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Efficient Algorithms for Abstract Flow with Partial Switching

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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.

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Acknowledgements

The first author (Durga Prasad Khanal) thanks to the German Academic Exchange Service - DAAD for Research Grants - Bi-nationally Supervised Doctoral Degrees/Cotutelle, 2021/22 and University Grants Commission Nepal for PhD Research Fellowship, 2020/21. Similarly, the second author (Urmila Pyakurel) thanks to the Alexander von Humboldt Foundation for Digital Cooperation Fellowship (August 1, 2021 - January 31, 2022) and fellowship for Remote Cooperation Abroad Project (March 1 - August 31, 2022).

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Authors and Affiliations

  1. Saraswati Multiple Campus, Tribhuvan University, Kathmandu, Nepal

    Durga Prasad Khanal

  2. Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal

    Urmila Pyakurel & Tanka Nath Dhamala

  3. Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

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  1. Durga Prasad Khanal
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  3. Tanka Nath Dhamala
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  4. Stephan Dempe
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Correspondence to Urmila Pyakurel.

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Khanal, D.P., Pyakurel, U., Dhamala, T.N. et al. Efficient Algorithms for Abstract Flow with Partial Switching. Oper. Res. Forum 3, 55 (2022). https://doi.org/10.1007/s43069-022-00168-2

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