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The robust network loading problem with dynamic routing

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  • Sara Mattia

Abstract

In this paper the Robust Network Loading problem with splittable flows and dynamic routing under polyhedral uncertainty for the demands is considered. Polyhedral results for the capacity formulation of the problem are given. The first exact approach for solving the problem is presented. A branch-and-cut algorithm based on the proposed capacity formulation is developed. Computational results using the hose polyhedron to model the demand uncertainty are discussed. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Sara Mattia, 2013. "The robust network loading problem with dynamic routing," Computational Optimization and Applications, Springer, vol. 54(3), pages 619-643, April.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:3:p:619-643
    DOI: 10.1007/s10589-012-9500-0
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    References listed on IDEAS

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    1. Gianpaolo Oriolo, 2008. "Domination Between Traffic Matrices," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 91-96, February.
    2. Sara Mattia, 2012. "Solving survivable two-layer network design problems by metric inequalities," Computational Optimization and Applications, Springer, vol. 51(2), pages 809-834, March.
    3. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
    4. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
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    Cited by:

    1. Josette Ayoub & Michael Poss, 2016. "Decomposition for adjustable robust linear optimization subject to uncertainty polytope," Computational Management Science, Springer, vol. 13(2), pages 219-239, April.
    2. Siqian Shen & Mingdi You & Yintai Ma, 2017. "Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(2), pages 154-173, March.
    3. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    4. Artur Alves Pessoa & Michael Poss, 2015. "Robust Network Design with Uncertain Outsourcing Cost," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 507-524, August.
    5. Álvarez-Miranda, Eduardo & Cacchiani, Valentina & Lodi, Andrea & Parriani, Tiziano & Schmidt, Daniel R., 2014. "Single-commodity robust network design problem: Complexity, instances and heuristic solutions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 711-723.
    6. Sara Mattia & Michael Poss, 2018. "A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation," Computational Optimization and Applications, Springer, vol. 69(3), pages 753-800, April.
    7. Christina Büsing & Arie M. C. A. Koster & Sabrina Schmitz, 2022. "Robust minimum cost flow problem under consistent flow constraints," Annals of Operations Research, Springer, vol. 312(2), pages 691-722, May.

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