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Network Reconfiguration with Orientation‐Dependent Transit Times

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  • Hari Nandan Nath
  • Urmila Pyakurel
  • Tanka Nath Dhamala

Abstract

Motivated by applications in evacuation planning, we consider a problem of optimizing flow with arc reversals in which the transit time depends on the orientation of the arc. In the considered problems, the transit time on an arc may change when it is reversed, contrary to the problems considered in the existing literature. Extending the existing idea of auxiliary network construction to allow asymmetric transit time on arcs, we present strongly polynomial time algorithms for solving single‐source‐single‐sink maximum dynamic contraflow problem and quickest contraflow problem. The results are substantiated by a computational experiment in a Kathmandu road network. An algorithm to solve the corresponding earliest arrival contraflow problem with a pseudo‐polynomial‐time complexity is also presented. The partial contraflow approach for the corresponding problems has also been discussed.

Suggested Citation

  • Hari Nandan Nath & Urmila Pyakurel & Tanka Nath Dhamala, 2021. "Network Reconfiguration with Orientation‐Dependent Transit Times," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jijmms:v:2021:y:2021:i:1:n:6613622
    DOI: 10.1155/2021/6613622
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    References listed on IDEAS

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    1. Urmila Pyakurel & Hari Nandan Nath & Stephan Dempe & Tanka Nath Dhamala, 2019. "Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    2. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    3. Ram Chandra Dhungana & Tanka Nath Dhamala, 2020. "Flow Improvement in Evacuation Planning with Budget Constrained Switching Costs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-10, June.
    4. W. L. Wilkinson, 1971. "An Algorithm for Universal Maximal Dynamic Flows in a Network," Operations Research, INFORMS, vol. 19(7), pages 1602-1612, December.
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    Cited by:

    1. Durga Prasad Khanal & Urmila Pyakurel & Stephan Dempe, 2025. "Temporally Repeated Maximum Dynamic Flow with Intermediate Storage," SN Operations Research Forum, Springer, vol. 6(3), pages 1-27, September.

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