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We discuss four frequently overlapping developments in the brief history of efficiency analysis. The developments involve modes of invention, graduate students, international travel, and influential but under-appreciated scholars. We suggest lessons to be learned from each. [ABSTRACT FROM AUTHOR]

We here critique the articles by Dmitruk & Koshevoy (1991, J Econ Theory 55:121–144) and by Bol (1986, J Econ Theory 38:380–385) by showing how to solve the examples they erected to show the non-existence of functions for evaluating performance efficiencies in DEA. We also show that functions satisfying these criteria—and other important criteria as well—were already available prior to the publications of D&K and by Bol and have since been greatly extended to increase the power and scope of DEA. [ABSTRACT FROM AUTHOR]

This paper surveys recently developed analytical methods for studying the sensitivity of DEA results to variations in the data. The focus is on the stability of classification of DMUs (Decision Making Units) into efficient and inefficient performers. Early work on this topic concentrated on developing solution methods and algorithms for conducting such analyses after it was noted that standard approaches for conducting sensitivity analyses in linear programming could not be used in DEA. However, some of the recent work we cover has bypassed the need for such algorithms. Evolving from early work that was confined to studying data variations in only one input or output for only one DMU at a time, the newer methods described in this paper make it possible to determine ranges within which all data may be varied for any DMU before a reclassification from efficient to inefficient status (or vice versa) occurs. Other coverage involves recent extensions which include methods for determining ranges of data variation that can be allowed when all data are varied simultaneously for all DMUs. An initial section delimits the topics to be covered. A final section suggests topics for further research. [ABSTRACT FROM AUTHOR]

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attaimnent of efficiency-as in standard versions of additive models. [ABSTRACT FROM AUTHOR]

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated to managed entities called DM Us (Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which arc usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient. [ABSTRACT FROM AUTHOR]

DEA (Data Envelopment Analysis) models and concepts are formulated here in terms of the ‘P-Models’ of Chance Constrained Programming, which are then modified to contact the ‘satisficing concepts’ of H.A. Simon. Satisficing is thereby added as a third category to the efficiency/inefficiency dichotomies that have heretofore prevailed in DEA. Formulations include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. Attention is also devoted to situations in which variations in inputs and outputs are related through a common random variable. Extensions include new developments in goal programming with deterministic equivalents for the corresponding satisficing models under chance constraints. [ABSTRACT FROM AUTHOR]

Using statistically designed experiments, 12,500 observations are generated from a ‘4-pieced Cobb­Douglas function’ exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes of n = 50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at ‘comer points’), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances—which suggests that COLS may have previously unidentified robustness properties—while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted. [ABSTRACT FROM AUTHOR]

The extensions, new developments and new interpretations for DEA covered in this paper include: (1) new measures of efficiency, (2) new models and (3) new ways of implementing established models with new results and interpretations presented that include treatments of ‘congestion’, ‘returns-to-scale’ and ‘mix’ and ‘technical’ inefficiencies and measures of efficiency that can be used to reflect all pertinent properties. Previously used models, such as those used to identify ‘allocative inefficiencies’, are extended by means of ‘assurance region’ approaches which are less demanding in their information requirements and underlying assumptions. New opportunities for research are identified in each section of this chapter. Sources of further developments and possible sources for further help are also suggested with references supplied to other papers that appear in this volume and which are summarily described in this introductory chapter. [ABSTRACT FROM AUTHOR]

This article presents a study which examined sensitivity and stability analysis in data envelopment analysis. Sensitivity analyses is regarded as a mathematical programming counterpart of significance testing in statistics since each is concerned with examining allowable ranges of variation in the data.

This article presents a study which examined data envelopment analysis and regression approaches as methods for efficiency estimation and evaluation. Example alternatives that will be examined are ratio analyses and statistical regressions. The study concluded that ratio analysis, the most commonly used approach to efficiency evaluation, is the worst performer.

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. [ABSTRACT FROM AUTHOR]

Systems approaches possess an ability to deal with large numbers of interacting variables and relations. They are here connected to citizen information systems (distinguished from management information systems) and to mixed, adaptive, conditional models for urban planning. The latter permit flexible and continuing responses to dynamically changing urban conditions, including citizen attitudes and reactions, as well as to changing economics and technologies. These models are "mixed" in that they allow actions and reactions from a multiplicity of decisionmakers. The resulting decisions are made only conditionally, rather than once-and-for-all, on a comprehensive basis as in the customary "master city plan." Proceeding in this conditional manner, the model then permits adaptation to changing values and objectives as, at each stage, it makes the systems consequences apparent. The systems approach is related to a host of important methodological developments in mathematics, statistics, etc., as well as in electronic computers and their use. These distinguish modern systems approaches from predecessors like the "holism" of Jan Christiaan Smuts and others in pre-war science. The mixed, conditional, adaptive models suggested here are compared with other approaches like "advocacy planning," the "comprehensive master city plan" and "ad hoc planning." It is found to be possible at least in principle, to accommodate all of these and even to extend matters further to include day-to-day as well as longer range facilities plans in the indicated systems approach by virtue of the improved methodologies that may now be used or developed for these purposes. [ABSTRACT FROM AUTHOR]

Presents an introduction to papers related to efficiency measurement that appear in the 2000 issue of the "Journal of Productivity Analysis."