Solving Siphons with the Minimal Cardinality for Deadlock Control

By modifying the objective function and adding new constraints to a Mixed Integer Programming (MIP) method proposed by Park and Reveliotis, this chapter presents a Revised MIP (RMIP) method to directly solve siphons, called smart siphons, with the minimal cardinality as well as the minimal number of resource places. Accordingly, a proper Control Place (CP) is added for each smart siphon in order to achieve the desired control. Both efficiency and practicality of this method are proved through a theoretical proof and several examples.