We study the order scheduling problem under the non-identical parallel machines environment in the fully flexible case. Our goal is to minimize total order completion time and the decision is to assign all jobs to all machines. We first show two lemmas for optimal solution and separate our problem into two stages based on these lemmas. Then, we develop a series of two-stage heuristics to solve our problem. Finally, we implement numerical studies to verify the performance of our heuristics, and find out several factors that influence the performance of heuristics.