• Data envelopment analysis
• data uncertainty
• efficiency measures.
• environmental regulation
• undesirable output

Starting from the pioneering papers by Charnes, Cooper and Rhodes (CCR model) and Banker, Charnes and Cooper (BCC model), a large number of papers concerning Data Envelopment Analysis (DEA) with outputs uncertainty appeared in the literature. In particular, chance-constrained programming is the most used technique to include noise variations in data and to solve data envelopment analysis problems with uncertainty in data. Chance-constrained programming admits random data variations and permits constraint violations up to specified probability limits, allowing linear deterministic equivalent formulations in case a normal distribution of the data uncertainty is assumed.
The standard DEA models rely on the assumption that inputs are minimized and outputs are maximized. However, both desirable and undesirable (e.g., pollutants or wastes) output factors may be present. The undesirable and desirable outputs should be treated differently when we evaluate the production performance: if inefficiency exists in the production, the undesirable pollutants should be reduced to improve efficiency. In order to include undesirable factors in DEA models, according to the literature, two different approaches can be used to model undesirable factors: one group of DEA models treats them as inputs, whereas a second group considers them as undesirable outputs. DEA models with undesirable factors are particularly suitable for models where several production inputs and desirable and undesirable outputs are taken into account, in order to provide an eco-efficiency measure.
In this Ph.D thesis alternative DEA models, which consider both uncertain and undesirable outputs, are proposed and studied. In particular, in the first part of this thesis two different models with uncertain outputs and deterministic inputs are proposed with the aim to move away the classical chance-constrained method and to obtain a more accurate DMU ranking whatever situation occurs. Specifically speaking, the proposed models remove the hypothesis of normal data distribution and use a scenario generation approach to include data perturbations.
For the sake of completeness, these models are compared with two further ones based on an expected value approach, where uncertainty is managed by means of the expected values of random factors both in the objective function and in the constraints. Deeply speaking, the main difference between the two proposed models and the expected value approaches lies in their mathematical formulation. In the new models, based on the scenario generation approach, the constraints concerning efficiency level are expressed for each scenario. On the other hand, in the expected value models the constraints are satisfied in expected value. As a consequence, the models proposed in the thesis result to be more selective in finding a ranking of efficiency, thus becoming useful strategic management tools aimed to determine a restrictive efficiency score ranking.
In the second part of this study, we focus on environmental policy and eco-efficiency. Nowadays, one of the most intensively discussed concepts in the international political debate is, in fact, the concept of sustainability and the need for eco-efficient solutions that enable the production of goods and services with less energy and resources and with less waste and emissions (eco-efficiency). In particular, we consider the environmental impact of CO2 in cement and clinker production processes. Cement industry is, in fact, responsible for approximately 5% of the current worldwide CO2 emissions. DEA models can provide an appropriate methodological approach for developing eco-efficiency indicators.
A cross-country comparison of the eco-efficiency level of the worldwide cement industry is presented by applying both a data envelopment analysis and a directional distance function approach. These tools result to be particularly suitable for models where several production inputs and desirable and undesirable outputs are taken into account. Strong and weak disposability assumptions are analyzed in order to evaluate the impact of environmental regulations interpreted as the cost of regulation. The few papers appeared in the literature of eco-efficiency in cement production analyze the emission performance trends only from an interstate point of view. In this thesis a worldwide study has been carried on, covering 90% of the world's cement production by means of 21 countries, European (EU) and non-European (non-EU) ones. The obtained results show that the efficiency level mainly depends on decisions to invest in alternative raw materials and alternative fuels, both in the case of regulated countries and in the case of voluntary emission-trading schemes. This study highlights, both at national and international levels, the possibility of reducing CO2 emissions and expanding cement production. The use of alternative raw materials, alternative fuels and the possibility of producing blended cements, which require less energy consumption and reduce pollutant emissions, seem to be appropriate means. Environmental regulations can provide incentives in terms of tax exemption benefits or more restrictive pollutant limits.
Finally, we try to answer to the following questions: do undesirable factors modify the efficiency levels of cement industry? Is it reasonable to omit CO2 emissions in evaluating the performances of the cement sector in different countries? In order to answer to these questions, alternative formulations of standard data envelopment analysis model and directional distance function are compared both in presence and in absence of undesirable factors. This analysis shows that the presence of undesirable factors greatly affects efficiency levels. Efficiency levels are influenced by investments in best available technologies and by the utilization of alternative fuels and raw materials in cement and clinker production processes.
The original results of this Ph.D. thesis have been collected in the following research papers:
• Riccardi R. and R. Toninelli. Data Envelopment Analysis with outputs uncertainty. Journal of Information & Optimization Sciences, to appear.
• Riccardi R., Oggioni G. and R. Toninelli. The cement industry: eco-efficiency country comparison using Data Envelopment Analysis. Journal of Statistics & Management Systems, accepted for publication.
• Riccardi R., Oggioni G. and R. Toninelli. Eco-efficiency of the world cement industry: A Data Envelopment Analysis. Energy Policy, Vol. 39, Issue 5, p. 2842-2854, 2011, available online at: http://dx.doi.org/10.1016/j.enpol.2011.02.057
• Riccardi R., Oggioni G. and R. Toninelli. Evaluating the efficiency of the cement sector in presence of undesirable output: a world based Data Envelopment Analysis. Technical Report n. 344, Department of Statistics and Applied Mathematics, University of Pisa, 2011, submitted to Resource and Energy Economics.
The research topic considered in this thesis shows many different lines for future developments. In particular, from a theoretical point of view, starting from the models proposed in Riccardi and Toninelli (2011), we are studying for a bi-objective like DEA formulation where both uncertainty desirable and undesirable factor are taken into account. As regards the applicative aspects, we are also studying and applying bootstrap techniques to manage uncertainty and generate empirical distributions of efficiency scores, in order to capture and analyze the sensitivity of samples with respect to changes in the estimated frontier.