The Budget-Constrained Maximum Flow Problem

An interesting application of Cmfp is for the case when the capacities of the arcs in the network are not fixed but can be increased at certain costs per unit (see e.g. [Ful59, KNR98, SK98]). One is allowed to spend a certain budget for raising capacities and wishes to maximize the throughput. This network improvement problem can be formulated as an instance of Cmfp where the cost functions on the arcs are piecewise linear. Observing that the cost functions are also convex and using techniques described in [AMO93] the problem can be reformulated as an instance of Cmfp with linear costs.