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Allocating Protection Resources to Facilities When the Effect of Protection is Uncertain

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  • Hugh R. Medal
  • Edward A. Pohl
  • Manuel D. Rossetti

Abstract

We study a new facility protection problem in which one must allocate scarce protection resources to a set of facilities given that allocating resources to a facility only has a probabilistic effect on the facility’s post-disruption capacity. This study seeks to test three common assumptions made in the literature on modeling infrastructure systems subject to disruptions: 1) perfect protection, e.g., protecting an element makes it fail-proof, 2) binary protection, i.e., an element is either fully protected or unprotected, and 3) binary state, i.e., disrupted elements are fully operational or non-operational. We model this facility protection problem as a two-stage stochastic program with endogenous uncertainty. Because this stochastic program is non-convex we present a greedy algorithm and show that it has a worst-case performance of 0.63. However, empirical results indicate that the average performance is much better. In addition, experimental results indicate that the mean-value version of this model, in which parameters are set to their mean values, performs close to optimal. Results also indicate that the perfect and binary protection assumptions together significantly affect the performance of a model. On the other hand, the binary state assumption was found to have a smaller effect.

Suggested Citation

  • Hugh R. Medal & Edward A. Pohl & Manuel D. Rossetti, 2016. "Allocating Protection Resources to Facilities When the Effect of Protection is Uncertain," IISE Transactions, Taylor & Francis Journals, vol. 48(3), pages 220-234, March.
    • Handle: RePEc:taf:uiiexx:v:48:y:2016:i:3:p:220-234
    DOI: 10.1080/0740817X.2015.1078013
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    Cited by:

    1. 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.
    2. Wu, Di & Liu, Xiang-dong & Yan, Xiang-bin & Peng, Rui & Li, Gang, 2019. "Equilibrium analysis of bitcoin block withholding attack: A generalized model," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 318-328.
    3. Li, Qing & Li, Mingchu & Tian, Yuan & Gan, Jianyuan, 2023. "A risk-averse tri-level stochastic model for locating and recovering facilities against attacks in an uncertain environment," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    4. Tezcan, Barış & Maass, Kayse Lee, 2023. "Human trafficking interdiction with decision dependent success," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    5. Zhang, Si & Sun, Huijun & Liu, Yang & Lv, Ying & Wu, Jianjun & Feng, Xiaoyan, 2024. "Carsharing equitable relocation problem: A two-stage stochastic programming approach with learning-embedded endogenous uncertainty in demand," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    6. Bhuiyan, Tanveer Hossain & Moseley, Maxwell C. & Medal, Hugh R. & Rashidi, Eghbal & Grala, Robert K., 2019. "A stochastic programming model with endogenous uncertainty for incentivizing fuel reduction treatment under uncertain landowner behavior," European Journal of Operational Research, Elsevier, vol. 277(2), pages 699-718.
    7. Zhou, Rui & Bhuiyan, Tanveer Hossain & Medal, Hugh R. & Sherwin, Michael D. & Yang, Dong, 2022. "A stochastic programming model with endogenous uncertainty for selecting supplier development programs to proactively mitigate supplier risk," Omega, Elsevier, vol. 107(C).

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