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Efficient Algorithms for Abstract Flow with Partial Switching

Author

Listed:
  • Durga Prasad Khanal

    (Tribhuvan University)

  • Urmila Pyakurel

    (Tribhuvan University)

  • Tanka Nath Dhamala

    (Tribhuvan University)

  • Stephan Dempe

    (TU Bergakademie Freiberg)

Abstract

The tragic circumstances caused by natural or human-made (unexpected human or technological errors) hazard such as earthquakes, floods, glaciers, fires or industrial explosions causing significant physical damages, loss of lives or destruction of environment as well as economic and social life of people are known as disasters. Planned evacuation is essential to save the maximum number of evacuees in minimum time, which also helps in minimize losses. Due to mass dispatch (movement) of people aftermath of disaster, traffic scenario at the intersection of roads may create the disappointing situation if the vehicles have to wait for hours to cross the intersection. The main reason behind this is the lack of crossing elimination. In this paper, we discuss the partial switching property on an abstract network, in which crossing effect of roads is eliminated to transship optimal flow of evacuees. Due to the switching property, crossing of the flows at the intersections is diverted to non-crossing sides which can be a milestone to smooth the flows during evacuation. We present polynomial time solution procedures to solve abstract maximum static and dynamic flow problems with partial switching of paths. We also introduce the abstract quickest flow and quickest contraflow problems with partial switching and present polynomial time algorithms to solve the problems. For disaster management, maximum, quickest and contraflow problems on partially switched paths play an important role as the flow on a path system without crossing effect is very essential during evacuation process.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:4:d:10.1007_s43069-022-00168-2
    DOI: 10.1007/s43069-022-00168-2
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    References listed on IDEAS

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    1. Urmila Pyakurel & Stephan Dempe, 2021. "Universal Maximum Flow with Intermediate Storage for Evacuation Planning," Springer Optimization and Its Applications, in: Ilias S. Kotsireas & Anna Nagurney & Panos M. Pardalos & Arsenios Tsokas (ed.), Dynamics of Disasters, pages 229-241, Springer.
    2. 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.
    3. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    4. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    5. Andrew V. Goldberg & Robert E. Tarjan, 1990. "Finding Minimum-Cost Circulations by Successive Approximation," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 430-466, August.
    6. Omkar Achrekar & Chrysafis Vogiatzis, 2018. "Evacuation Trees with Contraflow and Divergence Considerations," Springer Optimization and Its Applications, in: Ilias S. Kotsireas & Anna Nagurney & Panos M. Pardalos (ed.), Dynamics of Disasters, pages 1-46, Springer.
    7. Urmila Pyakurel & Stephan Dempe, 2020. "Network Flow with Intermediate Storage: Models and Algorithms," SN Operations Research Forum, Springer, vol. 1(4), pages 1-23, December.
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