Branch-and-Price for Prescriptive Contagion Analytics
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rame-mrame-sm-orc-2023-thesis.pdf
Description
Thesis PDF
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2.81 MB
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Adobe PDF
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Author(s)
Ramé, Martin
Advisor(s)
Jacquillat, Alexandre
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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