This paper presents a mixed-integer linear programming (MILP) model for the scheduling of a multistage process for the production of aluminum casts of different alloys, using parallel furnaces and casters. In contrast to the common approach in multistage models of considering a fixed set of orders being processed sequentially in the stages, the modeling approach in this paper accounts for actual material flows and, thus, provides flexibility with respect to the actual number of batches to be processed for meeting a given demand. This enables the model to handle parallel nonuniform units with variable capacities, where it is difficult to a priori decide on the number of batches that are required to satisfy the orders. The model also features a material balance over the furnace section, to capture processing details. A decomposition scheme that consists of a master problem and a sub-problem is developed and is used in an iterative algorithm to solve medium- to large-sized problems in reasonable computational time.