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Robust optimization for the hazardous materials transportation network design problem

Author

Listed:
  • Chunlin Xin

    (Beijing University of Chemical Technology)

  • Letu Qingge

    (Beijing University of Chemical Technology)

  • Jiamin Wang

    (Long Island University)

  • Binhai Zhu

    (Montana State University)

Abstract

In this paper, we reconsider the hazardous materials transportation network design problem with uncertain edge risk (HTNDPUR) which is proved as strong NP-hard. The natural ways to handle NP-hard problems are approximation solutions or FPT algorithms. We prove that the HTNDPUR does not admit any approximation, neither any FPT algorithm, unless P = NP. Furthermore, we utilize the minimax regret criterion to model the HTNDPUR as a bi-level integer programming formulation under edge risk uncertainty, where an interval of possible risk values is associated with each arc. We present a robust heuristic approach that always finds a robust and stable hazmat transportation network. At the end, we test our method on a network of Guangdong province in China to illustrate the efficiency of the algorithm. Our experimental results illustrate that the robust interval risk scenario network performs better than the deterministic scenario network.

Suggested Citation

  • Chunlin Xin & Letu Qingge & Jiamin Wang & Binhai Zhu, 2015. "Robust optimization for the hazardous materials transportation network design problem," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 320-334, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9751-z
    DOI: 10.1007/s10878-014-9751-z
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
    3. Erhan Erkut & Vedat Verter, 1998. "Modeling of Transport Risk for Hazardous Materials," Operations Research, INFORMS, vol. 46(5), pages 625-642, October.
    4. Vedat Verter & Bahar Y. Kara, 2008. "A Path-Based Approach for Hazmat Transport Network Design," Management Science, INFORMS, vol. 54(1), pages 29-40, January.
    5. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
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    Cited by:

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    2. M. Hosein Zare & Osman Y. Özaltın & Oleg A. Prokopyev, 2018. "On a class of bilevel linear mixed-integer programs in adversarial settings," Journal of Global Optimization, Springer, vol. 71(1), pages 91-113, May.
    3. Peng Zou & Letu Qingge & Qing Yang & Binhai Zhu, 2022. "Computing a consensus trajectory in a vehicular network," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3575-3594, December.
    4. Mohammadi, Mehrdad & Jula, Payman & Tavakkoli-Moghaddam, Reza, 2017. "Design of a reliable multi-modal multi-commodity model for hazardous materials transportation under uncertainty," European Journal of Operational Research, Elsevier, vol. 257(3), pages 792-809.
    5. Zohreh Hosseini Nodeh & Ali Babapour Azar & Rashed Khanjani Shiraz & Salman Khodayifar & Panos M. Pardalos, 2020. "Joint chance constrained shortest path problem with Copula theory," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 110-140, July.
    6. Yan Sun & Xinya Li & Xia Liang & Cevin Zhang, 2019. "A Bi-Objective Fuzzy Credibilistic Chance-Constrained Programming Approach for the Hazardous Materials Road-Rail Multimodal Routing Problem under Uncertainty and Sustainability," Sustainability, MDPI, vol. 11(9), pages 1-27, May.

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