On-line control of manufacturing systems represented as timed event graphs

A model of manufacturing systems is considered in which several classes of products are repeatedly manufactured, according to the requirements specified by customer orders. The problem considered is the development of control strategies capable of reacting to deviations of the system behaviour from a nominal behaviour defined solving a suitable problem at the scheduling level. The degrees of freedom allowed for the control problem are: the execution times of some elementary operations, the lot-sizes, and the variables expressing the timing of the production process. It is shown that, under suitable hypotheses about the nominal behaviour, the system can be represented by means of a particular class of timed Petri nets. Moreover, the structure of the control problem is that of a continuous variable problem with quadratic cost and linear (or sometimes quadratic) constraints.