This paper presents some new results on homogeneous multi-processor scheduling. Given the lengths, precedences and speedup functions of a set of tasks, the optimal scheduling problem is to determine the number of processors assigned to each task and the task sequencing to minimize the completion time. We show that the problem is tractable through the techniques of continuous optimization in many cases, that it includes intractable combinatorial complexity in the other cases and that the continuous optimization can produce a schedule which is within 4/3 times the length of the optimal non-preemptive schedule. We propose a heuristic method for further possible improvement. Finally, we show that the completion time is very close after the optimal integer perturbation.