In this paper, we introduce machine-job incidence (MJI) matrix that can be obtained from Steward sequencing matrix and Kusiak machine-part incidence matrix. Methods for determination of structural properties of free-choice multiple reentrant systems (FMRF) are proposed and an explanation on how the content (number of active jobs) of those structures can be controlled. This paper gives a new method on how to determine if allocation of resources, in a form of repeatable sequences, gives stable system behavior. Although efficiency of the proposed methods have been demonstrated on examples involving manufacturing workcells, the method can be used for other discrete-event systems as well, as long as the system under study belongs to FMRF class.

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This paper presents a method for modeling and simulation of particular class of manufacturing systems. The method is based on so called Machine-Job Incidence Matrix (MJI) that is formed from Steward sequencing matrix and Kusiak machine-part incidence matrix. A model of the system in a form of MJI matrix is easy to comprehend. It can be put in direct relation with other manufacturing systems analysis tools, such as Petri nets and MS matrix model. Moreover, structural properties of MJI matrix offer direct insight in the system configuration, hence, providing a ground for the system analysis and supervisory controller design. Properties, such as circular waits and conflicts, can be determined straightforwardly by using simple matrix manipulations, thus, allowing design of sequencing control algorithms. An extension of MJI matrix in time domain offers a foundation for determination of recursive equation that can be used for simulation of system's dynamics. Although manufacturing systems have been used for validation of the proposed modeling technique, the method can be applied on other discrete event systems as well.

This paper presents an extension of previously introduced method for manufacturing systems analysis and design based on so called Machine-Job Incidence matrix. Static model of a manufacturing system is augmented by introduction of timed machine-job incidence matrix that is comprised of operational times required for jobs in the system to be completed as well as times required for setting-up of resources upon completion of requested tasks. The proposed dynamic model has been validated by simulation of free-choice multiple reentrant flow line. Results presented in the paper demonstrate efficiency of the model. k L J J J J J = . We uniquely associate with each job sequence k J , the raw-part input k in J , and finishedproduct output k out J J J J J J J J J J J J J J J J J