Time-Expanded Networks, built by considering the vertices of a base network over some time space, are powerful modeling tools for optimization problems that simultaneously involve resource assignment and scheduling. However deriving algorithms from resulting models is most often difficult. We address here this algorithmic issue while referring to a multi-commodity flow model related to a relocation problem. We propose a generic Project and Lift decomposition scheme and focus on the Lift issue, concerning the way a solution defined on the base network may be turned into a solution of the whole problem. We propose several approaches and perform numerical experiments.