Mathematical Programming

, Volume 157, Issue 1, pp 297–342

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

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

DOI: 10.1007/s10107-016-0991-9

Cite this article as:
Cacchiani, V., Jünger, M., Liers, F. et al. Math. Program. (2016) 157: 297. doi:10.1007/s10107-016-0991-9

Abstract

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.

Keywords

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 

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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