Minimum cost paths over dynamic networks

Flows over time problems relate to finding optimal flows over a capacitated network where transit times on network arcs are explicitly considered. In this paper we study the problem of determining a minimum cost source-destination path where the cost of one arc depends on the time taken to travel from s to that particular arc along the path. We provide a computational complexity characterization for this problem and an exact solution algorithm based on an enumeration scheme on the corresponding time expanded network.