Flexible manufacturing systems have four key elements, a set of programmable robots and machines, an automated materials-handling system, a buffer storage system and a supervisory control system. This control system has to handle any on-line dynamic conflict that might emerge. Limited and shared resources have to be accounted for. Moreover, it is a discrete-event system which must be controlled. For this purpose, the authors present matrix models which are based on recent research. However, these matrices are defined over an ‘and or-(\(\wedge, \vee \))-algebra’. Thus, the rule-based system can be given a matrix representation. Moreover, links to other tools like directed graphs are discussed in some detail. Further, Petri nets are presented and their use in the study of manufacturing systems is presented. Links between Petri nets and the new matrix method are established. In addition, the authors describe and demonstrate their own graphical Petri-net-simulation tool. The book is completed by an report on other simulation tools for virtual factory modeling. From this together with two introductory chapters on flexible manufacturing systems and on discrete event systems, a self-contained monograph resulted. It is well readable for engineers and also for mathematicians interested not only in such applications but especially in this type of matrix algebra.