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The continuous maximum capacity path interdiction problem

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  • Tayyebi, Javad
  • Mitra, Ankan
  • Sefair, Jorge A.

Abstract

This paper studies the continuous maximum capacity path interdiction problem, where two players, user and interdictor, compete in a capacitated network. The user wants to send the maximum possible amount of flow through a path, whose capacity is given by the minimum capacity among its arcs. The budget-constrained interdictor decreases arc capacities by any continuous amount to reduce the quality of the user’s chosen path. We present an efficient algorithm based on a discrete version of the Newton’s method, which helps us solve the problem in polynomial time. We also prove that the problem can be transformed into a zero-sum game, which has always a pure Nash equilibrium point. We demonstrate the performance of our algorithm over a set of randomly generated networks.

Suggested Citation

  • Tayyebi, Javad & Mitra, Ankan & Sefair, Jorge A., 2023. "The continuous maximum capacity path interdiction problem," European Journal of Operational Research, Elsevier, vol. 305(1), pages 38-52.
    • Handle: RePEc:eee:ejores:v:305:y:2023:i:1:p:38-52
    DOI: 10.1016/j.ejor.2022.05.028
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    References listed on IDEAS

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