This paper focuses on the problem of deadlocks in automated flexible manufacturing systems (FMS). Based on Petri nets, a deadlock prevention policy is proposed for a special class of Petri nets, S3PR. We distinguish siphons in a net model by elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that it is invariant controlled and the mathematical programming technique is employed to guarantee that no emptiable control-induced siphon is generated due to the addition of the monitor. This novel deadlock prevention policy can usually lead to a more permissive supervisor by adding a small number of monitors and arcs than the existing methods for the design of liveness enforcing Petri net supervisors. A flexible manufacturing example is utilized to illustrate the methods proposed in this paper.