Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning.

We seek to provide practicable approximations of the two-stage robust stochastic optimization model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase (1) the significant improvement in practicability of the robust stochastic optimization counterparts with our proposed divergence functions compared to existing f-divergences, (2) the greater equity of humanitarian response that the objective function enforces and (3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered.

An optimization model for planning testing and control strategies to limit the spread of a pandemic - The case of COVID-19.

The global health crisis caused by the coronavirus SARS-CoV-2 has highlighted the importance of efficient disease detection and control strategies for minimizing the number of infections and deaths in the population and halting the spread of the pandemic. Countries have shown different preparedness levels for promptly implementing disease detection strategies, via mass testing and isolation of identified cases, which led to a largely varying impact of the outbreak on the populations and health-care systems. In this paper, we propose a new pandemic resource allocation model for allocating limited disease detection and control resources, in particular testing capacities, in order to limit the spread of a pandemic. The proposed model is a novel epidemiological compartmental model formulated as a non-linear programming model that is suitable to address the inherent non-linearity of an infectious disease progression within the population. A number of novel features are implemented in the model to take into account important disease characteristics, such as asymptomatic infection and the distinct risk levels of infection within different segments of the population. Moreover, a method is proposed to estimate the vulnerability level of the different communities impacted by the pandemic and to explicitly consider equity in the resource allocation problem. The model is validated against real data for a case study of COVID-19 outbreak in France and our results provide various insights on the optimal testing intervention time and level, and the impact of the optimal allocation of testing resources on the spread of the disease among regions. The results confirm the significance of the proposed modeling framework for informing policymakers on the best preparedness strategies against future infectious disease outbreaks.

Brazilian disaster datasets and real-world instances for optimization and machine learning.

We present comprehensive datasets of Brazilian disasters from January 2003 to February 2021 as well as real-world optimization instances built up from these data. The data were gathered through a series of open available reports obtained from different government and institutional sources. Afterwards, data consolidation and summarization were carried out using Excel and Python. The datasets include 9 types of disaster, such as flash floods, landslides and droughts, and the corresponding number of affected people during an 18-year or a 218-month observation period for 5,402 Brazilian municipalities, totaling more than 65,000 observations. Data on relevant geographical, demographic and socioeconomic aspects of the affected municipalities are also provided. These encompass geographic coordinates, regions, population, income, development indicators, amongst other information. From a statistical point of view, the data on disasters can address a number of applications using both supervised and unsupervised machine learning techniques such as, for time series analysis or other dynamic models using socioeconomic data as explanatory variables, i.e. data on the size of the poor population, income, education and general development. The geographic dataset can be useful for aggregating analyses concerning the various forms of territorial organization and allows for the visualization of data in maps. All the aforementioned data can be also used to devise realistic optimization instances related to diverse humanitarian logistics and/or disaster management problems, such as facility location, location-allocation, vehicle routing, and so forth. In particular, we describe two real-world instances for the location-allocation problem studied in [1]. For that purpose, we partially use the given datasets and included other information such as costs and distances relevant to the optimization model. Although using real-world cases to test optimization approaches is a common and encouraged practice in Operations Research, comprehensive datasets and practical optimization instances, as presented in this article, are rarely described and/or available in the academic literature.