Survivable Multi-commodity Network Flow Design; Case of Node Capacities and Arc Failure

This paper was concerned with the problem of designing a survivable multicommodity network with node capacities, which is about selecting a set of fixed-charge arcs in order to build a survivable network with minimum cost and satisfied flow requirements. The system is subject to failure and capacity restriction. Failure is defined as simultaneous failure of arcs. To solve the problem, first, a mixed integer linear program was introduced. Afterward, an appropriate Benders decomposition (BD) method was developed. Then, a theorem was stated in order to obtain the optimality condition for a certain scenario. Finally, in order to reduce the number of iterations of using the BD approach, a new strategy was proposed. Using this strategy, the length of time required for solving the problem was reduced by 30%on average.