This work presents a two-stage ordinal optimization theory-based approach for solving the throughput maximization problems with power constraints of sub-carrier assignment and power allocation in multi-user orthogonal frequency division multiplexing uplink systems. In the first stage, a crude but efficient model is employed to evaluate the performance of a sub-carrier assignment pattern and the genetic algorithm is used to search through the huge solution space. In the second stage, an exact model is employed to evaluate s best sub-carrier assignment patterns obtained in stage 1 and form the select subset. Finally, the best one of the select subset is the good enough solution that we seek. Via numerous tests, this work demonstrates the efficiency of the proposed algorithm and compares it with those of other heuristic methods.