Modeling and Simulation of Manufacturing Systems based on a Machine-Job Incidence Matrix

Abstract

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.

Machine-job incidence matrix based analysis of manufacturing systems in time domain

“…By static model of an MS we presume a model within all operations in the system have the same duration [10], and can, therefore, be modeled as an untimed system. The static model should provide information regarding idle resources and completed jobs at each discrete interval k. Hence, two vectors are defined: the completed jobs vector, v c -a vector with dimension equal to the number of jobs in the system ( ci v is the number of completed parts held by i-th job), and the idle resource vector, r c -a vector with dimension equal to the number of resources in the system ( ci r is the number of available part-slots of i-th resource).…”

“…In this paper we extend machine-job incidence matrix (MJI) static model, described in [10], in time domain, and give extended simulation algorithm for analysis of dynamic properties of an MS.…”

Resource Allocation in Free-Choice Multiple Reentrant Manufacturing Systems Based on Machine-Job Incidence Matrix

“…Consequently, the overall supervisor control policy consists of two already defined sequences and conditions [according to (12)] (as ). Results obtained by simulation with MJIWorkshop, software tool presented in [23], are shown in Figs. 6 and 7.…”