In this paper, we propose the first optimum process scheduling algorithm for an increasingly prevalent type of heterogeneous multicore (HEMC) system that combines high-performance big cores and energy-efficient small cores with the same instruction-set architecture (ISA). Existing algorithms are all heuristics-based, and the well-known IPC-driven approach essentially tries to schedule high scaling factor processes on big cores. Our analysis shows that, for optimum solutions, it is also critical to consider placing long running processes on big cores. Tests of SPEC 2006 cases on various big-small core combinations show that our proposed optimum approach is up to 34% faster than the IPC-driven heuristic approach in terms of total workload completion time. The complexity of our algorithm is O(NlogN) where N is the number of processes. Therefore, the proposed optimum algorithm is practical for use.