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The Robust Network Loading Problem with Dynamic Routing

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  • Sara Mattia

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

Abstract

The Robust Network Loading Problem (RNL) can be stated as follows. Given a graph and a set of traffic matrices, install minimum cost integer capacities on the edges such that all the matrices can be routed non simultaneously on the network. The routing scheme is said to be dynamic if we can choose a (possibly) different routing for every matrix, it is called static if the routing must be the same for all the matrices. The flows are unsplittable if each point-to-point demand (commodity) must use a single path, they are splittable if the flow for every commodity can be splitted along several paths. In this paper we present the first exact approach for solving the RNL problem with splittable flows and dynamic routing under polyhedral uncertainty for the demands. A branch-and-cut algorithm based on the capacity formulation of the problem defined by metric inequalities is developed, and polyhedral results are given. The separation problem is formulated as a bilevel programming problem and a corresponding single level problem is derived. Computational results are presented.

Suggested Citation

  • Sara Mattia, 2010. "The Robust Network Loading Problem with Dynamic Routing," DIS Technical Reports 2010-03, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:wpaper:2010-3
    as

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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2010-03.pdf
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    3. Sara Mattia, 2010. "Solving Survivable Two-Layer Network Design Problems by Metric Inequalities," DIS Technical Reports 2010-02, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. 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.
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    Cited by:

    1. Chungmok Lee & Kyungsik Lee & Kyungchul Park & Sungsoo Park, 2012. "Technical Note---Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations," Operations Research, INFORMS, vol. 60(3), pages 604-610, June.

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