Mathematical Programming

, Volume 86, Issue 1, pp 17–39

A branch-and-cut algorithm for capacitated network design problems


  • Oktay Günlük
    • School of ORIE, Cornell University, Ithaca, New York, e-mail: Current Address: NDPA Department, AT&T Labs. Middletown, NJ 07748, e-mail:

DOI: 10.1007/s101070050077

Cite this article as:
Günlük, O. Math. Program. (1999) 86: 17. doi:10.1007/s101070050077


We present a branch-and-cut algorithm to solve capacitated network design problems. Given a capacitated network and point-to-point traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so that the overall cost is minimized. We study a mixed-integer programming formulation of the problem and identify some new facet defining inequalities. These inequalities, together with other known combinatorial and mixed-integer rounding inequalities, are used as cutting planes. To choose the branching variable, we use a new rule called “knapsack branching”. We also report on our computational experience using real-life data.

Key words: mixed-integer programming – branch-and-cut – computing
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© Springer-Verlag Berlin Heidelberg 1999