The mixed integer programming (MIP)-based deadlock detection method plays an important role in the development of deadlock prevention policies for flexible manufacturing systems (FMS). In this paper, an optimal deadlock prevention policy is proposed for a class of Petri nets called Systems of Simple Sequential Processes with Resources (S3PR) without any ξ-resource. A ξ-resource is a one-unit resource place shared by two or more minimal siphons that do not mutually contain each other. Compared with the MIP-based deadlock prevention policies that suffer from the problem of limited behavior permissiveness and high structural complexity, the proposed one can obtain an optimal liveness-enforcing supervisor with lower structural complexity. An FMS example is used to illustrate the application of the proposed deadlock prevention policy.