Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks

P-time event graphs are discrete systems suitable for modeling processes in which tasks must be executed predefined time windows. Their dynamics can represented by max-plus linear-dual inequalities (LDIs), i.e., of linear dynamical the algebra and its dual, min-plus algebra. We define a new class models called switched LDIs (SLDIs), allow to switch between different modes operations, each corresponding an LDI, according infinite sequence schedule. In this paper, we focus on analysis SLDIs when schedule is fixed periodic. show that model single-robot multi-product processing networks, every product has requirements corresponds specific mode operation. Based SLDIs, propose algorithm compute minimum maximum cycle times these improves complexity other existing approaches.