Skip to main content
SpringerLink
Log in

Saving a path minimizing egress time of a dynamic contraflow: a bi-objective programming approach

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

Reversing the direction of traffic flow in necessary road segments is an important strategy to optimize the flow, especially, in an emergency evacuation. The configuration may, however, block the paths toward the source. Sometimes, it may be necessary to save a path for some facility movements from a specific node towards the source. We consider such a problem as a biobjective optimization problem that minimizes the length of the saved path and the egress time of the given amount of flow. An algorithm based on the \(\epsilon\)-constraint method is proposed to find the non-dominated solutions and its computational performance has been tested on a road network of Kathmandu city and randomly generated networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Luan, S., Yang, Q., Zhou, H., Jiang, Z., Wang, W., Wang, Z., Chu, R.: The HSABA for emergency location-routing problem. Math. Probl. Eng. 2019, 1–12 (2019)

    Article  Google Scholar 

  2. Caunhye, A.M., Zhang, Y., Li, M., Nie, X.: A location-routing model for prepositioning and distributing emergency supplies. Trans. Res. Part E Log. Transp. Rev. 90, 161–176 (2016)

    Article  Google Scholar 

  3. Köhler, E., Langkau, K., Skutella, M.: Time-expanded graphs for flow-dependent transit times. In: European symposium on algorithms, pp. 599–611. Springer, (2002)

  4. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice hall, New Jersey (1993)

    Google Scholar 

  5. Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Oper. Res. 6, 419–433 (1958)

    Article  MathSciNet  Google Scholar 

  6. Baumann, N., Skutella, M.: Earliest arrival flows with multiple sources. Math. Oper. Res. 34(2), 499–512 (2009)

    Article  MathSciNet  Google Scholar 

  7. Burkard, R.E., Dlaska, K., Klinz, B.: The quickest flow problem. Z. Oper. Res. 37(1), 31–58 (1993)

    MathSciNet  Google Scholar 

  8. Hamacher, H.W., Tjandra, S.A.: Mathematical modelling of evacuation problems: a state of art (2001)

  9. Kim, S., Shekhar, S., Min, M.: Contraflow transportation network reconfiguration for evacuation route planning. IEEE Trans. Knowl. Data Eng. 20(8), 1115–1129 (2008)

    Article  Google Scholar 

  10. Rebennack, S., Arulselvan, A., Elefteriadou, L., Pardalos, P.M.: Complexity analysis for maximum flow problems with arc reversals. J. Comb. Optim. 19(2), 200–216 (2010)

    Article  MathSciNet  Google Scholar 

  11. Pyakurel, U., Dhamala, T.N.: Models and algorithms on contraflow evacuation planning network problems. Int. J. Op. Res. 12(2), 36–46 (2015)

    MathSciNet  Google Scholar 

  12. Pyakurel, U., Nath, H.N., Dhamala, T.N.: Partial contraflow with path reversals for evacuation planning. Ann. Oper. Res. 283(1–2), 591–612 (2019)

    Article  MathSciNet  Google Scholar 

  13. Ford, L.R., Fulkerson, D.R.: Flows in networks. Princeton University Press, New Jersey (1962)

    Google Scholar 

  14. Fleischer, L., Tardos, É.: Efficient continuous time dynamic network flow algorithms. Oper. Res. Lett. 23(3), 71–80 (1998)

    Article  MathSciNet  Google Scholar 

  15. Lin, M., Jaillet, P.: On the quickest flow problem in dynamic networks: a parametric min-cost flow approach, in: Proceedings of the twenty-sixth annual ACM-SIAM symposium on discrete algorithms, pp. 1343–1356. Society for Industrial and Applied Mathematics (2015)

  16. Saho, M., Shigeno, M.: Cancel-and-tighten algorithm for quickest flow problems. Networks 69(2), 179–188 (2017)

    Article  MathSciNet  Google Scholar 

  17. Dhamala, T.N., Pyakurel, U., Dempe, S.: A critical survey on the network optimization algorithms for evacuation planning problems. Int. J. Op. Res. 15(3), 101–133 (2018)

    MathSciNet  Google Scholar 

  18. Pyakurel, U., Nath, H.N., Dempe, S., Dhamala, T.N.: Efficient dynamic flow algorithms for evacuation planning problems with partial lane reversal. Mathematics 7(10), 993 (2019)

