Linear Min-Plus system control under generalized mutual exclusion constraints: application to managing the replenishment policy of a supply chain in the presence of disturbances

This paper provides an algebraic control strategy for solving the problem of generalized mutual exclusion constraints in a network of timed event graphs with disturbance transitions. To this end, linear Min-Plus equations are used to describe the behavior of this class of timed Petri nets, and weighted Min-Plus inequalities translate the constraints to be satisfied. By combining these mathematical formalisms, sufficient conditions for the existence of control laws guaranteeing these mutual exclusion constraints are proposed. The theoretical results presented in this study are applied to accommodate supply disruptions from two suppliers to reconfigured manufacturing line.