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Robust network design in telecommunications under polytope demand uncertainty

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  • Lemaréchal, Claude
  • Ouorou, Adam
  • Petrou, Georgios

Abstract

We consider a model for robust network design in telecommunications, in which we minimize the cost of the maximum mismatch between supply and demand. In the present study, the demand is uncertain and takes its values in a polytope defined by constraints. This problem is hardly tractable, so we limit ourselves to computing lower bounds (by a column-generation mechanism) and upper bounds (using an algorithm due to Falk and Soland for maximizing a separable convex function over a polytope). The experimental gap obtained turns out to be large, and this seems to be mainly due to poor upper bounds. Two possible solutions are suggested for further research aimed at improving them: dc optimization (to minimize the difference of two convex functions) and AARC modeling (affinely adjustable robust counterpart).

Suggested Citation

  • Lemaréchal, Claude & Ouorou, Adam & Petrou, Georgios, 2010. "Robust network design in telecommunications under polytope demand uncertainty," European Journal of Operational Research, Elsevier, vol. 206(3), pages 634-641, November.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:3:p:634-641
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    References listed on IDEAS

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    1. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
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    Cited by:

    1. 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.
    2. 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.

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