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Dual frontiers data envelopment analysis: multiple ranking approaches from optimistic and pessimistic perspectives

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking.

This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic
DEA models without convexity are developed from both input and output orientation.

Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic
and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.