decision making units (DMUs). As described by Banker (1980b) and Banker, Charnes, and Cooper (1984), DEA also encompasses estimation of production frontiers making minimal assumptions—such as convexity—about the production possibility set. DEA may be employed to estimate technical and scale efficiencies as in Banker, Charnes, and Cooper, rates of substitution between inputs as in Banker, Charnes, and Cooper and Charnes, Cooper, and Rhodes (1978), and returns to scale and most productive scale sizes as in Banker (1984) and Banker, Charnes, and Cooper (1984). These estimates of different production characteristics pertain to the efficient production surface, unlike the commonly employed regression techniques which estimate the average production correspondence. In this chapter, we report on the results of a simulation study in which DEA was employed to estimate the production frontier from input and output data randomly generated from a known technology.

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.