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Quickest flow over time network interdiction: mathematical formulation and a solution method

Author

Listed:
  • Shahram Morowati-Shalilvand

    (University of Tabriz)

  • Sedaghat Shahmorad

    (University of Tabriz)

  • Kamal Mirnia

    (University of Tabriz)

  • Javad Mehri-Tekmeh

    (University of Tabriz)

Abstract

This paper proposes a new problem entitled as “the quickest flow over time network interdiction problem”. This problem stands for removing some of network links using a limited interdiction resource with the aim of maximizing the minimum time required to transfer a predefined flow value through a given network. We formulate the quickest flow problem as a linear fractional programming problem and then, we transform it to a linear formulation. Using the linear formulation of the quickest flow problem we formulate the quickest flow network interdiction problem as a mixed integer linear programming problem. We also provide an improved formulation for the quickest flow network interdiction problem which is computationally more efficient than basic linear formulation. Finally, we apply the basic and improved formulations of the quickest flow network interdiction problem on a real world network and several grid networks.

Suggested Citation

  • Shahram Morowati-Shalilvand & Sedaghat Shahmorad & Kamal Mirnia & Javad Mehri-Tekmeh, 2021. "Quickest flow over time network interdiction: mathematical formulation and a solution method," Operational Research, Springer, vol. 21(2), pages 1179-1209, June.
    • Handle: RePEc:spr:operea:v:21:y:2021:i:2:d:10.1007_s12351-019-00472-6
    DOI: 10.1007/s12351-019-00472-6
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    References listed on IDEAS

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