  In this paper, an industrial bakery shop is modeled by switched max-plus
linear-dual inequalities (SLDIs). SLDIs are timed discrete event systems
suitable for describing flow shops with time-window constraints and switching
operating modes, where each mode corresponds to a job type. We consider the
scheduling problem of minimizing the makespan of the shop, and we show that the
application of methods based on the max-plus algebra leads to a faster solution
compared to standard techniques. The results of the paper are general, in the
sense that they can be applied to any permutation flow shop with time-window
constraints.
