To solve the $Pm/r_{j}, nr, FPM/(C_{\max}, NT)$ problem, a mixed integer programming (MIP) model is constructed and a modified NSGA-II algorithm (M-NSGA-II) is designed in this paper. Simulation experiment results show that for small scale problems (the number of jobs $\mathrm{n}\leq 12$), the effectiveness of MIP is better than that of M-NSGA-II and NSGA-II algorithms. For medium-to-large scale problems (the number of jobs $\mathrm{n} > 12$), although the number of pareto solutions of the NSGA-II algorithm is more than that of M-NSGA-II algorithm, the efficiency and effectiveness are inferior to that of the M-NSGA-II algorithm.