Due to existence of concurrent part flows and resource sharing in modern automated flexible manufacturing systems (FMS), deadlock is a common problem and its occurrence causes loss of productivity. When a manufacturing system is modeled by a digraph, existence of circuits in such a graph is a necessary condition for deadlock. Our previous work further showed that the knot and order of a circuit is closely related to impending deadlocks - a type of deadlock that is more difficult to detect. In this paper, we extend our previous work on deadlock avoidance for flexible manufacturing systems to allow choices in process flows (a.k.a., flexible part routing). Due to introduction of choices, part flow dynamics become more sophisticated and our previous results are no longer valid. A systematic circuit analysis is performed in this paper. New concepts such as broken circuit, basic circuit, choice circuit and supremal circuit are introduced to reduce significantly the number of circuits thus improving efficiency of our approach. The extended method is highly permissive with the adjusted effective free space calculation to capture more necessary parts flow dynamics, especially when multiple knots exist in the digraph model. The online policy runs in polynomial time once the set of basic circuits of the digraph is computed offline. Simulation results on selected examples are given.
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