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Incremental network design with maximum flows


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


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

    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.
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    Cited by:

    1. Ni, Ni & Howell, Brendan J. & Sharkey, Thomas C., 2018. "Modeling the impact of unmet demand in supply chain resiliency planning," Omega, Elsevier, vol. 81(C), pages 1-16.
    2. Averbakh, Igor & Pereira, Jordi, 2015. "Network construction problems with due dates," European Journal of Operational Research, Elsevier, vol. 244(3), pages 715-729.
    3. Chagas, Rosklin Juliano & Valle, Cristiano Arbex & da Cunha, Alexandre Salles, 2018. "Exact solution approaches for the Multi-period Degree Constrained Minimum Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 57-71.
    4. Garrett, Richard A. & Sharkey, Thomas C. & Grabowski, Martha & Wallace, William A., 2017. "Dynamic resource allocation to support oil spill response planning for energy exploration in the Arctic," European Journal of Operational Research, Elsevier, vol. 257(1), pages 272-286.
    5. Sharkey, Thomas C. & Cavdaroglu, Burak & Nguyen, Huy & Holman, Jonathan & Mitchell, John E. & Wallace, William A., 2015. "Interdependent network restoration: On the value of information-sharing," European Journal of Operational Research, Elsevier, vol. 244(1), pages 309-321.


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