Determination of circular waits in multiple-reentrant flowlines based on machine-job incidence matrix

As the first step in resolving stability of a manufacturing system in the sense of deadlock, calculation of circular waits might involve time and memory consuming calculations. In this paper we propose an efficient method for determination of circular waits in multiple-reentrant flowline class (MRF) of manufacturing systems. We introduce machine-job incidence (MJI) matrix that can be obtained from Steward sequencing matrix and Kusiak machine-part incidence matrix. The method uses index vector and MJI matrix in order to allocate circular wait auxiliary vector. Resources involved in the circular wait are directly computed from the auxiliary vector. Although efficiency of the proposed method has been demonstrated on examples involving single- and multi- part type manufacturing workcells, the method can be used for other discrete event systems as well, as long as the system under study belongs to MRF class.