Policy to cope with deadlocks and livelocks for flexible manufacturing systems using the max′-controlled new smart siphons

Both deadlocks and livelocks can result in the serious problems in running process of a flexible manufacturing system (FMS). This study proposes an iterative control policy for an FMS modelled with Petri nets on the basis of a combination of revised mixed integer programming and the concept of max´-controlled siphon, which can not only solve the smart siphons associated with deadlocks and livelocks in Petri nets directly, but also make them max´-controlled. Accordingly, an original Petri net system with deadlocks and livelocks can be turned into the live controlled one with a simple structure, and meanwhile no smart siphons can be found in it. It lays foundations for further analysis and control on deadlocks and livelocks. Compared with the existing methods in the literature, the proposed one is more general and effective. A theoretical analysis and several examples are given to demonstrate its efficiency and practical potentials.