In this paper a new heuristic algorithm has been developed and presented for minimizing the total completion time of a scheduling problem in a multi stage automated machining and assembly systems. The proposed Higher Ratio First(HRF) algorithm is based on the idea that jobs with higher processing time ratio should be a higher priority. The heuristic algorithm is implemented on the various problem cases by number of jobs and machines. The proposed algorithm provided smaller makespan than the makespan applied by three previously documented heuristics. The results obtained show a superior solution by the new heuristic over previous heuristics on all problem sizes.