A Hybrid CP-LP Method for a Shortest Path Routing Problem Abstract: We consider a network routing problem, where the task is to decide paths for known data flows in such a way that the network capacity is not exceeded in any part of the network. We address the case where a shortest path routing protocol (e.g. OSPF) is used, which constrains the set of paths that can be used for different flows. We will present a CP/LP hybrid solution for this problem, where a CP-based approach is used for constraining the set of allowed paths, and an LP relaxation is used to deal with capacity constraints.