Study on Capacity Expansion Problems on Maximum Flow

This article studies capacity expansion problems on maximum flow. The capacity expansion problems can be described as: how can the network capacity be increased as much as possible with a minimum total cost? In view of three types of expanding models: the node-expanding model, the arc- expanding model, the combination of the arc-expanding and node-expanding model; we discuss the characteristics of the problems separately. Considering the upper bound of the expansion capacity caused by every node or arc, we also present a unified capacity expansion formulation. Finally, an example is provided in detail.