Chance-constrained data envelopment analysis

Data envelopment analysis (DEA) is extended to the case of stochastic inputs and outputs through the use of chance-constrained programming. The chance-constrained frontier envelops a given set of observations ‘most of the time’. As an empirical illustration, we re-examine the pioneering 1981 study of Program Follow Through by Charnes, Cooper and Rhodes.     

Performance measurement and best-practice benchmarking of mutual funds: combining stochastic dominance criteria with data envelopment analysis

We propose a method for mutual fund performance measurement and best-practice benchmarking, which endogenously identifies a dominating benchmark portfolio for each evaluated mutual fund. Dominating benchmarks provide information about efficiency improvement potential as well as portfolio strategies for achieving them. Portfolio diversification possibilities are accounts for by using Data Envelopment Analysis (DEA). Portfolio risk is accounted for in terms of the full return distribution by utilizing Stochastic Dominance (SD) criteria. The approach is illustrated by an application to US based environmentally responsible mutual funds.     

Efficiency aggregation with enhanced Russell measures in data envelopment analysis

In aggregation for data envelopment analysis (DEA), a jointly determined aggregate measure of output and input efficiency is desired that is consistent with the individual decision making unit measures. An impasse has been reached in the current state of the literature, however, where only separate measures of input and output efficiency have resulted from attempts to aggregate technical efficiency with the radial measure models commonly employed in DEA. The latter measures are “incomplete” in that they omit the non-zero input and output slacks, and thus fail to account for all inefficiencies that the model can identify. The Russell measure eliminates the latter deficiency but is difficult to solve in standard formulations. A new approach has become available, however, which utilizes a ratio measure in place of the standard formulations. Referred to as an enhanced Russell graph measure (ERM), the resulting model is in the form of a fractional program. Hence, it can be transformed into an ordinary linear programming structure that can generate an optimal solution for the corresponding ERM model. As shown in this paper, an aggregate ERM can then be formed with all the properties considered to be desirable in an aggregate measure—including jointly determined input and output efficiency measures that represent separate estimates of input and output efficiency. Much of this paper is concerned with technical efficiency in both individual and system-wide efficiency measures. Weighting systems are introduced that extend to efficiency-based measures of cost, revenue, and profit, as well as derivatives such as rates of return over cost. The penultimate section shows how the solution to one model also generates optimal solutions to models with other objectives that include rates of return over cost and total profit. This is accomplished in the form of efficiency-adjusted versions of these commonly used measures of performance.     

Detecting influential observations in data envelopment analysis

This paper provides diagnostic tools for examining the role of influential observations in Data Envelopment Analysis (DEA) applications. Observations may be prioritized for further scrutiny to see if they are contaminated by data errors; this prioritization is important in situations where data-checking is costly and resources are limited. Several empirical examples are provided using data from previously published studies.This research was performed while under contract with the Management Science Group, U.S. Department of Veterans Affairs, Bedford, MA 01730. Shawna Grosskopf and Richard Grabowski graciously provided data used in two of the empirical examples.     

Hypothesis tests using data envelopment analysis

A substantial body of recent work has opened the way to exploring the statistical properties of DEA estimators of production frontiers and related efficiency measures. The purpose of this paper is to survey several possibilities that have been pursued, and to present them in a unified framework. These include the development of statistics to test hypotheses about the characteristics of the production frontier, such as returns to scale, input substitutability, and model specification, and also about variation in efficiencies relative to the production frontier.     

Stability and integrity tests in data envelopment analysis

Studies that apply data envelopment analysis often neglect testing the stability of the efficient frontier to data perturbations, and, to a lesser extent, the ability of efficiency scores to correctly discriminate between units on performance (integrity). Our primary motivation is to demonstrate methods that can help reduce the number of managerial decisions based on results that may be unreliable. To this end, we illustrate multiple tests of stability and integrity in an environment of fully units-invariant efficiency measurement. This application of tests of stability and integrity using a slacks-based measure of efficiency is the first in a peer-reviewed journal.     

