Many manufacturing systems are subject to synchronization phenomenabut do not include choice. This class of manufacturing systems can be describedas timed event graphs, which have a linear representation in an algebraic structurecalled dioids. Among the best known dioids is the max-plus algebra; there are, how-ever, other dioids which, depending on the specific manufacturing system to be mod-eled, may be preferable. This chapter introduces basic notions of dioid theory andprovides simple illustrative examples. Furthermore, the notion of standard dioids isextended such that minimal and maximal operation times as well as minimal andmaximal numbers of parts being processed simultaneously can be modeled. Usingthis extension it is possible to model manufacturing systems with nested schedules,i.e., manufacturing processes in which parts may visit the same resource more thanonce and in which some activities related to partkmay be executed prior to activi-ties related to partk−1 on the same resource. The resulting model of manufacturingsystems may then be used to synthesize various forms of feedback control.