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Stochastic survivable network design problems: theory and practice. (English) Zbl 1394.90450
Summary: We study survivable network design problems with edge-connectivity requirements under a two-stage stochastic model with recourse and finitely many scenarios. For the formulation in the natural space of edge variables we show that facet defining inequalities of the underlying polytope can be derived from the deterministic counterparts. Moreover, by using graph orientation properties we introduce stronger cut-based formulations. For solving the proposed mixed integer programming models, we suggest a two-stage branch & cut algorithm based on a decomposed model. In order to accelerate the computations, we suggest a new technique for strengthening the decomposed L-shaped optimality cuts which is computationally fast and easy to implement. A computational study shows the benefit of the decomposition and the cut strengthening – which significantly reduces the number of master iterations and the computational running time. Moreover, we evaluate the stability of the scenario generation method and analyze the value of the stochastic solution.

##### MSC:
 90C15 Stochastic programming 90C11 Mixed integer programming 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 90B10 Deterministic network models in operations research 90C27 Combinatorial optimization
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