Showing papers by "William W. Cooper published in 1984"

Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

Abstract: 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."

A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. air forces

Abstract: : There are four basic questions related to efficiency and capability which are of particular interest to officials in the military services who are interested in better ways of evaluating military capability and efficiency: (1) What level of military capability can the services achieve with available resources? (2) What capability is required, and where are the shortfalls? (3) What resource acquisitions or redistributions are needed to achieve maximum improvement in efficiency and effectiveness? and (4) How can management systems be changed to improve the identification and correction of factors which limit the readiness and efficiency of our military operations? The last question, which differs in its emphasis from the other three, provides an opening to the topics that will be addressed in this report. In particular, reported are results from a study of DEA (Data Envelopment Analysis) as a method for evaluating the efficiency of Air Force Wings--or, more precisely, their maintenance operations--as elements in Numbered Units in the U.S. Air Force.

Preface to topics in data envelopment analysis

Abstract: This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.

Sensitivity and stability analysis in dea

Abstract: : Sensitivity analyses may be regarded as a mathematical programming counterpart of significance testing in statistics since each is concerned with examining allowable ranges of variation in the data. In statistical analysis, this may take the form of examining ranges of possible chi sq values obtained from the data relative to a fitted function from and hypothesized class of statistical distributions. In linear programming, it may take the form of ascertaining ranges within which data may be varied without requiring a change in the set of vectors that constitute an optimum basis. Additional keywords: Reprints.

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

Abstract: 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.