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

Funding of research projects is considered as encompassing three stages: 1 an initial short run plan for funding based upon projected regular demands and availability subject to random deviations; 2 adjustment of the initial plan to take into account the actual regular demands and availability and the funding of significant break-throughs which occur at random intervals preempting other demands; and 3 a plan for longer-run availability and demands which constitute a “posture” desired subsequent to the funding adjustments of 2. The essence of the distribution of the unexpected demands is multi-modality with low probability of occurrence but high resource demand when they do occur. This approach represents a substantial departure from the usual planning model development which produces only an optimal plan based on forecasted developments without provision for adjustment when the forecasted events actually materialize and additional unexpected demands are placed on resources. The adjustment process explored here---which provides the mechanism for optimal implementation of the original plan or control of resource allocation-enables optimal response to information received in “real-time” avoiding the frequently observed over-or under-response to receipt of such information without reference to the impact of the interim decision on future capabilities.

A Chance-Constrained Model for Real-Time Control in Research and Development Management

/pdf/duality-and-asymptotic-solvability-over-cones-2cd2n7i6r1.pdf

Duality and asymptotic solvability over cones

A measure of efficiency for not-for-profit entities - developed by the authors in association with Edward Rhodes - is explained and illustrated by data from Program Follow Through, a large scale social experiment in U.S. public school education. A division into Follow Through and Non-Follow Through participants facilitates a distinction between “program efficiency” and “managerial efficiency” which is also illustrated and examined for its use in evaluating such programs. Relations to comprehensive audits and other possible uses are explored.

Auditing and accounting for program efficiency and management efficiency in not-for-profit entities

The assignment model of linear programming is here extended to allow for vector optimizations and dynamic interactions between assigned personnel and positions in each of which a variety of possible measures and approaches are explored. Formulations involving people-to-people as well as people-to-position matchings are also examined from the standpoint of organizations in which jobs may be fitted to people or vice versa as well as in weighted combinations. Possible uses of such models for dealing with the problems of placing disadvantsged or handicapped persons are noted, but the analysis stops short of the still further possibilities offered by new types of machine-technology and information systems designs.

Static and Dynamic Assignment Models with Multiple Objectives, and Some Remarks on Organization Design

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations.



We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.

Abraham Charnes

Papers

A Chance-Constrained Model for Real-Time Control in Research and Development Management

Duality and asymptotic solvability over cones

Auditing and accounting for program efficiency and management efficiency in not-for-profit entities

Static and Dynamic Assignment Models with Multiple Objectives, and Some Remarks on Organization Design

On the theory of semi‐infinite programming and a generalization of the kuhn‐tucker saddle point theorem for arbitrary convex functions