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The stochastic interdiction median problem with disruption intensity levels

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  • Chaya Losada
  • M. Scaparra
  • Richard Church
  • Mark Daskin

Abstract

In this paper we introduce a stochastic interdiction problem for median systems in which the operational state of the system’s disrupted elements in the aftermath of the disruption is uncertain as it is based on the intensity of the disruption. We assume that a disruption disables a facility with a given probability and this probability depends on the intensity of the disruption. The objective of this problem is to identify which disruption scenario entails a maximum overall traveling distance in serving all customers. We show that the initial two stage stochastic formulation can be reformulated into a deterministic counterpart whose size is polynomial in the number of facilities and intensity levels. Then, our ensuing efforts to solve the problem efficiently focus on studying alternative deterministic formulations that allow the solution of realistic size instances of the model. We observe that the most efficient of the deterministic formulations provide great scalability with respect to variations in the input parameters and size of the instances solved. Finally, we analyze the robustness of the optimal solutions due to misestimations in the probability functions that relate disruption intensity levels with the probabilities of facility survivability. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:345-365:10.1007/s10479-012-1170-x
    DOI: 10.1007/s10479-012-1170-x
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    3. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2021. "The impact of congestion on protection decisions in supply networks under disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    4. Bhuiyan, Tanveer Hossain & Medal, Hugh R. & Harun, Sarah, 2020. "A stochastic programming model with endogenous and exogenous uncertainty for reliable network design under random disruption," European Journal of Operational Research, Elsevier, vol. 285(2), pages 670-694.
    5. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2018. "Multiple allocation hub interdiction and protection problems: Model formulations and solution approaches," European Journal of Operational Research, Elsevier, vol. 270(1), pages 230-245.
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    7. Sachuer Bao & Chi Zhang & Min Ouyang & Lixin Miao, 2019. "An integrated tri-level model for enhancing the resilience of facilities against intentional attacks," Annals of Operations Research, Springer, vol. 283(1), pages 87-117, December.
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    11. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2016. "Hub Interdiction & Hub Protection problems: Model formulations & Exact Solution methods. (Revised)," IIMA Working Papers WP2016-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
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