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Circuits and knots in the diagraph model of a manufacturing system are the rudimentary causes of deadlocks - a type of deadlock that is difficult to detect. A new deadlock avoidance algorithm that dynamically evaluates the order of circuits is presented. The algorithm is highly permissive since the order evaluation captures more parts flow dynamics, especially when there exist multiple knots in the diagraph model. It also runs in polynomial time once the set of circuits of the diagraph is given. Simulation results are provided to illustrate the application of the algorithm.