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

/pdf/a-computational-method-for-solving-dea-problems-with-3oy6pzfjcs.pdf

A COMPUTATIONAL METHOD FOR SOLVING DEA PROBLEMS WITH INFINITELY MANY DMUs

: Data Envelopment Analysis (DEA) began in generalization of the usual scientific-engineering efficiency valuation of a single input, single output system as the ratio of the output input (in the same physical measure, e.g., energy) to multi-input, multi-output systems (or organizations or production units) without known physical laws or the same measure for all inputs and outputs. This was accomplished by (i) reduction of the multi-inputs and outputs to single virtual inputs and outputs, (ii) replacing absolute efficiency by efficiency relative to all members of a sample of units (called DMU's) having the same inputs and outputs, (iii) evaluating a unit's relative efficiency as the maximum of the ratio of its virtual output to virtual input subject to virtual outputs being less than or equal to virtual inputs for each (all) of the DMU's. The origin, history, current status and problems of Data Envelopment Analysis (DEA) on empirical multi-input, multi-output data are surveyed in relation to efficiency valuation, production function determination and stochastic frontier estimation.

Data Environment Analysis

M. Kress proved for a special case of Location-Scale probability distributions there always exists a probability level for which the Chance Constrained Critical Path (CCCP) remains unchanged for all probabilities greater than or equal to that value. His chance constrained problem has zero-order decision rules and individual chance constraints. This paper extends his results to most of the common probability distributions.

Almost sure critical paths

In this note we use the concept of intersection cut, introduced by Balas for integer programming problems, to develop a cutting-plane algorithm for solving integer interval linear programming problems. The idea is to apply the cutting-plane algorithm directly on the interval problem without transforming the problem into an equivalent standard integer problem. Such a transformation would significantly increase the effective size of the problem.

Technical Note-On Intersection Cuts in Interval Integer Linear Programming

: Error bounds are developed for a class of quadratic programming problems. The absolute error between an approximate feasible solution, generated via a dual formulation, and the true optimal solution is measured. Furthermore, these error bounds involve considerably less work computationally than existing estimates.

Abraham Charnes

Papers

A COMPUTATIONAL METHOD FOR SOLVING DEA PROBLEMS WITH INFINITELY MANY DMUs

Data Environment Analysis

Almost sure critical paths

Technical Note-On Intersection Cuts in Interval Integer Linear Programming

Practical error bounds for a class of quadratic programming problems