Abstract
Grasping the intricacy and diversity of complex systems dealing with ever-growing amounts of data is essential to public and private institutions' continuous improvement. Composite indicators (CIs) emerge as aggregators of key performance indicators, providing a single measure that reflects those multidimensional performance aspects. One way to build such measures is based on the use of data envelopment analysis (DEA). Several DEA models can be used to generate CIs. Still, not many of them can deal concurrently with desirable and undesirable outputs, and incorporate the decision-making actors' preference information. Based on the directional 'Benefit-of-the-Doubt' model, we propose a novel approach consisting of the simultaneous use of weight restrictions and an artificial target reached via a range directional vector. The resulting CI assesses the Portuguese public hospitals' performance under two perspectives of hospital activity: users and providers. In the end, managerial and policy implications are withdrawn from the results of this study conducted in cooperation with the Portuguese Ministry of Health.

Abstract
Convergence in productivity examines if entities in an industry get closer to the best practices or if the gap between the frontiers of the best and worst performers decreases over time. In a multi-input multioutput setting, the assessment of sigma- and beta-convergence can be measured with the use of non-parametric frontier techniques, such as data envelopment analysis. We propose an innovative approach to estimate convergence in the context of performance assessments resting on composite indicators, accounting for desirable and undesirable indicators. This methodology rests on 'Benefit-of-the-Doubt' models, specified with a directional distance function. It is applied to the Member States of the World Health Organization (WHO) in order to study their convergence in terms of the United Nations' Sustainable Development Goal (SDG) 'Good health and well-being'. We collected data for all years since the proposal of the SDGs, covering the period between 2016 and 2020. The results show that all WHO regions are (beta) over cap -divergent, especially because of the generalised decline of the Worst Practice Frontier (WPF), alongside an improvement at a lower rate of the Best Practice Frontier (BPF). The regional analysis also revealed (sigma) over cap -convergence in the Region of the Americas and the Eastern Mediterranean Region; the South-East Asia and African Regions exhibited (sigma) over cap -divergence; the Western Pacific and European Regions remained stable in terms of the performance spread regarding the BPF. At the worldwide level, we also observed an increase of the gap between the BPF and the WPF, although the performance spread around the worldwide BPF remained relatively stable.

Abstract
This paper proposes an innovative framework based on optimisation techniques that can support decision-making in water services. The proposed models estimate a Best-Practice frontier recurring to a ‘Benefit-of-the-Doubt’ formulation that enables benchmarking performance across decision-making units. We propose an innovative estimation of a pseudo-Malmquist index to compare the performance of groups. The framework’s relevance is illustrated using data of the Brazilian water and sanitation regulator, collected at the municipality level for the year 2019. The groups compared correspond to three Brazilian macro-regions. The results obtained show that the Southeast exhibits the best overall performance. The Northeast has a few municipalities with the best practices at a national level, but this macro-region has significant heterogeneity in performance levels. The South has a more homogeneous performance, but the best-performing municipalities in this macro-region are still far from Brazil’s best practices. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Driven by the need for decarbonizing energy carriers across sectors, and the increasing availability of low-cost renewable electricity generation future energy systems will see a rise of power-to-gas technology. For example, hydrogen and its derivates can make enable the usage of carbon-neutral electricity for hard-to abate industry sectors and serve as long-term seasonal storage. Given recent drafts of ambitious political hydrogen strategies around the world, the question arises which power-to-gas configurations provide the highest value for money from a power system perspective. This work provides a flexible framework to compare the performance of current power-to-gas sites all over the world. Power-to-gas technologies are assessed with a benchmarking framework based on Composite Indicators to compare the system value of existing conversion technologies, plant sizes, cost structures, and configurations. Our analysis confirms recent research that suggests that plant performance is higher for larger projects and improves as projects move from research stage over pilot stage to commercial stage. Our findings inform policy makers and electricity system planners who aim to identify the economically and technically most promising solutions for investment.

Abstract
This paper explores robust unconditional and conditional nonparametric approaches to support performance evaluation in problematic samples. Real-world assessments often face critical problems regarding available data, as samples may be relatively small, with high variability in the magnitude of the observed indicators and contextual conditions. This paper explores the possibility of mitigating the impact of potential outlier observations and variability in small samples using a robust nonparametric approach. This approach has the advantage of avoiding unnecessary loss of relevant information, retaining all the decision-making units of the original sample. We devote particular attention to identifying peers and targets in the robust nonparametric approach to guide improvements for underperforming units. The results are compared with a traditional deterministic approach to highlight the proposed method's benefits for problematic samples. This framework's applicability in internal benchmarking studies is illustrated with a case study within the wastewater treatment industry in Portugal.

Abstract
Wastewater treatment plants constitute an essential part of the sewage system. They have the role of removing pollutants from wastewater to enable the safe disposal of the treated effluent in the natural environment. This research seeks to evaluate plants' efficiency and effectiveness, which involves minimizing energy consumption while obtaining a quality level of the treated water aligned with legislation requirements. We explore two policy scenarios regarding the measurement of effluent quality. The first assumes that pollutants' emission quotas (EQs) are fixed at each plant. The second assumes that quotas are set for the receiving waters (e.g., river or watercourse in the natural environment) so that trade-offs in EQs among plants sharing the same discharge site are possible. This latter scenario requires a system-wide analysis to identify optimal targets for pollutants removal at each plant that allow fulfilling the expected average quality levels of the effluent discharged. This paper develops a methodology to fully realize the potential for energy savings based on an innovative mixed-integer linear programming model. This model follows the data envelopment analysis axioms to estimate the frontier of the production possibility set. The approach proposed is tested in a real-world context using the plants of a Portuguese water company. The results show that the two scenarios combining efficiency and effectiveness perspectives have advantages in terms of energy savings compared to the conventional situation focused only on efficiency gains. The saving potential is slightly higher in the scenario allowing reallocation of EQs among plants.