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A basic mathematical model for evacuation problems in urban areas

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  • Bretschneider, S.
  • Kimms, A.

Abstract

Real life situations like floods, hurricanes or chemical accidents may cause the evacuation of a certain area to rescue the affected population. To enable a fast and a safe evacuation a basic mixed-integer evacuation model has been developed that provides a reorganization of the traffic routing of a certain area for the case of an evacuation. This basic problem of evacuation minimizes the evacuation-time while prohibiting conflicts within intersections. Our evacuation model is a dynamic network flow problem with additional variables for the number and direction of used lanes and with additional complicating constraints. Because of the size of the time-expanded network, the computational effort required by standard software is already very high for tiny instances. To deal with realistic instances we propose a heuristic approach.

Suggested Citation

  • Bretschneider, S. & Kimms, A., 2011. "A basic mathematical model for evacuation problems in urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 523-539, July.
    • Handle: RePEc:eee:transa:v:45:y:2011:i:6:p:523-539
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    References listed on IDEAS

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    Cited by:

    1. Durga Prasad Khanal & Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2022. "Efficient Algorithms for Abstract Flow with Partial Switching," SN Operations Research Forum, Springer, vol. 3(4), pages 1-17, December.
    2. Hadas, Yuval & Laor, Amir, 2013. "Network design model with evacuation constraints," Transportation Research Part A: Policy and Practice, Elsevier, vol. 47(C), pages 1-9.
    3. Huan Cao & Tian Li & Shuxia Li & Tijun Fan, 2017. "An integrated emergency response model for toxic gas release accidents based on cellular automata," Annals of Operations Research, Springer, vol. 255(1), pages 617-638, August.
    4. Pillac, Victor & Van Hentenryck, Pascal & Even, Caroline, 2016. "A conflict-based path-generation heuristic for evacuation planning," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 136-150.
    5. Bretschneider, S. & Kimms, A., 2012. "Pattern-based evacuation planning for urban areas," European Journal of Operational Research, Elsevier, vol. 216(1), pages 57-69.
    6. Yiping Jiang & Yufei Yuan, 2019. "Emergency Logistics in a Large-Scale Disaster Context: Achievements and Challenges," IJERPH, MDPI, vol. 16(5), pages 1-23, March.
    7. Melissa Gama & Bruno Filipe Santos & Maria Paola Scaparra, 2016. "A multi-period shelter location-allocation model with evacuation orders for flood disasters," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(3), pages 299-323, September.
    8. Knut Haase & Mathias Kasper & Matthes Koch & Sven Müller, 2019. "A Pilgrim Scheduling Approach to Increase Safety During the Hajj," Operations Research, INFORMS, vol. 67(2), pages 376-406, March.
    9. Abhishek Behl & Pankaj Dutta, 2019. "Humanitarian supply chain management: a thematic literature review and future directions of research," Annals of Operations Research, Springer, vol. 283(1), pages 1001-1044, December.
    10. Jin, Jian Gang & Shen, Yifan & Hu, Hao & Fan, Yiqun & Yu, Mingjian, 2021. "Optimizing underground shelter location and mass pedestrian evacuation in urban community areas: A case study of Shanghai," Transportation Research Part A: Policy and Practice, Elsevier, vol. 149(C), pages 124-138.
    11. Xinhua Mao & Changwei Yuan & Jiahua Gan & Jibiao Zhou, 2019. "Optimal Evacuation Strategy for Parking Lots Considering the Dynamic Background Traffic Flows," IJERPH, MDPI, vol. 16(12), pages 1-20, June.
    12. Bayram, Vedat & Yaman, Hande, 2024. "A joint demand and supply management approach to large scale urban evacuation planning: Evacuate or shelter-in-place, staging and dynamic resource allocation," European Journal of Operational Research, Elsevier, vol. 313(1), pages 171-191.
    13. Kimms, A. & Maiwald, M., 2018. "Bi-objective safe and resilient urban evacuation planning," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1122-1136.

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