Abstract: Models and optimization approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimization procedure is proposed. First, the makespan value is minimized with the smallest sublots defined for the problem instance. This makes it possible to shorten the makespan significantly, because each sublot is transferred separately to the next operation of a job. In the second stage, the sizes of the sublots are maximized without increasing the obtained makespan value. In this way, the number of sublots and transport activities is limited together with the related manufacturing cost. Two objectives are defined for the second stage. The first one is the maximization of the sum of the sublot sizes of all operations, the second one is the maximization of the number of the operations which do no need to be split at all. A mixed-integer linear programming, constraint programming, and graph-based models are implemented for the problem. Two optimization approaches are developed and compared in computational experiments for each stage and objective, one approach is based on a third-party solver, and the second one on an independent own implementation, namely a tabu search and a greedy constructive heuristic.