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Selecting Optimal Alternatives and Risk Reduction Strategies in Decision Trees

Author

Listed:
  • Hanif D. Sherali

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

  • Evrim Dalkiran

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

  • Theodore S. Glickman

    (Department of Decision Sciences, The George Washington University, Washington, DC 20052)

Abstract

In this paper we conduct a quantitative analysis for a strategic risk management problem that involves allocating certain available failure-mitigating and consequence-alleviating resources to reduce the failure probabilities of system safety components and subsequent losses, respectively, together with selecting optimal strategic decision alternatives, to minimize the risk or expected loss in the event of a hazardous occurrence. Using a novel decision tree optimization approach to represent the cascading sequences of probabilistic events as controlled by key decisions and investment alternatives, the problem is modeled as a nonconvex mixed-integer 0-1 factorable program. We develop a specialized branch-and-bound algorithm in which lower bounds are computed via tight linear relaxations of the original problem that are constructed by utilizing a polyhedral outer-approximation mechanism in concert with two alternative linearization schemes having different levels of tightness and complexity. We also suggest three alternative branching schemes, each of which is proven to guarantee convergence to a global optimum for the underlying problem. Extensive computational results and sensitivity analyses are presented to provide insights and to demonstrate the efficacy of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:631-647
    DOI: 10.1287/opre.1110.0923
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    References listed on IDEAS

    as
    1. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    2. 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.
    3. Robin L. Dillon & M. Elisabeth Paté-Cornell & Seth D. Guikema, 2003. "Programmatic Risk Analysis for Critical Engineering Systems Under Tight Resource Constraints," Operations Research, INFORMS, vol. 51(3), pages 354-370, June.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
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    Cited by:

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    2. 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).
    3. 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.
    4. Jing Ai & Patrick L. Brockett & Tianyang Wang, 2017. "Optimal Enterprise Risk Management and Decision Making With Shared and Dependent Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1127-1169, December.
    5. Dadsena, Krishna Kumar & Sarmah, S.P. & Naikan, V.N.A. & Jena, Sarat Kumar, 2019. "Optimal budget allocation for risk mitigation strategy in trucking industry: An integrated approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 121(C), pages 37-55.
    6. Eman Ismail & Yasser Tawfik Halim & Mohamed Samy EL-Deeb, 2023. "Corporate reputation and shareholder investment: a study of Egypt's tourism listed companies," Future Business Journal, Springer, vol. 9(1), pages 1-15, December.

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