In this work, we consider the Delay Constrained Unsplittable Shortest Path Routing problem which arises in the field of traffic engineering for IP networks. This problem consists, given a directed graph and a set of commodities, to compute a set of routing paths and the associated administrative weights such that each commodity is routed along the unique shortest path between its origin and its destination, according to these weights. We propose two exact algorithms to solve the problem. First, we present a compact MILP formulation for the problem, extending the work in [A. Bley (2011), A. Bley, B. Fortz, E. Gourdin, K. Holmberg, O. Klopfenstein, M. Pióro, A.Tomaszewski, and H. Ümit (2010)] along with some valid inequalities to strengthen its linear relaxation. Then, we further propose a dynamic programming algorithm based on a tree decomposition of the graph. To the best of our knowledge, this is the first exact combinatorial algorithm for the problem. Finally, we outline the main steps of an hybrid exact algorithm combining both approaches.