Modeling considerations in data envelopment analysis

Although data envelopment analysis, DEA, has been widely applied in a variety of areas, there are basic modeling issues that still need to be addressed. This thesis focuses on three important issues: (1) characterizing and mitigating the effects of noise, (2) examining the effects of integral inputs and outputs along with the development of models to incorporate integrality, and (3) relating model complexity to the number of decision making units, DMUs, that should be included in a DEA data set.; Chapter three focused on quantifying the effects of noise and presenting a method for reducing these effects. A variation of DEA for counteracting the noise effects called noise extended DEA was developed. This procedure was tested using an application drawn from baseball batting. Rather than relying on strictly simulated data sets, a hybrid approach was used that started with actual historical baseball batting statistics to create new data sets with multinomial noise. It was found that the noise extended DEA procedure was able to reduce mean bias and mean-squared-error in the majority of cases examined.; Chapter four developed variations of DEA that allow for inputs and outputs that are restricted to integers. DEA implicitly assumes continuous inputs and outputs. The new integral DEA models were based on explicitly defining a target in terms of inputs and outputs. The target input and output variables were then constrained to integer values. Examples illustrated the effects of including integral inputs and outputs. Since the integrality conditions make it more difficult to construct targets, it tends to yield higher DEA efficiency scores.; Chapter five explored the relationship between model size and the number of DMUs. It started with a section on the marginal effects on DEA of adding or deleting DMUs from a data set. The effects largely depend on the efficiency classification of the DMU that is added or deleted. Next, an empirical analysis was conducted on several very large data sets to determine how many DMUs were needed to obtain stable DEA evaluations. It was found that ranking generally required fewer DMUs than estimation of efficiency scores, particularly for more complex models.