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Branch-and-Price for Prescriptive Contagion Analytics

Author

Listed:
  • Alexandre Jacquillat

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Michael Lingzhi Li

    (Harvard Business School, Harvard University, Cambridge, Massachusetts 02163)

  • Martin Ramé

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Kai Wang

    (School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China)

Abstract

Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by continuous-time contagion dynamics. These problems feature a large-scale mixed-integer nonconvex optimization structure with constraints governed by ordinary differential equations. This paper develops a branch-and-price methodology for this class of problems based on (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a state-clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a tripartite branching scheme to circumvent nonlinearities. We apply the methodology to four real-world cases: vaccine distribution, vaccination centers deployment, content promotion, and congestion mitigation. Extensive experiments show that the algorithm scales to large and otherwise-intractable instances, outperforming state-of-the-art benchmarks. Our methodology provides practical benefits in contagion systems—In particular, we show that it can increase the effectiveness of a vaccination campaign in a setting replicating the rollout of COVID-19 vaccines in 2021. We provide an open-source implementation of the methodology to enable replication.

Suggested Citation

  • Alexandre Jacquillat & Michael Lingzhi Li & Martin Ramé & Kai Wang, 2025. "Branch-and-Price for Prescriptive Contagion Analytics," Operations Research, INFORMS, vol. 73(3), pages 1558-1580, May.
  • Handle: RePEc:inm:oropre:v:73:y:2025:i:3:p:1558-1580
    DOI: 10.1287/opre.2023.0308
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