    Article  Google Scholar 

  19. Nath, H.N., Pyakurel, U., Dhamala, T.N.: Network reconfiguration with orientation-dependent transit times. Int. J. Math. Math. Sci. (2021). https://doi.org/10.1155/2021/6613622

    Article  MathSciNet  Google Scholar 

  20. Hamacher, H.W., Heller, S., Rupp, B.: Flow location (FlowLoc) problems: dynamic network flow and location models for evacuation planning. Ann. Oper. Res. 207(1), 161–180 (2013)

    Article  MathSciNet  Google Scholar 

  21. Heller, S., Hamacher, H.W.: The multi terminal q-FlowLoc problem: A heuristic. In: International conference on network optimization, pp. 523–528 (2011). Springer

  22. Dhungana, R.C., Dhamala, T.N.: Maximum FlowLoc problems with network reconfiguration. Int. J. Op. Res. 16(1), 13–26 (2019)

    MathSciNet  Google Scholar 

  23. Nath, H.N., Pyakurel, U., Dhamala, T.N., Dempe, S.: Dynamic network flow location models and algorithms for quickest evacuation planning. J. Ind. Manag. Optim. (2020). https://doi.org/10.3934/jimo.2020102

    Article  Google Scholar 

  24. Nath, H.N.: Optimization models and algorithms for evacuation plannning. Ph.d thesis, IOST, Tribhuvan Univeristy, Kathmandu, Nepal (2020)

  25. Nath, H.N., Dempe, S., Dhamala, T.N.: A bicriteria approach for saving a path maximizing dynamic contraflow. Asia-Pacific J. Oper. Res. (2021). https://doi.org/10.1142/S0217595921500275

    Article  Google Scholar 

  26. Nath, H.N., Pyakurel, U., Dempe, S., Dhamala, T.N.: Saving a path and maximizing dynamic contraflow: a bilevel programming approach. GANIT J. Bangladesh Math. Soc. 42(1), 010–024 (2022)

    Article  MathSciNet  Google Scholar 

  27. Apostol, T.M.: Mathematical Analysis, 2nd edn. Addison-Wesley Publishing Company Inc, Boston (1974)

    Google Scholar 

  28. Skutella, M.: An introduction to network flows over time. In: Research trends in combinatorial optimization, pp. 451–482. Springer, Berlin (2009)

  29. Pyakurel, U., Nath, H.N., Dhamala, T.N.: Efficient contraflow algorithms for quickest evacuation planning. Science China Math. 61(11), 2079–2100 (2018)

    Article  MathSciNet  Google Scholar 

  30. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2005)

    Google Scholar 

  31. Torres, F.E.: Linearization of mixed-integer products. Math. Program. 49(1), 427–428 (1990)

    Article  MathSciNet  Google Scholar 

  32. Vogiatzis, C., Yoshida, R., Aviles-Spadoni, I., Imamoto, S., Pardalos, P.M.: Livestock evacuation planning for natural and man-made emergencies. Int. J. Mass Emerg. Disasters 31(1), 25–37 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

The second author (Tanka Nath Dhamala) highly acknowledges the periodic research supports (including June 1 - August 31, 2023 at TU Bergakademie Freiberg) of the Alexander von Humboldt Foundation. We are also thankful to anonymous reviewers for their constructive suggestions to enhance the quality of this work.

Author information

Authors and Affiliations

  1. Department of Mathematics, Tribhuvan University, Bhaktapur Multiple Campus, Dhudhpati, Bhaktapur, Nepal

    Hari Nandan Nath

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

    Tanka Nath Dhamala

  3. Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Stephan Dempe

Authors
  1. Hari Nandan Nath
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tanka Nath Dhamala
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephan Dempe
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

HNN, TND, and SD conceptualized the research problem. HNN carried out the formal analysis, write-up of the manuscript, programming, and data analysis under the supervision of TND and SD. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Tanka Nath Dhamala.

Ethics declarations

Conflict of interest

The authors declare that they have no competing interests.

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nath, H.N., Dhamala, T.N. & Dempe, S. Saving a path minimizing egress time of a dynamic contraflow: a bi-objective programming approach. OPSEARCH 61, 98–120 (2024). https://doi.org/10.1007/s12597-023-00690-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-023-00690-9

Keywords

Mathematics Subject Classification

Search

Navigation