Computational tools for emergency medical services and semidefinite programming
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2025
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Guigues, Vincent Gérard Yannick
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This thesis develops mathematical models, optimization methods, and computational tools aimed at improving the operation of Emergency Medical Services (EMS) and advancing the efficient solution of large-scale optimization problems. The first part of the thesis focuses on EMS operations, proposing optimization models and heuristics for ambulance dispatch and fleet management. The proposed methods are validated using real EMS data from Rio de Janeiro, showing improvements in both response times and the adequacy of ambulance–emergency assignments compared to existing approaches. The second part of the thesis addresses the modeling and forecasting of emergencies. It presents LASPATED, an open-source software library for estimating nonhomogeneous spatio-temporal Poisson process models using space–time discretization, with support for regularization, covariates, and missing data. These models are applied to real EMS data to improve the prediction of emergency call arrivals. In addition, an online visualization and simulation platform is developed, allowing users to explore EMS data, animate ambulance operations, and compare dispatch strategies interactively. The third part of the thesis includes an independent contribution to large-scale optimization: cuHALLaR, a GPU-accelerated implementation of a hybrid low-rank augmented Lagrangian method for semidefinite programming. Experiments on three classes of SDPs demonstrate that cuHALLaR is able to achieve more than 100x speedups in comparison with the CPU implementation, and it is also able to outperform other GPU solvers.