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

In this paper, we employ alternate techniques to examine whether passage of the Sarbanes-Oxley (SOX) Act has had positive effects on the efficiency of public accounting firms. These alternate techniques extend from use of the non-parametric, 'frontier'-oriented method of Data Envelopment Analysis (DEA), and include more traditional regression-based approaches using central tendency estimates. Using data from 58 of the 100 largest accounting firms in the USA, we find that efficiency increased at high levels of statistical significance and discover that this result is consistent for all of the different methods - frontier and central tendencies used in this paper. We also find that this result is not affected by inclusion or exclusion of the Big 4 firms. All results are found to be robust as well as consistent.

The Sarbanes-Oxley act and the production efficiency of public accounting firms in supplying accounting auditing and consulting services: an application of data envelopment analysis

This paper indicates how an information theoretic approach via the MDI minimum discrimination information statistic can be used to help provide a uniform approach to both statistical testing and estimation in various kinds of marketing analyses. Extensions to constrained versions of the MDI statistic also make it possible to test the consistency of market information with management plans or policies that can be represented in “external” constraints, i.e., constraints formulated without reference to the data base, and to estimate their impact on the market. Composite hypotheses, which are difficult to deal with by the more customary methods used in market research, can be dealt with naturally and easily via these MDI approaches. Basically MDI is more efficient than classical approaches because distribution estimation and hyopthesis testing are done simultaneously and the resulting estimates obtain regardless of the conclusion of the test. Numerical illustrations are supplied and discussed. Recent developments in mathematical programming duality theory and methods, which are also pertinent, are briefly examined for their bearing on still further possibilities for constrained MDI modeling.

/pdf/an-mdi-model-and-an-algorithm-for-composite-hypotheses-4empsmg8jg.pdf

An MDI Model and an Algorithm for Composite Hypotheses Testing and Estimation in Marketing

I. Introduction, 131. — II. Scope of the model, 132. — III. Mathematical statement of the model, 134. — IV. Profit maximization, 140. — V. Cost-quantity silhouettes, 145.

Silhouette Functions of Short-Run Cost Behavior

Congestion is a term that is applicable in a variety of disciplines which range from medical science to traffic engineering. It has also many uses in practical everyday life. This brings with it a certain looseness in usage. We therefore expand (and refine) our discussion of congestion with reference to its use in economics where we have access to a precise meaning which we can develop in this chapter. This chapter covers the standard approaches used for treating congestion in data envelopment analysis.

Congestion: Its Identification and Management with DEA

The existence of a solution to the problem of minimizing a convex function subject to restriction of the variables to a closed convex set in w-space (\"convex programming\") has been characterized (for suitable differentiability conditions) by the Kuhn-Tucker theorem [5]. In general, no dual programming problem (not involving the variables of the direct problem) has been associated with this situation except in the linear programming case, and very recently by E. Eisenberg in [3], for homogeneity of order one in the function and linear inequality constraints, and by R. J. Duffin [2] in an inverse manner for a highly specialized problem. Starting with a little known paper of A. Haar [4] in the light of current linear programming constructs (e.g., \"regularization\" [ l ] ) , we effect a generalization of these ideas (with maximal finite algebra and minimal topology) so that a dual theory practically as straightforward as linear programming theory is obtained, and which includes a dual theorem covering the most general convex programming situation (e.g. no differentiability conditions qualifying the convex function or constraints, or homogeneity, etc.). This general theorem is made possible by associating a suitably restricted, usually infinite-dimensional space problem with the minimization problem in w-space instead of the usual association of another finite w-space problem. The space we use is a \"generalized finite sequence space\" (g.f.s.s.), defined with respect to an index set / of arbitrary cardinality as the vector space, S> of all vectors X— [Xt: i G / ] over an ordered field F with only finitely many nonzero entries. Such spaces possess the following key characteristics for linear programming of ordinary w-spaces. Let F be a vector space over F and consider a collection of vectors: PQ, P*: i £ I in V. Let R be the subspace spanned by these vectors, and let

/pdf/a-duality-theory-for-convex-programs-with-convex-constraints-2k90af3q3x.pdf

William W. Cooper

Papers

The Sarbanes-Oxley act and the production efficiency of public accounting firms in supplying accounting auditing and consulting services: an application of data envelopment analysis

An MDI Model and an Algorithm for Composite Hypotheses Testing and Estimation in Marketing

Silhouette Functions of Short-Run Cost Behavior

Congestion: Its Identification and Management with DEA

A duality theory for convex programs with convex constraints