Solving Two-Stage Stochastic Steiner Tree Problems by Two-Stage Branch-and-Cut

  • Immanuel Bomze
  • Markus Chimani
  • Michael Jünger
  • Ivana Ljubić
  • Petra Mutzel
  • Bernd Zey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6506)

Abstract

We consider the Steiner tree problem under a 2-stage stochastic model with recourse and finitely many scenarios (SSTP). Thereby, edges are purchased in the first stage when only probabilistic information on the set of terminals and the future edge costs is known. In the second stage, one of the given scenarios is realized and additional edges are purchased to interconnect the set of (now known) terminals. The goal is to choose an edge set to be purchased in the first stage while minimizing the overall expected cost of the solution.

We provide a new semi-directed cut-set based integer programming formulation that is stronger than the previously known undirected model. To solve the formulation to provable optimality, we suggest a two-stage branch-and-cut framework, facilitating (integer) L-shaped cuts. The framework itself is also applicable to a range of other stochastic problems.

As SSTP has yet been investigated only from the theoretical point of view, we also present the first computational study for SSTP, showcasing the applicability of our approach and its benefits over solving the extensive form of the deterministic equivalent directly.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Immanuel Bomze
    • 1
  • Markus Chimani
    • 2
  • Michael Jünger
    • 3
  • Ivana Ljubić
    • 1
  • Petra Mutzel
    • 4
  • Bernd Zey
    • 4
  1. 1.Faculty of Business, Economics and StatisticsUniversity of ViennaAustria
  2. 2.Institute of Computer ScienceFriedrich-Schiller-University of JenaGermany
  3. 3.Department of Computer ScienceUniversity of CologneGermany
  4. 4.Department of Computer ScienceTU DortmundGermany

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