A multiple criteria approach for building a pandemic impact assessment composite indicator: The case of COVID-19 in Portugal.

The COVID-19 pandemic has caused major damage and disruption to social, economic, and health systems (among others). In addition, it has posed unprecedented challenges to public health and policy/decision-makers who have been responsible for designing and implementing measures to mitigate its strong negative impact. The Portuguese health authorities have used decision analysis techniques to assess the impact of the pandemic and implemented measures for counties, regions, or across the entire country. These decision tools have been subject to some criticism and many stakeholders requested novel approaches. In particular, those which considered the dynamic changes in the pandemic's behaviour due to new virus variants and vaccines. A multidisciplinary team formed by researchers from the COVID-19 Committee of Instituto Superior Técnico at the University of Lisbon (CCIST analyst team) and physicians from the Crisis Office of the Portuguese Medical Association (GCOM expert team) collaborated to create a new tool to help politicians and decision-makers to fight the pandemic. This paper presents the main steps that led to the building of a pandemic impact assessment composite indicator applied to the specific case of COVID-19 in Portugal. A multiple criteria approach based on an additive multi-attribute value theory aggregation model was used to build the pandemic assessment composite indicator. The parameters of the additive model were devised based on an interactive socio-technical and co-constructive process between the CCIST and GCOM team members. The deck of cards method was the adopted technical tool to assist in the assessment the value functions as well as in the assessment of the criteria weights. The final tool was presented at a press conference and had a powerful impact on the Portuguese media and on the main health decision-making stakeholders in the country. In this paper, a completed mathematical and graphical description of this tool is presented.

A network Data Envelopment Analysis to estimate nations' efficiency in the fight against SARS-CoV-2.

The ongoing outbreak of SARS-CoV-2 has been deeply impacting health systems worldwide. In this context, it is pivotal to measure the efficiency of different nations' response to the pandemic, whose insights can be used by governments and health authorities worldwide to improve their national COVID-19 strategies. Hence, we propose a network Data Envelopment Analysis (DEA) to estimate the efficiencies of fifty-five countries in the current crisis, including the thirty-seven Organisation for Economic Co-operation and Development (OECD) member countries, six OECD prospective members, four OECD key partners, and eight other countries. The network DEA model is designed as a general series structure with five single-division stages - population, contagion, triage, hospitalisation, and intensive care unit admission -, and considers an output maximisation orientation, denoting a social perspective, and an input minimisation orientation, denoting a financial perspective. It includes inputs related to health costs, desirable and undesirable intermediate products related to the use of personal protective equipment and infected population, respectively, and desirable and undesirable outputs regarding COVID-19 recoveries and deaths, respectively. To the best of the authors' knowledge, this is the first study proposing a cross-country efficiency measurement using a network DEA within the context of the COVID-19 crisis. The study concludes that Estonia, Iceland, Latvia, Luxembourg, the Netherlands, and New Zealand are the countries exhibiting higher mean system efficiencies. Their national COVID-19 strategies should be studied, adapted, and used by countries exhibiting worse performances. In addition, the observation of countries with large populations presenting worse mean efficiency scores is statistically significant.

Hypervolume Subset Selection in Two Dimensions: Formulations and Algorithms.

The hypervolume subset selection problem consists of finding a subset, with a given cardinality k, of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article, two new formulations are provided for the two-dimensional variant of this problem. The first is a (linear) integer programming formulation that can be solved by solving its linear programming relaxation. The second formulation is a k-link shortest path formulation on a special digraph with the Monge property that can be solved by dynamic programming in [Formula: see text] time. This improves upon the result of [Formula: see text] in Bader ( 2009 ), and slightly improves upon the result of [Formula: see text] in Bringmann et al. ( 2014b ), which was developed independently from this work using different techniques. Numerical results are shown for several values of n and k.

On local search for bi-objective knapsack problems.

In this article, a local search approach is proposed for three variants of the bi-objective binary knapsack problem, with the aim of maximizing the total profit and minimizing the total weight. First, an experimental study on a given structural property of connectedness of the efficient set is conducted. Based on this property, a local search algorithm is proposed and its performance is compared to exact algorithms in terms of runtime and quality metrics. The experimental results indicate that this simple local search algorithm is able to find a representative set of optimal solutions in most of the cases, and in much less time than exact algorithms.