Measuring the efficiency of decision making units

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."

http://www.utdallas.edu/~ryoung/phdseminar/BCC1984.pdf

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

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.

https://www.springer.com/productFlyer_978-0-7923-7435-0.pdf?SGWID=0-0-1297-33300503-0

Fuzzy Set Theory - and Its Applications

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.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

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.

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

We review the literature of extensions and enhancements of the DEA basic methodology from the perspective of the problems that can be addressed by dealing with the dual multiplier formulation of the DEA models. We describe different approaches that allow incorporating into the analysis price information, reflecting meaningful trade-offs, incorporating value information and managerial goals, making a choice among alternate optima for the weights, avoiding non-zero weights, avoiding large differences in the values of multipliers, improving discrimination and ranking units. We confine attention to the methodological aspects of these approaches and show in many instances how others have used these approaches in applications in practise.

Choices and Uses of DEA Weights

This paper describes a research strategy and its results, which guided a 40+ year collaboration between Abraham Charnes and William W. Cooper, which was initiated in a research center established at the (then) new Graduate School of Industrial Administration at Carnegie Institute of Technology (now Carnegie Mellon University). Initiated in collaboration with Bob Mellon of Gulf Oil Company, this strategy involved on-site collaborations with company personnel in more than 100 different companies and government agencies. An appendix to this paper describes the efforts of another team working from the same research center. This team, consisting of Charles Holt, Franco Modigliani, John Muth, and Herbert A. Simon, used a different research strategy with an accompanying application that also had important impacts on operations research/management science and other disciplines.

https://pubsonline.informs.org/doi/pdf/10.1287/opre.50.1.35.17778

Abraham Charnes and W. W. Cooper et al.: A Brief History of a Long Collaboration in Developing Industrial Uses of Linear Programming

A Model for Programming and Sensitivity Analysis in an Integrated Oil Company

In this paper a dynamic, adaptive model, called DEMON,4 is interpreted in terms of a network. The latter is here employed to reduce the problem of selecting optimal decision procedures so that these can be interpreted in terms of a conditional sequential designation of links from such a network. More is involved, however, than is immediately apparent from the network possibilities only. Thus, in the DEMON applications to new product marketing—as discussed in the present paper—it is necessary to comprehend additional chance and deterministic constraints such as (1) payback, or breakeven, conditions that may be specified for fulfillment over a given time horizon, (2) minimum expected level of profits required and (3) study budget limits which should not be exceeded. By means of preemptions or over-rides, which also form a part of DEMON, however, it is possible to relate these additional constraints to the network as we also show by means of a development via ideas associated with the right inverse of an inc...

William W. Cooper

Papers

Choices and Uses of DEA Weights

Abraham Charnes and W. W. Cooper et al.: A Brief History of a Long Collaboration in Developing Industrial Uses of Linear Programming

A Model for Programming and Sensitivity Analysis in an Integrated Oil Company

Demon: Decision Mapping Via Optimum Go-No Networks—A Model for Marketing New Products

Fundamental theorems of nondominated solutions associated with cones in normed linear spaces