Weak congestion in output additive data envelopment analysis

Our earlier work [Wei QL, Yan H. Congestion and returns to scale in data envelopment analysis. European Journal of Operational Research 2004;153:641–60] discussed necessary and sufficient conditions for the existence of congestion together with aspects of returns to scale under an output-oriented DEA framework. In line with this work, the current paper investigates the issue of “weak congestion”, wherein congestion occurs when the reduction of selected inputs causes some, rather than all, outputs to increase, without a worsening of others. We define output efficiency for decision making units under a series of typical DEA output additive models. Based on this definition, we offer necessary and sufficient conditions for the existence of weak congestion. Numerical examples are provided for purposes of illustration.     

Technically and cost-efficient centralized allocations in data envelopment analysis

In data envelopment analysis and with a variable returns to scale production-technology, we apply Banker's [2] approach to determine the relationship between technically and cost-efficient industry structures, featuring reallocation of outputs and a variable number of firms. The interpretation based on the most productive and optimal scale-size notions allows us to both establish an inequality relationship between the corresponding industry-efficiency measures and provide adequate information on optimal solutions. At the applicative level, we introduce an exact algorithm to solve related non-linear programming problems, thus providing the decision maker with an accurate method for computing and comparing the input and output mixes and the optimal number of units obtained in the two allocations. Empirical illustration, given with reference to the Italian local-public-transit sector and employing a multiple inputs and outputs technology, reveals striking differences with regard to the managerial and regulatory implications of the two centralized allocations.     

Directional congestion in the framework of data envelopment analysis

This study first proposes a definition for directional congestion in certain input and output directions within the framework of data envelopment analysis. Second, two methods from different viewpoints are proposed to estimate the directional congestion. Third, we address the relationship between directional congestion and classic (strong or weak) congestion. Finally, we present a case study investigating the analysis performed by the research institutes of the Chinese Academy of Sciences to demonstrate the applicability and usefulness of the methods developed in this study.     

Extending the zero-sum gains data envelopment analysis model

Journal of Productivity Analysis - In this paper, we adapt the ZSG-DEA model to the case of a reverse output, whose larger (smaller) values reflect lower (higher) achievements. Then, we introduce...     

A data envelopment analysis of gas utilities' efficiency

This study examines the Natural Gas Policy Act of 1978 and Federal Energy Regulatory Commission (FERC) policies that culminated in Order 636 in 1992. The regulatory environment in which natural gas distribution utilities operate was altered. FERC policies forced local gas distribution utilities into an increasingly competitive environment. Restructuring of the industry may affect economic efficiency. Data Envelopment Analysis is used to examine the economic efficiency of gas distributors during 1975–94. Federal policy appears to lead to a reduction in scale due to restructuring and more competition. Reduced scale economies have not altered the economic efficiency of the utilities.     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.     

A new method for measuring congestion in data envelopment analysis

In data envelopment analysis (DEA), there are two principal methods for identifying and measuring congestion: Those of Färe et al. [Färe R, Grosskopf S. When can slacks be used to identify congestion. An answer to W. W. Cooper, L. Seiford, J. Zhu. Socio-Economic Planning Sciences 2001;35:1–10] and Cooper et al. [Cooper WW, Deng H, Huang ZM, Li SX. A one-model approach to congestion in data envelopment analysis. Socio-Economic Planning Sciences 2002;36:231–8]. In the present paper, we focus on the latter work in proposing a new method that requires considerably less computation. Then, by proving a selected theorem, we show that our proposed methodology is indeed equivalent to that of Cooper et al.     

Improving discrimination in data envelopment analysis: some practical suggestions

In some contexts data envelopment analysis (DEA) gives poor discrimination on the performance of units. While this may reflect genuine uniformity of performance between units, it may also reflect lack of sufficient observations or other factors limiting discrimination on performance between units. In this paper, we present an overview of the main approaches that can be used to improve the discrimination of DEA. This includes simple methods such as the aggregation of inputs or outputs, the use of longitudinal data, more advanced methods such as the use of weight restrictions, production trade-offs and unobserved units, and a relatively new method based on the use of selective proportionality between the inputs and outputs.     

