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

Shahram Morowati-Shalilvand (), Sedaghat Shahmorad (), Kamal Mirnia () and Javad Mehri-Tekmeh ()
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Shahram Morowati-Shalilvand: University of Tabriz
Sedaghat Shahmorad: University of Tabriz
Kamal Mirnia: University of Tabriz
Javad Mehri-Tekmeh: University of Tabriz

Operational Research, 2021, vol. 21, issue 2, No 16, 1179-1209

Abstract: 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.

Keywords: Quickest flow; Network interdiction; Flows over time; Mixed integer programming (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s12351-019-00472-6

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