We address the problem of optimally planning the two main phases in tires production, namely building and curing. They are executed by different machines subject to specific constraints; furthermore, the buffer capacity between the two phases is limited. We present a mathematical model of the optimization problem, that turns out to be a computationally difficult MILP problem. Computational tests show that reducing the symmetries by variable aggregation allows to solve large size instances arising in a real production plant to near-optimality within a reasonable amount of computing time.