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Optimal Group Testing: Structural Properties and Robust Solutions, with Application to Public Health Screening

Author

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  • Hrayer Aprahamian

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843;)

  • Douglas R. Bish

    (Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061)

  • Ebru K. Bish

    (Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061)

Abstract

We provide a novel regret-based robust formulation of the Dorfman group size problem considering the realistic setting where the prevalence rate is uncertain, establish key structural properties of the optimal solution, and provide an exact algorithm. Our analysis also leads to exact closed-form expressions for the optimal Dorfman group size under a deterministic prevalence rate, which is the problem studied in the extant literature. Thus, our structural results not only unify existing, and mostly empirical, results on the Dorfman group size problem under a deterministic prevalence rate, but, more importantly, enable us to efficiently solve the robust version of this problem to optimality. We demonstrate the value of robust testing schemes with a case study on disease screening using realistic data. Our case study indicates that robust testing schemes can significantly outperform their deterministic counterparts, by not only substantially reducing the maximum regret value, but, in the majority of the cases, reducing testing costs as well. Our findings have important implications on public health screening practices.

Suggested Citation

  • Hrayer Aprahamian & Douglas R. Bish & Ebru K. Bish, 2020. "Optimal Group Testing: Structural Properties and Robust Solutions, with Application to Public Health Screening," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 895-911, October.
    • Handle: RePEc:inm:orijoc:v:32:y:4:i:2020:p:895-911
    DOI: 10.1287/ijoc.2019.0942
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    References listed on IDEAS

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    Cited by:

    1. Jiayi Lin & Hrayer Aprahamian & George Golovko, 2024. "An optimization framework for large-scale screening under limited testing capacity with application to COVID-19," Health Care Management Science, Springer, vol. 27(2), pages 223-238, June.
    2. Hrayer Aprahamian & Vedat Verter & Manaf Zargoush, 2024. "Editorial: management science for pandemic prevention, preparedness, and response," Health Care Management Science, Springer, vol. 27(3), pages 479-482, September.
    3. Hussein El Hajj & Douglas R. Bish & Ebru K. Bish & Denise M. Kay, 2022. "Novel Pooling Strategies for Genetic Testing, with Application to Newborn Screening," Management Science, INFORMS, vol. 68(11), pages 7994-8014, November.
    4. Ramy Elitzur & Dmitry Krass & Eyal Zimlichman, 2023. "Machine learning for optimal test admission in the presence of resource constraints," Health Care Management Science, Springer, vol. 26(2), pages 279-300, June.

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