Data envelopment analysis: a taxonomy, a meta review and an extension (confident-dea) with application to predicting cross (OECD) country banking systems' efficiency
Gattoufi, Said (2002) Data envelopment analysis: a taxonomy, a meta review and an extension (confident-dea) with application to predicting cross (OECD) country banking systems' efficiency. [Thesis]
This work contributes to the Data Envelopment Analysis (DEA) literature at three ways. First, it extends the roots of DEA by providing an analytical approach deriving the basic Charties-Cooper-Rhodes (1978) model from the Weak Axiom of Profit Maximization (WAPM) of Finn Theory. This in turn, develops the Approximate-Weak Axiom of Profit Maximization (A-WAPM). Additional;/, a direct connection is established between the sensitivity of DEA provided results to sample size and the A-WAPhL Second, this work provides a systematic way for classifying the existing DLL A literature by offering a taxonomy. The contents of 989 post-1995 DEA articles in refereed journals are reviewed using a scheme developed by Re is man (1988 and 1992). This scheme analyzes the literature based on the nature of the articles (Theoretica!, Application or both e.g. an advance in theory associated with a real world application) and on the basis of the research strategy used by the respective authors. Results of this classification arc analyzed from an episteino logical point of view. Finally, a theoretical contribution to the literature, Confident-DEA approach, is proposed involving a biievel convex optimization model, and hence NP-Hard, to which a solution method is suggested. Confident-DEA constitutes a generalization of DEA for dealing with imprecise data and hence allows prediction. Complementing the methodology proposed by Cooper et al (1999) which provides single valued efficiency measures, Confident-DEA provides a range of values for the efficiency measures, e.g an efficiency confidence interval, reflecting the imprecision in data. For the case of bounded data, a theorem delining the bounds of the efficiency confidence interval is provided. For the general case of imprecise data, a Genetic-Algorithm-based metahenristic is used to determine the upper and lower bounds defining the efficiency confidence interval. In both c;ises, a Monte-Carlo type simulation is used to determine the distribution of the efficiency measures, taking into account the distribution of the bounded imprecise data over their corresponding intervals. Previous DEA work dealing with imprecise data implicitly assumed o uniform distribution. Confident-DEA, on the other hand, allows for any type of distribution and hence expands the scope of the analysis. The bounded data used in iEluslmivc examples arc assumed to have a truncated normal distribution. Jn partial reaction to the anemia in relevance to the real world, characterising a targe segment of recent OR/MS literature, Confldent-DEA is applied to predict the efficiency of banking systems id OECD countries.
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