Abstarct: This paper investigates a flexible flow shop scheduling problem in which the parallel machines in the first stage are considered unrelated with different technology levels. Some of these machines are multifunctional that can do several processes on jobs. Therefore, the jobs that are assigned to these machines don’t required to process in some other next stages. This problem is defined by the inspiration of a real problem, derived from the spring industry. Therefore, the jobs that are assigned to these machines don’t required to process in some other next stages. Furthermore, setup times are assumed as sequence-dependent and are need when a machine starts to process a new job. Also, in this problem addresses different release dates and machine eligibility. Three linear mathematical models baxsed on MIP is developed to solve the problem in small-sized scales. The first model was studied simultaneously with the aim of optimizing production costs and maximum completion time (Makespan). Due to the great importance of environmental issues, in the second model, the reduction of energy consumption and the reduction of production costs were studied simultaneously. In the third model, the effect of auxiliary resource constraints on production scheduling as a variable factor measured by the model was investigated with the aim of minimizing the Makespan. Since the problem is discussed in an NP-hard environment, to solve them in medium and large dimensions, mexta-heuristic algorithms NSGA-II and SPEA-II for two-objective problems and mexta-heuristic algorithms GA and SA for solving one-objective problem were proposed. The experimental results showed that all three proposed models were able to schedule jobs well considering the applied constraints. Also, by measuring the evaluation indicators, it was found that NSGA-II algorithm against SPEA-II algorithm and GA algorithm against SA algorithm had better performance and achieved more appropriate answers.