Modelling routing phenomenon with bounds estimation in dioids

AbstractIn job-shop systems, each product is routed according to its own production cycle. However routings or conflicts cannot be modelled in scalar dioid algebraic structures such as (Z¯,min,+) or (Z¯,max,+) (also denoted Z¯min and Z¯max). The main reason is that choices cannot be represented in such modellings. In this article the input/output behaviour of a whole system with several sub-systems in conflict is bounded by those of two linear systems in dioid Z¯min. By doing so, we model behaviours as intervals. An interval contains all the possible system behaviours (in terms of number of pallets coming and going, delays and production rates), when the routing policy therein is periodic. As a consequence, even though the input/output behaviour of such a system is not linear in a scalar dioid, we can nevertheless use an imprecise modelling over a dioid of intervals. This allows for using dioid theory contributions, as for control problem synthesis issues