Mathematical Programming

, Volume 157, Issue 1, pp 297–342 | Cite as

Single-commodity robust network design with finite and Hose demand sets

  • Valentina Cacchiani
  • Michael Jünger
  • Frauke Liers
  • Andrea Lodi
  • Daniel R. SchmidtEmail author
Full Length Paper Series B


We study a single-commodity robust network design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of scenarios or as a polytope. We propose a branch-and-cut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming formulation. It is strengthened with valid inequalities derived as \(\{0,\frac{1}{2}\}\)-Chvátal–Gomory cuts. Since the formulation contains exponentially many constraints, we provide practical separation algorithms. Extensive computational experiments show that our approach is effective, in comparison to existing approaches from the literature as well as to solving a flow based formulation by a general purpose solver.


Robust network design Branch-and-cut Cut-set inequalities Polyhedral demand uncertainty Separation under uncertainty 

Mathematics Subject Classification

90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 90C90 Applications of mathematical programming  90B10 Network models, deterministic 90C27 Combinatorial optimization 90C11 Mixed integer programming 



We thank two anonymous reviewers for their valuable comments and are grateful to the Ateneo Italo-Tedesco VIGONI program for its financial support. The authors would like to acknowledge networking support by the COST Action TD1207, in particular, this work was supported by a STSM Grant from COST Action TD1207. We thank the DFG for their support within Project B06 in CRC TRR 154.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  1. 1.DEIUniversity of BolognaBolognaItaly
  2. 2.Institut für InformatikUniversität zu KölnCologneGermany
  3. 3.Department MathematikFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany
  4. 4.École Polytechnique de MontréalQuébecCanada

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