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Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period

Author

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  • Natashia Boland

    (University of Newcastle
    Georgia Institute of Technology)

  • Thomas Kalinowski

    (University of Newcastle)

  • Simranjit Kaur

    (University of Newcastle)

Abstract

We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard, and several special instance classes have been studied. Here we propose an additional constraint which limits the number of maintenance jobs per time period, and we study the impact of this on the complexity.

Suggested Citation

  • Natashia Boland & Thomas Kalinowski & Simranjit Kaur, 2016. "Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 885-905, October.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9910-x
    DOI: 10.1007/s10878-015-9910-x
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    References listed on IDEAS

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    1. Ronald Koch & Ebrahim Nasrabadi & Martin Skutella, 2011. "Continuous and discrete flows over time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(3), pages 301-337, June.
    2. Baxter, Matthew & Elgindy, Tarek & Ernst, Andreas T. & Kalinowski, Thomas & Savelsbergh, Martin W.P., 2014. "Incremental network design with shortest paths," European Journal of Operational Research, Elsevier, vol. 238(3), pages 675-684.
    3. Kalinowski, Thomas & Matsypura, Dmytro & Savelsbergh, Martin W.P., 2015. "Incremental network design with maximum flows," European Journal of Operational Research, Elsevier, vol. 242(1), pages 51-62.
    4. Nurre, Sarah G. & Cavdaroglu, Burak & Mitchell, John E. & Sharkey, Thomas C. & Wallace, William A., 2012. "Restoring infrastructure systems: An integrated network design and scheduling (INDS) problem," European Journal of Operational Research, Elsevier, vol. 223(3), pages 794-806.
    5. Mohit Tawarmalani & Yanjun Li, 2011. "Multi‐period maintenance scheduling of tree networks with minimum flow disruption," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 507-530, August.
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    Cited by:

    1. Mehryar, Mehdi & Hafezalkotob, Ashkan & Azizi, Amir & Sobhani, Farzad Movahedi, 2023. "Dynamic zoning of the network using cooperative transmission and maintenance planning: A solution for sustainability of water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 235(C).

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