Multicommodity Flow Problem with Variable Arcs Capacities

The problem of maximizing the sum of the flows of all commodities in a network where the capacities of some arcs can be increased by integer numbers within a fixed budget is solved in this paper. Benders' technique is used to decompose the problem. Then Rosen's primal partitioning and non-linear duality theory are used to solve the subproblems generated by the Benders' decomposition. An application of a multicommodity network to the defence problem is mentioned.