{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/151633"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/151633","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Branch-and-Price for Prescriptive Contagion Analytics","abstract":"Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This thesis formalizes prescriptive contagion analytics problems where a centralized decision-maker allocates shared resources across multiple segments of a population, each governed by contagion dynamics. We define four real-world problems under this umbrella: distributing vaccines, deploying vaccination centers, mitigating urban congestion, promoting online content, and combating drug addiction. Prescriptive contagion problems involve mixed-integer non-convex optimization models with constraints governed by ordinary differential equations, thus combining the challenges of combinatorial optimization, non-linear optimization, and continuous-time system dynamics. This thesis develops a branch-and-price methodology for these problems based on: (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a novel state clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a novel tri-partite branching scheme to circumvent non-linearities. Extensive experiments show that the algorithm scales to large and otherwise- intractable instances, significantly outperforming state-of-the-art benchmarks. Our methodology provides a novel decision-making tool to support resource allocation in contagion systems. In particular, its application can increase the effectiveness of vaccination campaigns by an estimated 50-70%, resulting in 12,000 extra saved lives over 12 weeks in a situation mirroring the COVID-19 pandemic.","abstract_html":"Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This thesis formalizes prescriptive contagion analytics problems where a centralized decision-maker allocates shared resources across multiple segments of a population, each governed by contagion dynamics. We define four real-world problems under this umbrella: distributing vaccines, deploying vaccination centers, mitigating urban congestion, promoting online content, and combating drug addiction. Prescriptive contagion problems involve mixed-integer non-convex optimization models with constraints governed by ordinary differential equations, thus combining the challenges of combinatorial optimization, non-linear optimization, and continuous-time system dynamics. This thesis develops a branch-and-price methodology for these problems based on: (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a novel state clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a novel tri-partite branching scheme to circumvent non-linearities. Extensive experiments show that the algorithm scales to large and otherwise- intractable instances, significantly outperforming state-of-the-art benchmarks. Our methodology provides a novel decision-making tool to support resource allocation in contagion systems. In particular, its application can increase the effectiveness of vaccination campaigns by an estimated 50-70%, resulting in 12,000 extra saved lives over 12 weeks in a situation mirroring the COVID-19 pandemic.","abstract_has_math":false,"creators":["Ramé, Martin"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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This thesis develops a branch-and-price methodology for these problems based on: (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a novel state clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a novel tri-partite branching scheme to circumvent non-linearities. Extensive experiments show that the algorithm scales to large and otherwise- intractable instances, significantly outperforming state-of-the-art benchmarks. Our methodology provides a novel decision-making tool to support resource allocation in contagion systems. In particular, its application can increase the effectiveness of vaccination campaigns by an estimated 50-70%, resulting in 12,000 extra saved lives over 12 weeks in a situation mirroring the COVID-19 pandemic."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Branch-and-Price for Prescriptive Contagion Analytics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jacquillat, Alexandre"],"dc:contributor.department":["Massachusetts Institute of Technology. Operations Research Center"],"dc:creator":["Ramé, Martin"],"dc:date.accessioned":["2023-07-31T19:54:34Z"],"dc:date.available":["2023-07-31T19:54:34Z"],"dc:date.issued":["2023-06"],"dc:description.abstract":["Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. 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This thesis develops a branch-and-price methodology for these problems based on: (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a novel state clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a novel tri-partite branching scheme to circumvent non-linearities. Extensive experiments show that the algorithm scales to large and otherwise- intractable instances, significantly outperforming state-of-the-art benchmarks. Our methodology provides a novel decision-making tool to support resource allocation in contagion systems. 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