AND/OR search spaces have recently been introduced as a unifying paradigm for advanced algorithmic schemes for graphical models. The main virtue of this representation is its sensitivity to the structure of the model, which can translate into exponential time savings for search algorithms. In this paper we extend the recently introduced AND/OR Branch-and-Bound algorithm  for solving 0/1 Mixed Integer Linear Programming problems. We propose a static version based on pseudo-trees, as well as a dynamic one based on hypergraph separators. Preliminary evaluation on problem instances from MIPLIB2003 shows promise that the new schemes are likely to improve over the traditional methods.