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

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