Gutiérrez, E., & Lozano, S. (2010). Data Envelopment Analysis of multiple response experiments. Applied Mathematical Modelling, 34(5), 1139–1148.
Abstract: Taguchi method is the usual strategy in robust design and involves conducting experiments using orthogonal arrays and estimating the combination of factor levels that optimizes a given performance measure, typically a signal-to-noise ratio. The problem is more complex in the case of multiple responses since the combinations of factor levels that optimize the different responses usually differ. In this paper, an Artificial Neural Network, trained with the experiments results, is used to estimate the responses for all factor level combinations. After that, Data Envelopment Analysis (DEA) is used first to select the efficient (i.e. non-dominated) factor level combinations and then for choosing among them the one which leads to a most robust quality loss penalization. Mean Square Deviations of the quality characteristics are used as DEA inputs. Among the advantages of the proposed approach over traditional Taguchi method are the non-parametric, non-linear way of estimating quality loss measures for unobserved factor combinations and the non-parametric character of the performance evaluation of all the factor combinations. The proposed approach is applied to a number of case studies from the literature and compared with existing approaches.
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Lozano, S., & Gutiérrez, E. (2008). Non-parametric frontier approach to modelling the relationships among population, GDP, energy consumption and CO2 emissions. Ecological Economics, 66(4), 687–699.
Abstract: In this paper, a non-parametric approach based in Data Envelopment Analysis (DEA) is proposed as an alternative to the Kaya identity (a.k.a ImPACT). This Frontier Method identifies and extends existing best practices. Population and GDP are considered as input and output, respectively. Both primary energy consumption and Greenhouse Gas (GHG) emissions are considered as undesirable outputs. Several Linear Programming models are formulated with different aims, namely: a) determine efficiency levels, b) estimate maximum GDP compatible with given levels of population, energy intensity and carbonization intensity, and c) estimate the minimum level of GHG emissions compatible with given levels of population, GDP, energy intensity or carbonization index. The United States of America case is used as illustration of the proposed approach.
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Lozano, S., & Gutiérrez, E. (2008). Data envelopment analysis of mutual funds based on second-order stochastic dominance. European Journal of Operational Research, 189(1), 230–244.
Abstract: Although data envelopment analysis (DEA) has been extensively used to assess the performance of mutual funds (MF), most of the approaches overestimate the risk associated to the endogenous benchmark portfolio. This is because in the conventional DEA technology the risk of the target portfolio is computed as a linear combination of the risk of the assessed MF. This neglects the important effects of portfolio diversification. Other approaches based on mean-variance or mean-variance-skewness are non-linear. We propose to combine DEA with stochastic dominance criteria. Thus, in this paper, six distinct DEA-like linear programming (LP) models are proposed for computing relative efficiency scores consistent (in the sense of necessity) with second-order stochastic dominance (SSD). The aim is that, being SSD efficient, the obtained target portfolio should be an optimal benchmark for any rational risk-averse investor. The proposed models are compared with several related approaches from the literature.
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