The nested partitions (NP) method has been proven to be a useful framework for effectively solving large-scale discrete optimization problems. In this chapter, we provide a brief review of the NP method and its applications. We then present a hybrid algorithm that integrates mathematical programming with the NP framework. The efficiency of the hybrid algorithm is demonstrated by the intermodal hub location problem (IHLP), a class of discrete facility location problems. Computational results show that the hybrid approach is superior to the integer programming approach and the Lagrangian relaxation method.