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Register a new userOn the optimal layout of a dining room in the era of COVID-19 using mathematical optimization
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Added by
Luciano Costa
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We consider the problem of maximizing the number of people that a dining room can accommodate provided that the chairs belonging to different tables are socially distant. We introduce an optimization model that incorporates several characteristics of the problem, namely: the type and size of surface of the dining room, the shapes and sizes of the tables, the positions of the chairs, the sitting sense of the customers, and the possibility of adding space separators to increase the capacity. We propose a simple yet general set-packing formulation for the problem. We investigate the efficiency of space separators and the impact of considering the sitting sense of customers in the room capacity. We also perform an algorithmic analysis of the model, and assess its scalability to the problem size, the presence of (or lack thereof) room separators, and the consideration of the sitting sense of customers.
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Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compartmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a real-world disease. Different models of disease including the SIR, SIRm and SEIR model are compared with respect to their ability to predict disease spread. Physical distancing impacts and personal protection equipment use will be discussed in relevance to the COVID-19 spread.
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.
In late-2020, many countries around the world faced another surge in number of confirmed cases of COVID-19, including United Kingdom, Canada, Brazil, United States, etc., which resulted in a large nationwide and even worldwide wave. While there have been indications that precaution fatigue could be a key factor, no scientific evidence has been provided so far. We used a stochastic metapopulation model with a hierarchical structure and fitted the model to the positive cases in the US from the start of outbreak to the end of 2020. We incorporated non-pharmaceutical interventions (NPIs) into this model by assuming that the precaution strength grows with positive cases and studied two types of pandemic fatigue. We found that people in most states and in the whole US respond to the outbreak in a sublinear manner (with exponent k=0.5), while only three states (Massachusetts, New York and New Jersey) have linear reaction (k=1). Case fatigue (decline in peoples vigilance to positive cases) is responsible for 58% of cases, while precaution fatigue (decay of maximal fraction of vigilant group) accounts for 26% cases. If there were no pandemic fatigue (no case fatigue and no precaution fatigue), total positive cases would have reduced by 68% on average. Our study shows that pandemic fatigue is the major cause of the worsening situation of COVID-19 in United States. Reduced vigilance is responsible for most positive cases, and higher mortality rate tends to push local people to react to the outbreak faster and maintain vigilant for longer time.
Timely, creditable, and fine-granular case information is vital for local communities and individual citizens to make rational and data-driven responses to the COVID-19 pandemic. This paper presents CovidNet, a COVID-19 tracking project associated with a large scale epidemic dataset, which was initiated by 1Point3Acres. To the best of our knowledge, the project is the only platform providing real-time global case information of more than 4,124 sub-divisions from over 27 countries worldwide with multi-language supports. The platform also offers interactive visualization tools to analyze the full historical case curves in each region. Initially launched as a voluntary project to bridge the data transparency gap in North America in January 2020, this project by far has become one of the major independent sources worldwide and has been consumed by many other tracking platforms. The accuracy and freshness of the dataset is a result of the painstaking efforts from our voluntary teamwork, crowd-sourcing channels, and automated data pipelines. As of May 18, 2020, the project website has been visited more than 200 million times and the CovidNet dataset has empowered over 522 institutions and organizations worldwide in policy-making and academic researches. All datasets are openly accessible for non-commercial purposes at https://coronavirus.1point3acres.com via a formal request through our APIs.
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called textit{level of abstraction} used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online.
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