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Optimal Allocation of Risk-Reduction Resources in Event Trees

Author

Listed:
  • Hanif D. Sherali

    (Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061)

  • Jitamitra Desai

    (Department of Industrial and Systems Engineering, University of Arizona, Tucson, Arizona 85719)

  • Theodore S. Glickman

    (Department of Decision Sciences, The George Washington University, Washington, D.C. 20052)

Abstract

In this paper, we present a novel quantitative analysis for the strategic planning decision problem of allocating certain available prevention and protection resources to, respectively, reduce the failure probabilities of system safety measures and the total expected loss from a sequence of events. Using an event tree optimization approach, the resulting risk-reduction scenario problem is modeled and then reformulated as a specially structured nonconvex factorable program. We derive a tight linear programming relaxation along with related theoretical insights that serve to lay the foundation for designing a tailored branch-and-bound algorithm that is proven to converge to a global optimum. Computational experience is reported for a hypothetical case study, as well as for several realistic simulated test cases, based on different parameter settings. The results on the simulated test cases demonstrate that the proposed approach dominates the commercial software BARON v7.5 when the latter is applied to solve the original model by more robustly yielding provable optimal solutions that are at an average of 16.6% better in terms of objective function value; and it performs competitively when both models are used to solve the reformulated problem, particularly for larger test instances.

Suggested Citation

  • Hanif D. Sherali & Jitamitra Desai & Theodore S. Glickman, 2008. "Optimal Allocation of Risk-Reduction Resources in Event Trees," Management Science, INFORMS, vol. 54(7), pages 1313-1321, July.
    • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:7:p:1313-1321
    DOI: 10.1287/mnsc.1070.0844
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    Citations

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    Cited by:

    1. Zuo, Fei & Zio, Enrico & Xu, Yue, 2023. "Bi-objective optimization of the scheduling of risk-related resources for risk response," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    2. E. Borgonovo & C. L. Smith, 2011. "A Study of Interactions in the Risk Assessment of Complex Engineering Systems: An Application to Space PSA," Operations Research, INFORMS, vol. 59(6), pages 1461-1476, December.
    3. Brian J. Lunday & Hanif D. Sherali & Theodore S. Glickman, 2010. "The Nested Event Tree Model with Application to Combating Terrorism," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 620-634, November.
    4. Mumtaz Karatas & Ertan Yakıcı & Abdullah Dasci, 2022. "Solving a bi-objective unmanned aircraft system location-allocation problem," Annals of Operations Research, Springer, vol. 319(2), pages 1631-1654, December.
    5. Hanif D. Sherali & Evrim Dalkiran & Theodore S. Glickman, 2011. "Selecting Optimal Alternatives and Risk Reduction Strategies in Decision Trees," Operations Research, INFORMS, vol. 59(3), pages 631-647, June.
    6. Zhang, Yao & Zuo, Fei & Guan, Xin, 2020. "Integrating case-based analysis and fuzzy optimization for selecting project risk response actions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Yılmaz, Emre & German, Brian J. & Pritchett, Amy R., 2023. "Optimizing resource allocations to improve system reliability via the propagation of statistical moments through fault trees," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    8. Khakzad, Nima, 2021. "Optimal firefighting to prevent domino effects: Methodologies based on dynamic influence diagram and mathematical programming," Reliability Engineering and System Safety, Elsevier, vol. 212(C).

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