This paper, by using Petri nets (PNs), reports a general approach, called a think globally, act locally (TGAL) method, to compute liveness-enforcing supervisors (LES) for flexible manufacturing systems (FMSs) prone to deadlocks. A place called global sink/source place (GP) is introduced provisionally help us to decide a set of monitors such that deadlock states can be removed. The TGAL method proceeds with liveness enforcement by an iterative way in which a complete state enumeration is computed at each step. The resulting LES is generally maximally permissive or suboptimal, without solving intractable integer linear programming (ILP) problems. Given a system, a sufficient condition is developed to decide whether the TGAL method can find maximally permissive, that is, optimal supervisors. Several typical FMSs popularly studied in the literature are used as the examples to demonstrate the proposed method.