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 a failure, flow is rerouted along the slacks reserved on directed cycles. We give strong valid inequalities that use the survivability requirements. We present a computational study with a column–and–cut generation algorithm for designing capacitated survivable networks. October 2002, April 2003