A class of flexible machining and assembly systems is considered. In this class, each end item is assembled from a number of components. Each component undergoes a sequence of operations on various machines. The assembly structure of all items is flat. At least for some operations on some machines, setups are not negligible. Aggregation of constraints and items is employed and the problem of aggregate capacitated lot-size scheduling is formulated. Three different approaches for efficiently solving the resulting mixed binary programming problem are presented and discussed. The first is based on Lagrangian relaxation, die second on a mixed-integer network flow reformulation, while the third is based on a sub-linearization scheme.