Polyhedral properties of the network restoration problem-with the convex hull of a special case

The network restoration problem is a specialized capacitated network design problem in which spare capacity must be installed in a network to fully restore disrupted demands in the event of any link failure. We consider the installation of spare capacity using a single type of capacitated facility. The problem is to determine the number of facilities to be installed on the edges of the network so that it is capable of routing point-to-point traffic when any single edge fails. This paper develops a new family of facets for an integer programming formulation for the problem and shows that these facets completely characterize the convex hull of feasible integer solutions for a special case, the parallel path network restoration problem, which arises in larger networks if we aggregate nodes.

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