In this paper, we challenge the issue of resource management and scheduling in the grid context, which is compliant with WS-Resource Framework. Firstly, we focus on the high performance application, and model the large-scale scientific computing problem that can be decomposed into multiple sub-problems, which evolves to be represented by a DAG. Then, a hierarchical infrastructure for resource management in the grid context is proposed in accordance with the specifications of WS-Resource Framework. Thirdly, we discuss the scheduling issue in the presented scenario and present a modification of the DLS algorithm. At last we analyze the presented modified algorithm with simulation experiments.