Mathematical Programming

, Volume 92, Issue 2, pp 315–333

On splittable and unsplittable flow capacitated network design arc–set polyhedra

  • Alper Atamtürk
  • Deepak Rajan

DOI: 10.1007/s101070100269

Cite this article as:
Atamtürk, A. & Rajan, D. Math. Program. (2002) 92: 315. doi:10.1007/s101070100269

Abstract.

We study the polyhedra of splittable and unsplittable single arc–set relaxations of multicommodity flow capacitated network design problems. We investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them. In particular, we give a linear–time separation algorithm for the residual capacity inequalities [19] and show that the separation problem of c–strong inequalities [7] is ??–hard, but can be solved over the subspace of fractional variables only. We introduce two classes of inequalities for the unsplittable flow problems. We present a summary of computational experiments with a branch-and-cut algorithm for multicommodity flow capacitated network design problems to test the effectiveness of the results presented here empirically.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alper Atamtürk
    • 1
  • Deepak Rajan
    • 1
  1. 1.Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA, e-mail: {atamturk, deepak}@ieor.berkeley.eduUS

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