A stream multiprocessor, a GPU, and related methods are provided. The stream multiprocessor executes thread blocks. Each thread block includes warps. The stream multiprocessor includes stream processors and a local dispatcher. Each stream processor executes one or more warps. The local dispatcher includes a warp state table, a warp resource detection unit and a warp launching unit. The warp state table records dispatching states and processing states of warps of the thread blocks. The warp resource detection unit selects all the first warps of a first thread block and at least one second warp of a second thread block according to hardware resources available to the stream multiprocessor and hardware resources required for thread blocks. The warp launching unit dispatches the first warps to idle stream processors and at least one second warp to at least one idle stream processor.