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Polyhedral attributes of production possibility sets in data envelopment analysis, with applications to sensitivity analysis and cross-evaluation methodologies.

Argyris, Nikolaos (2007) Polyhedral attributes of production possibility sets in data envelopment analysis, with applications to sensitivity analysis and cross-evaluation methodologies. PhD thesis, London School of Economics and Political Science (United Kingdom).

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Abstract

In this thesis we study some critical problems in the area of Data Envelopment Analysis (DEA) within the unifying framework of polyhedral characteristics of the production possibility sets and efficiency frontiers of important DEA models. Recent developments in DEA have made it possible to identify the efficient frontier explicitly. This thesis builds on these developments to make the following contributions. We establish theoretical results on the efficiency classifications of surfaces of the boundaries of the production possibility sets. These systematise existing research in the field and fill in many gaps. Our main results provide necessary and sufficient conditions for characterising fully-dimensional efficient surfaces. In addition, the new theoretical framework leads us to discover and address inconsistencies in the related literature. Next we study the sensitivity of efficiency classifications of Decision Making Units (DMUs) to data perturbations. In contrast to existing approaches, we study the effects of arbitrary data perturbations on the efficiency classifications of all DMUs. Theoretical constructs based on the polyhedral nature of production possibility sets lead to identifying a Conditional Stability Region for each DMU within which its data can be perturbed without affecting the efficiency classification of any other DMU. Finally, we develop a new methodology for cross-evaluation in DEA which replaces the traditional approach of peer evaluation by evaluating DMUs across all possible weights obtained from our explicit identification of the DEA production possibility set. The new approach eliminates some major flaws and weaknesses of the traditional approach and produces more meaningful results. Moreover, a set of extensions to the new approach lead to tools that allow identification of DMUs with unrealistic efficiency scores as well as the identification of under-achieving DMUs, a concept that is introduced here.

Item Type: Thesis (PhD)
Uncontrolled Keywords: Operations Research
Sets: Collections > ProQuest Etheses
Departments > Management
URI: http://etheses.lse.ac.uk/id/eprint/2714

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