Research on Network Max-flow Pareto Expansion Problem

The network capacity is defined as the value of the maximum s-t flow, and a unified model is introduced for the network capacity expansion with the time and cost constraints. By the transformation of the underlying network, the network capacity is converted to a minimum cost flow problem instead. Also developed are the algorithm to find all pareto optimal solutions about time and cost with given expanded network max-flow. The model and algorithm are proven to be valid with an example, and they not only allow capturing various types of capacity expansion, but also are useful in network programming.