Modeling of maximum flow and shortest path problems in dynamic networks

This paper considers dynamic network in which, the flow commodity is dynamically generated at a source node and dynamically consumed at a sink node and the arc-flow bounds are time dependent. Then, the maximum dynamic flow problem in such networks for a pre-specified time horizon T is defined and mathematically formulated in both arc flow and path flow presentations. By exploiting the special structure of the problem, is showed to solve the general form of the dynamic problem as a minimum cost static flow problem and the generic augmenting path algorithm is used for solving this problem.