A graph-theoretic, linear-time scheme to detect and resolve deadlocks in flexible manufacturing cells

A linear-time deadlock detection and resolution scheme is presented that effectively captures deadlock in manufacturing cells with alternate part routing. The deadlock handling scheme is based on a bipartite graph model of the part-machine relationship in the manufacturing cell. Two controller commands are proposed that facilitate the dynamic preparation of the evolving part-machine relationship and encapsulate the controller directives required to detect and resolve deadlocks. A distinction is made between permanent deadlock and transient deadlock. Permanent deadlock depicts a manufacturing system state where parts are irrevocably blocked and where external intervention is required to resolve the deadlock, whereas a transient deadlock indicates that there is a positive probability that the deadlock will resolve itself over time. To recover from deadlocks, two control policies are studied: either resolve permanent deadlocks or resolve both permanent and transient deadlocks in the manufacturing cell. Under both these policies, it is shown that it is sufficient to resolve any cycle in the set of deadlocked parts to resolve the deadlock. In addition, experimental results are presented comparing the proposed control policies versus a prevention strategy of providing sufficient in-process buffer spaces.