Formal Methods in Manufacturing

2.6 CONCLUSIONS

In this chapter, we have shown that TEGs are 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. We have introduced several such idempotent semirings, for example, max-plus algebra min-plus algebra and ${ℳ}_{in}^{ax}〚\text{γ},\text{δ}〛$ , and demonstrated with several examples their usefulness. As many manufacturing systems and their operation are subject to additional constraints, the standard notion of linear systems in dioids has been extended. Using our approach, it is possible to model minimal and maximal operation times, that is, time window constraints, as well ...