Management of nursing homes using data envelopment analysis.

Data envelopment analysis (DEA) is used to evaluate the relative technical efficiency and assist in the management of a chain of nursing homes. As with any DEA model, variables chosen are particularly important. The study looks at two possibly critical issues. The first is the appropriateness of models that include only financial and economic measures to evaluate administrators when quality care is an expected output. The second issue is the appropriateness of using noncontrollable variables, in this case operating income, to evaluate administrators. We show how efficiency scores differ when quality variables and/or operating income are included. We also demonstrate the usefulness of DEA information to both the home administrator and chain managers for improving operating efficiency.     

Inverse data envelopment analysis without convexity: double frontiers

Decisions in Economics and Finance - In this research, inverse data envelopment analysis (IDEA) approaches are proposed to measure inputs changes for output perturbations made while the convexity...     

Distance optimization approach to ratio-form efficiency measures in data envelopment analysis

This paper examines the development pattern of the DEA (Data Envelopment Analysis) research field using Social Network Analysis. Nine stylized facts are verified: it is shown that the distribution of research performance is highly skewed, satisfying a power law, and that collaborative research activity is concentrated achieving higher performance. Moreover, economics and OR (operations research)/MS (management science) groups developed without collaboration until the 1980s; however, the merger of the two groups began in 1994 with the collaboration of frontier researchers. Now the two groups have merged significantly, but they are still identifiable. Finally, research hubs and the emergence of new groups are examined. Nine stylized facts show that DEA has developed with unique attributes. Although it shares common characteristics with other academic fields, including a highly skewed distribution of publications and expansion of the network over time, the DEA field has had a pattern of development that is different from those of other academic fields. Independent development and interrelated evolution between economics and OR/MS contributed to the exchange of knowledge of these two separate fields.     

Data envelopment analysis and Malmquist indices for measuring group performance

This paper develops measures, based on the Malmquist index, that enable the decision making units’ internal inefficiencies to be distinguished from those associated with their group (or program) characteristics. The applicability of these measures is illustrated with the assessment of bank branches’ performance. The analysis involves the construction of an index reflecting the relative performance of branches in four different regions, which can be decomposed into an index for the comparison of within-group efficiency spread, evaluating internal managerial efficiencies, and an index for the comparison of frontier productivity, reflecting the impact of environmental factors and regional managerial policies on branches’ productivity.     

Performance evaluation using data envelopment analysis in the presence of time lags

Data Envelopment Analysis (DEA) is a methodology that computes efficiency values for decision making units (DMU) in a given period by comparing the outputs with the inputs. In many applications, inputs and outputs of DMUs are monitored over time. There might be a time lag between the consumption of inputs and the production of outputs. We develop an approach that aims to capture the time lag between the outputs and the inputs in assigning the efficiency values to DMUs. We propose using weight restrictions in conjunction with the model. Our computational results on randomly generated problems demonstrate that the developed approach works well under a large variety of experimental conditions. We also apply our approach on a real data set to evaluate research institutions.     

Some extensions of techniques to handle non-discretionary factors in data envelopment analysis

Data Envelopment Analysis (DEA) assumes, in most cases, that all inputs and outputs are controlled by the Decision Making Unit (DMU). Inputs and/or outputs that do not conform to this assumption are denoted in DEA asnon-discretionary (ND) factors. Banker and Morey [1986] formulated several variants of DEA models which incorporated ND with ordinary factors. This article extends the Banker and Morey approach for treating nondiscretionary factors in two ways. First, the model is extended to allow for thesimultaneous presence of ND factors in both the input and the output sets. Second, a generalization is offered which, for the first time, enables a quantitative evaluation ofpartially controlled factors. A numerical example is given to illustrate the different models.The editor for this paper was Wade D. Cook.