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Deadlock prevention plays an important role in the modeling and control of flexible manufacturing systems (FMS). This paper presents a novel and computationally efficient method to design optimal control places, and an iteration approach that only computes the reachability graph of a plant Petri net model once in order to obtain a maximally permissive liveness-enforcing supervisor for an FMS. By using a vector covering approach, a minimal covering set of legal markings and a minimal covered set of first-met bad markings (FBM) are computed. At each iteration, an FBM from the minimal covered set is selected. By solving an integer linear programming problem, a place invariant is designed to prevent the FBM from being reached and no marking in the minimal covering set of legal markings is forbidden. This process is carried out until no FBM can be reached. In order to make the considered problem computationally tractable, binary decision diagrams (BDD) are used to compute the sets of legal markings and FBM, and solve the vector covering problem to get a minimal covering set of legal markings and a minimal covered set of FBM. Finally, a number of FMS examples are presented to illustrate the proposed approaches.