In modern factories, the optimization of production lines is essential to reduce energy consumption and costs. A well-known model of production line optimization is the Permutation Flow Shop Problem (PFSP) with makespan minimization. PFSP instances arising in industry often have some special features: the problem may contain jobs whose processing times are equal on every machine. Such jobs are said to be of the same type. Due to technological reasons, some of the permutations may be forbidden. For example, only those job permutations are allowed in which, for each job type, the length of a maximal block of jobs from that type is divisible by a prescribed number (the lot size of that type). Considering these features, this paper introduces a generalization of the Permutation Flow Shop with Repetition and Lot Size Problem, in which different types of jobs have different lot sizes. We present two new mixed integer linear programming formulations of the problem and compare their effectiveness on a set of benchmark problems. Both models found the optimal solution within a few seconds for all problem instances involving 10 machines, 100 jobs, and five different types. These results show that even large-scale problems containing a small number of different jobs can be solved using these models.