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Incremental network design with maximum flows

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  • Kalinowski, Thomas
  • Matsypura, Dmytro
  • Savelsbergh, Martin W.P.

Abstract

We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the entire planning horizon. After presenting two mixed integer programming (MIP) formulations for this NP-complete problem, we describe several heuristics and prove performance bounds for some special cases. In a series of computational experiments, we compare the performance of the MIP formulations as well as the heuristics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:242:y:2015:i:1:p:51-62
    DOI: 10.1016/j.ejor.2014.10.003
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Ukkusuri, Satish V. & Patil, Gopal, 2009. "Multi-period transportation network design under demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 625-642, July.
    4. Burak Cavdaroglu & Erik Hammel & John Mitchell & Thomas Sharkey & William Wallace, 2013. "Integrating restoration and scheduling decisions for disrupted interdependent infrastructure systems," Annals of Operations Research, Springer, vol. 203(1), pages 279-294, March.
    5. Byung Kim & Wonkyu Kim & Byung Song, 2008. "Sequencing and scheduling highway network expansion using a discrete network design model," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 42(3), pages 621-642, September.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    2. Hongtan Sun & Thomas C. Sharkey, 2017. "Approximation guarantees of algorithms for fractional optimization problems arising in dispatching rules for INDS problems," Journal of Global Optimization, Springer, vol. 68(3), pages 623-640, July.
    3. Aybike Ulusan & Ozlem Ergun, 2018. "Restoration of services in disrupted infrastructure systems: A network science approach," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-28, February.
    4. 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.
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    8. Averbakh, Igor & Pereira, Jordi, 2015. "Network construction problems with due dates," European Journal of Operational Research, Elsevier, vol. 244(3), pages 715-729.
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    11. Andreas Bärmann & Alexander Martin & Hanno Schülldorf, 2017. "A Decomposition Method for Multiperiod Railway Network Expansion—With a Case Study for Germany," Transportation Science, INFORMS, vol. 51(4), pages 1102-1121, November.
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