Petri nets have been proved to be a tool with prominent capabilities to describe discrete event systems, such as flexible manufacturing systems (FMS), thanks to their excellent properties over other models. Characterization in terms of special structural elements in a Petri net called siphons has been a major approach for the investigation of deadlock-freeness in context of FMS. Utilizing the optimal elementary siphons and the modified mixed integer programming (MIP) algorithm proposed in this paper, one can detect and solve deadlock problems arising in FMS in an iterative mode with tractable computational complexity. Moreover, the MIP approach can be exploited to implement the flexibility enhancement in the resultant net system so that the obtained system is less restricted. In contrast to the conventional typical policies, this approach evolves without explicitly enumerating all the strict minimal siphons. Its legitimacy and feasibility are proved and validated through an experimental study.
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