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A dynamic discrete network design problem for maintenance planning in traffic networks

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  • Pirmin Fontaine

    (Technical University of Munich)

  • Stefan Minner

    (Technical University of Munich)

Abstract

We propose a dynamic model for network maintenance planning by extending the Discrete Network Design Problem. The leader decides which road in the network is maintained in which period and the follower, as in the Discrete Network Design Problem, optimizes its own path through the network. The non-linear bilevel problem is first linearized and then transformed into a single-level mixed-integer program by using the Karush–Kuhn–Tucker conditions. This model is solved with Benders Decomposition. The numerical study shows that this method finds better solutions faster compared to solving the mixed-integer formulation directly and using a genetic algorithm. Furthermore, we show the benefit of this approach compared to simple greedy heuristics.

Suggested Citation

  • Pirmin Fontaine & Stefan Minner, 2017. "A dynamic discrete network design problem for maintenance planning in traffic networks," Annals of Operations Research, Springer, vol. 253(2), pages 757-772, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:2:d:10.1007_s10479-016-2171-y
    DOI: 10.1007/s10479-016-2171-y
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    References listed on IDEAS

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    Cited by:

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    5. Klavžar, Sandi & Azubha Jemilet, D. & Rajasingh, Indra & Manuel, Paul & Parthiban, N., 2018. "General Transmission Lemma and Wiener complexity of triangular grids," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 115-122.
    6. Fontaine, Pirmin & Minner, Stefan, 2018. "Benders decomposition for the Hazmat Transport Network Design Problem," European Journal of Operational Research, Elsevier, vol. 267(3), pages 996-1002.
    7. David Rey & Hillel Bar-Gera & Vinayak V. Dixit & S. Travis Waller, 2019. "A Branch-and-Price Algorithm for the Bilevel Network Maintenance Scheduling Problem," Transportation Science, INFORMS, vol. 53(5), pages 1455-1478, September.

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