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
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.

Abstract
This paper describes the development of a mechanism to deal with time windows constraints. To the best of our knowledge, the time windows constraints are difficult to be fulfilled even for state-of-the-art methods. Therefore, the main contribution of this paper is to propose a new computational technique to deal with such constraints to ensure the algorithm convergence. We test such technique in two metaheuristics to solve the discrete and dynamic Berth Allocation Problem. A data set generator was created, resulting in a diversity of problems in terms of time windows constraints. A detailed computational analysis was carried out to compare the performance for each metaheuristic.

Abstract
A área de conhecimento associada à gestão de ativos potencia a extração de valor de ativos físicos, incorporando uma abordagem integrada que envolve riscos, custos e desempenho. Este trabalho propõe uma nova abordagem para selecionar projetos de investimento em infraestruturas no âmbito da gestão de ativos. A métrica padrão utilizada para a seleção de projetos em ativos múltiplos é o Índice de Valor de Infraestruturas (IVI), que tem sido utilizado para caracterizar ativos do setor de águas em diversos países. Este trabalho desenvolveu dois modelos de programação linear inteira mista. O primeiro modelo de otimização trata de um problema de alocação de orçamento de capital selecionando projetos de investimento com vista à maximização da condição dos ativos. O segundo modelo de otimização trata de um problema de planeamento de orçamento, visando minimizar o capital necessário para manter os ativos nas condições desejadas. A aplicação dos modelos é ilustrada por um estudo de caso de uma empresa que opera no setor da água em Portugal. Os resultados obtidos nos diferentes cenários analisados são discutidos com vista a apoiar o desenho de políticas de gestão de ativos mais eficientes.

Abstract
The Strategic Framework for European Cooperation in Education and Training (ET 2020) aimed to pro-mote the exchange of best practices among the Member States. This paper assesses the performance evo-lution of European countries in terms of the common objectives for the education sector. The framework used to evaluate European education systems is based on constructing a composite indicator adopting a benefit-of-the-doubt approach. The evaluation of performance change over time is done using a Global Malmquist Index. Sigma and beta convergence of EU countries are also explored using non-parametric frontier techniques. The results are analysed for the period 2009-2018 and discussed in light of the goals envisaged and the national policies adopted. The results revealed a trend of improvement in the perfor-mance of education systems in most European countries in the period analysed. Although most European countries moved closer to the European best practice frontier over time, as confirmed by the values of sigma-convergence, a few countries are still lagging considerably below their peers, as revealed by the existence of divergence in beta.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Abstract
Assessing the evolution of the performance of water supply and sanitation services is essential to monitor progress towards the universalization of water services, as specified by the Sustainable Development Goal 6 of Agenda 2030, adopted by United Nations member countries. Brazil, a developing country with a continental size and geographical diversity, will face significant challenges to achieve this goal. The main objective of this paper is to evaluate the evolution of productivity of water supply and sanitation services in Brazilian municipalities in the period 2012-2019. The analysis also explores whether water services' performance is balanced across the country, with a specific analysis of performance at the macroregion level. From a methodological perspective, this research evaluates productivity change over time using a Malmquist Productivity Index estimated with a metafrontier, satisfying the circularity property. It also develops a pseudo Malmquist index that compares productivity levels across macro-regions. The results revealed a productivity loss of approximately 4% at the national level, with an unequal profile across the macro-regions. The Southeast municipalities stand out for exhibiting, on average, higher productivity levels than the South and Northeast municipalities.