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

Page cuts for integer interval linear programming

A new class of constrained stochastic network models is formulated in a manner that can be used to support a variety of analyses of optimal design modifications for special weapons systems under budgetary and other constraints. Alternative expressions in terms of geometric programming are also explored. These, however, are far more inconvenient to compute or manipulate especially as the model size increases. Component modifications to the B52G system are considered in a prototype example.

Optimal design modifications by geometric programming and constrained stochastic network models

Separably-infinite programs are a class of linear infinite programs that are related to semi-infinite programs and which have applications in economics and statistics. These programs have an infinite number of variables and an infinite number of constraints. However, only a finite number of variables appear in an infinite number of constraints, and only a finite number of constraints have an infinite number of variables. Duality in this class of programs is studied and used to develop a system of nonlinear equations satisfied by optimal solutions of the primal and dual programs. This nonlinear system has uses in numerical techniques for solving separably-infinite programs.

Separably-infinite programs

: Extensions of a 'multi-modal' goal-arc EEO model are discussed in the context of prototype studies to check-out the model structure and computational efficiencies using PNET and other computer codes. The model presented provides for the information assistance needed after one has EEO goals to develop the strategies involving trade-offs between internal vs. external recruitment. (Author)

/pdf/model-extension-and-computation-in-goal-arc-network-3hf5tnpv1s.pdf

Abraham Charnes

Papers

Page cuts for integer interval linear programming

Optimal design modifications by geometric programming and constrained stochastic network models

Separably-infinite programs

Model Extension and Computation in Goal-Arc Network Approaches for EEO Planning.

Successive linear programming for ratio goal problems