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

Management Models and Industrial Applications of Linear Programming

In memoriam Russell G. Thompson

As is true with the application of any analytical approach to the “art of reckoning” (Eilon, 1984), the use of data envelopment analysis (DEA) requires knowledge about formulation of models, choice of variables, underlying assumptions, data representation, interpretation of results, and knowledge of limitations. In this chapter, we discuss the process of conducting DEA studies and various uses such as exploratory data analysis, implementation of DEA solutions, and recent model formulations, as well as caveats in applying the method. It should be noted that this chapter represents the accumulated experience of many DEA practitioners and researchers in applying DEA. It represents another concrete example of how the practice of DEA not only shaped the evolution of theoretical and model development but also informed the process and understanding of DEA analysis.

The DEA Process, Usages, and Interpretations

This paper shows that the Lagrange multiplier method suggested by H. Everett does not have "Fail-Safe" properties when applied to simple situations with nonconvexity only in the functional. Although each Lagrange multiplier problem for these situations has immediate solutions no means of combining them to obtain a solution to any reasonable approximation appears to be visible.

Letter to the Editor-A Note on the Fail-Safe Properties of the Generalized Lagrange Multiplier Method

To help resolve a long-standing debate in the US Government on advertising strategies for military recruitment, this study applies ordinary least squares (OLS), which here includes (1) stochastic frontier analysis (SFA) and (2) frontierized least squares (FLS), to evaluate two distinct advertising strategies: Service Specific vs. Joint. Thus, in contrast to the customary use of a single central tendency method, such as OLS, on different models, we here use multiple methods on a single model to cross check and validate results. In addition to serving as cross checks, the methods can be used to identify classic problems, including biases in the data and shortcomings in one or more of the methodologies employed. To avoid dealing with problems on identifying motives underlying various patterns in advertising expenditure, data are drawn from a statistically designed experiment where the expenditures were controlled as part of the experiment to resolve the issue of a choice between the two advertising strategies of interest. In contrast to earlier studies, the current paper finds that all methods used lead to the same conclusion: Service Specific is more efficient than Joint, at least for the US Army—which is, by far, the largest military advertiser. Finally, the paper introduces a new method for reallocating advertising budgets between the Uniformed Services which (a) is simpler than the customary use of cross partial derivatives, (b) avoids the need for the ceteris paribus assumptions for each such allocation, as in customary reallocation methods and (c) simplifies matters so that, for instance, it is not necessary to introduce an entirely new organization to administer the desired coordinating activities.

William W. Cooper

Papers

Management Models and Industrial Applications of Linear Programming

In memoriam Russell G. Thompson

The DEA Process, Usages, and Interpretations

Letter to the Editor-A Note on the Fail-Safe Properties of the Generalized Lagrange Multiplier Method

Estimating elasticities with frontier and other regressions in evaluating two advertising strategies for US Army recruiting