Partition inequalities for capacitated survivable network design based on directed p-cycles

Partition inequalities for capacitated survivable network design based on directed p-cycles

We study the design of capacitated survivable networks using directed p-cycles. A p-cycle is a cycle with at least three arcs, used for rerouting disrupted flow during edge failures. Survivability of the network is accomplished by reserving sufficient slack on directed p-cycles so that if an edge fails, its flow can be rerouted along the p-cycles. We describe a model for designing capacitated s...

Strong inequalities for capacitated survivable network design problems

We present several classes of facet-deening inequalities to strengthen polyhedra arising as subsystems of network design problems with survivability constraints. These problems typically involve assigning capacities to a network with multicommodity demands, such that after a vertex-or edge-deletion at least some prescribed fraction of each demand can be routed.

A directed cycle-based column-and-cut generation method for capacitated survivable network design

A network is said to be survivable if it has sufficient capacity for rerouting all of its flow under the failure of any one of its edges. Here we present a polyhedral approach for designing survivable networks. We describe a mixed–integer programming model, in which sufficient slack is explicitly introduced on the directed cycles of the network while flow routing decisions are made. In case of ...

On cut-based inequalities for capacitated network design polyhedra

In this article we study capacitated network design problems. We unify and extend poly-hedral results for directed, bidirected and undirected link capacity models. Based on validinequalities for a network cut we show that regardless of the link capacity model, facets of thepolyhedra associated with such a cut translate to facets of the original network design polyhedraif the...

Survivable network design: the capacitated minimum spanning network problem