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

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 fi...

• Type: Journal
• Year: 2010
• Where: ISAAC
• Authors: Immanuel M. Bomze, Markus Chimani, Michael Jünger, Ivana Ljubic, Petra Mutzel, Bernd Zey
• Keywords: 2-stage Stochastic Model, Algorithms, Future Edge Costs, ISAAC 2010, Steiner Tree Problem