Abstract
Environmental performance assessments are often conducted using environmental indicators. Although these indicators provide a starting point for performance assessments, they do not provide guidelines that countries should follow to improve performance. This paper develops an enhanced Data Envelopment Analysis (DEA) model that provides a single summary measure of countries' environmental performance, based on the aggregation of the indicators that underlie the estimation of the Environmental Performance Index (EPI). The DEA model used is based on a novel specification of weight restrictions. The main contribution of the methodology used in this paper is to enable benchmarking in such a way that it becomes possible to identify the strengths and weaknesses of each country, as well as the peers with similar features to the country under assessment. These peers provide examples of good environmental practices that countries with worse performance should follow to improve performance. Journal of the Operational Research Society (2013) 64, 426-438. doi:10.1057/jors.2012.62 Published online 16 May 2012

Abstract
Assessing eco-efficiency of companies is important to ensure the creation of wealth without compromising the needs of future generations. This work aims to extend the eco-efficiency concept by including in the assessment new features related to environmental benefits and environmental burdens. This concept is implemented using an innovative Directional Distance Function model, which searches for improvements in the magnitude of the indicators and in the composition of the resources consumed. This framework can help firms to become more sustainable by replacing non-renewable inputs with "greener" alternatives. We present an empirical application to large mining companies. Different scenarios regarding managerial priorities for adjustments to firms' economic and environmental indicators are explored. The results obtained and their managerial implications are discussed in the context of mining firms activity.

Abstract
This paper discusses different models that can be used to construct composite indicators with both desirable and undesirable output indicators. Two approaches are considered. The first is an indirect approach, based on a traditional Data Envelopment Analysis model, requiring a prior transformation in the measurement scale of the undesirable outputs. The second is a direct approach, based on a directional distance function model. The use of a directional distance function allows for the accommodation of undesirable indicators in their original form. The main limitations of these approaches are discussed related to the data transformation in the case of the indirect approach and the possibility to obtain negative margin rates of substitution between the desirable and undesirable outputs in the case of the direct approach. These issues lead to the proposal of a new composite indicator model based on a directional distance function that overcomes the limitations associated with the existing approaches. The incorporation of information on the relative importance of individual indicators using weight restrictions is discussed. Proposed here is an enhanced formulation of weight restrictions, in the form of assurance regions type I, that reflects the relative importance of the indicators in percentage terms. The models are illustrated in the assessment of Brazilian hydropower plants and are suitable for any assessment involving the aggregation of key performance indicators whenever undesirable outputs are present.

Abstract
Assessing firms' Eco-efficiency is important to ensure they succeed in creating wealth without compromising the needs of future generations. This work aims to extend the Eco-efficiency concept by including in the assessment new features related to environmental benefits. Eco-efficiency is evaluated using a DEA model specified with a Directional Distance Function. The new methodology proposed in this paper is illustrated with an application to world-class mining companies, whose results and managerial implications are discussed.

Abstract
This study develops a tool to assess livability in European cities covering two components of livability: human wellbeing and environmental impact. First, we propose a conceptual model to assess cities' livability, that extends the concept of urban livability to include a component related to environmental sustainability. Second, we address the measurement of cities' livability. For this purpose, a new composite indicator was constructed based on a data envelopment analysis model specified using a directional distance function. In addition to assigning a summary measure of performance for each city, the composite indicator can be used to guide improvements concerning different livability objectives. One of the innovative features of the model proposed is to enable, by the specification of different directional vectors, focusing separately on each component of livability (e.g., human wellbeing and environmental impact) or alternatively considering cities' potential for improvement in all indicators simultaneously. In addition, it is possible to incorporate a new type of weight restrictions, specified as assurance regions type I, that reflect the relative importance of both desirable and undesirable outputs in percentage terms. Finally, this paper approached the assessment of the evolution of cities' performance over time using the Luenberger productivity indicator.

Abstract
This paper investigates the performance of the largest Brazilian hydropower plants. This study covers 78% of the total installed capacity from hydros in the country, and considers indicators reflecting operational and maintenance costs as well as quality of service. The assessment was conducted using a new approach for the construction of composite indicators, based on a directional distance function model. First, we assessed the hydropower plants allowing for complete flexibility in the definition of weights, enabling the identification of underperforming plants, and quantification of their potential for improvement. Next, we assessed the plants considering different perspectives regarding the importance attributed to each indicator. This allowed reflecting different points of view, focusing primarily on operation and maintenance costs or quality issues. The results identify the hydropower plants that can be considered benchmarks in different scenarios, and allow testing the robustness of plants' classification as benchmarks in the unrestricted model.