We consider scheduling issues at Beycelik, a Turkish automotive stamping company that uses presses to give shape to metal sheets in order to produce auto parts. The problem concerns the minimization of the total completion time of job orders (i.e., makespan) during a planning horizon. This problem may be classified as a combined generalized flowshop and flexible flowshop problem with special characteristics. We show that the Stamping Scheduling Problem is NP-Hard. We develop an integer programming-based method to build realistic and usable schedules. Our results show that the proposed method is able to find higher quality schedules (i.e., shorter makespan values) than both the company's current process and a model from the literature. However, the proposed method has a relatively long run time, which is not practical for the company insituations when a (new) schedule is needed quickly (e.g., when there is a machine breakdown or a rush order). To improve the solution time, we develop a second method that is inspired by decomposition. We show that the second method provides higher-quality solutionsand in most cases optimal solutionsin a shorter time. We compare the performance of all three methods with the company's schedules. The second method finds a solution in minutes compared to Beycelik's current process, which takes 28hours. Further, the makespan values of the second method are about 6.1% shorter than the company's schedules. We estimate that the company can save over Euro187,000 annually by using the second method. We believe that the models and methods developed in this study can be used in similar companies and industries.