6,705 research outputs found

    Uncertain Data Envelopment Analysis

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    Data Envelopment Analysis (DEA) is a nonparametric, data driven method to conduct relative performance measurements among a set of decision making units (DMUs). Efficiency scores are computed based on assessing input and output data for each DMU by means of linear programming. Traditionally, these data are assumed to be known precisely. We instead consider the situation in which data is uncertain, and in this case, we demonstrate that efficiency scores increase monotonically with uncertainty. This enables inefficient DMUs to leverage uncertainty to counter their assessment of being inefficient. Using the framework of robust optimization, we propose an uncertain DEA (uDEA) model for which an optimal solution determines 1) the maximum possible efficiency score of a DMU over all permissible uncertainties, and 2) the minimal amount of uncertainty that is required to achieve this efficiency score. We show that the uDEA model is a proper generalization of traditional DEA and provide a first-order algorithm to solve the uDEA model with ellipsoidal uncertainty sets. Finally, we present a case study applying uDEA to the problem of deciding efficiency of radiotherapy treatments

    Comparing Voting Districts with Uncertain Data Envelopment Analysis

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    Gerrymandering voting districts is one of the most salient concerns of contemporary American society, and the creation of new voting maps, along with their subsequent legal challenges, speaks for much of our modern political discourse. The legal, societal, and political debate over serviceable voting districts demands a concept of fairness, which is a loosely characterized, but amorphous, concept that has evaded precise definition. We advance a new paradigm to compare voting maps that avoids the pitfalls associated with an a priori metric being used to uniformly assess maps. Our evaluative method instead shows how to use uncertain data envelopment analysis to assess maps on a variety of metrics, a tactic that permits each district to be assessed separately and optimally. We test our methodology on a collection of proposed and publicly available maps to illustrate our assessment strategy.Comment: 24 pages, 2 figure

    Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach

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    This article integrates fuzzy set theory in Data Envelopment Analysis (DEA) framework to compute technical efficiency scores when input and output data are imprecise. The underlying assumption in convectional DEA is that inputs and outputs data are measured with precision. However, production agriculture takes place in an uncertain environment and, in some situations, input and output data may be imprecise. We present an approach of measuring efficiency when data is known to lie within specified intervals and empirically illustrate this approach using a group of 34 dairy producers in Pennsylvania. Compared to the convectional DEA scores that are point estimates, the computed fuzzy efficiency scores allow the decision maker to trace the performance of a decision-making unit at different possibility levels.fuzzy set theory, Data Envelopment Analysis, membership function, α-cut level, technical efficiency, Farm Management, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, Risk and Uncertainty, D24, Q12, C02, C44, C61,

    Fuzziness in Performance Evaluation Problems Using Data Envelopment Analysis

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    Efficiency evaluation is an important part of decision making in many areas particularly in management and manufacturing sectors. Uncertainty and fuzziness of the real world problems have increased utilization of fuzzy sets theory in many research areas and data envelopment analysis is one of them. Utilizing data envelopment analysis to evaluate efficiency scores of decision making units in fuzzy environment requires fuzzy models and mathematical methods for solving fuzzy models with minimum calculation and maximum precision. Since current fuzzy data envelopment analysis models are not able to solve some problems in fuzzy environment, our attempt is to provide fuzzy data envelopment analysis models related to following various problems. Some problems include uncontrollable data (for manager) that regularly have fuzzy essence. An uncontrollable fuzzy data envelopment analysis model is represented for these types of problems. The advantages of the proposed model are in capability of it in including uncontrollable factors particularly those with fuzzy nature in problems with fuzzy data and controlling factor weights by additional constraints which can avoid the model to become infeasibility. The disadvantage of the method is in using too many restrictions (one restriction for each fuzzy data) which makes the model complicated and expensive to solve. For cases that interval efficiency scores are helpful, a method for solving fuzzy data envelopment analysis models is represented which interval efficiency scores can be achieved without adding restrictions to the model for each fuzzy data. In comparison with other methods, this method is simple, easy and with no additional constraint for each fuzzy data. In addition a fuzzy weights data envelopment analysis model is proposed to determine effect of data on the efficiency score. The model is informative in problems that the manager needs to know about uncertain effects of factors on efficiency score. The method of solving the model is simple and informative. By suggesting categorical data envelopment analysis method for problems with uncertain membership in various categories, we can help the decision maker to recognize the efficient decision making units fairly. In comparison with available method for categorical problems, our method is more informative and the traditional categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues. categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues

    Creating Composite Indicators with DEA and Robustness Analysis: the case of the Technology Achievement Index

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    Composite indicators are regularly used for benchmarking countries’ performance, but equally often stir controversies about the unavoidable subjectivity that is connected with their construction. Data Envelopment Analysis helps to overcome some key limitations, viz., the undesirable dependence of final results from the preliminary normalization of sub-indicators, and, more cogently, from the subjective nature of the weights used for aggregating. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries’ composite indicator values and relative rankings. Uncertainty and sensitivity analysis are therefore needed to assess robustness of final results and to analyze how much each individual source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration.factor is more important in explaining the observed progress.composite indicators, aggregation, weighting, Internal Market

    Creating composite indicators with DEA and robustness analysis: The case of the technology achievement index.

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    Composite indicators are regularly used for benchmarking countries’ performance, but equally often stir controversies about the unavoidable subjectivity that is connected with their construction. Data Envelopment Analysis helps to overcome some key limitations, viz., the undesirable dependence of final results from the preliminary normalization of sub-indicators, and, more cogently, from the subjective nature of the weights used for aggregating. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries’ composite indicator values and relative rankings. Uncertainty and sensitivity analysis are therefore needed to assess robustness of final results and to analyze how much each individual source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration.Indexes; Indicators; Robustness; Technology;
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