Abstract
This chapter discusses the timed event graphs (TEGs) a suitable tool for the modelling of manufacturing systems characterized by synchronization and delay phenomena but devoid of choices. Furthermore, TEGs have a linear representation in an algebraic structure called idempotent semirings. The chapter introduces several idempotent semirings, for example, max-plus algebra min-plus algebra and minax and demonstrates with several examples. As many manufacturing systems and the operation are subject to additional constraints, the standard notion of linear systems in dioids has been extended. Using the approach, it is possible to model minimal and maximal operation times, that is, time window constraints, as well as minimal and maximal numbers of work in progress, for example, in systems operating with a nested schedule. The chapter shows that the approach is relatively robust to mistakes in the modelling procedure. More precisely, if unfeasible constraints are requested, the resulting system will indicate that some transitions are blocked from the beginning.
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