The matrix-based approach presented here is a solution to the real-time application of control in discrete event systems and flexible manufacturing systems (FMS) in particular. 'and/or' algebra enables fast and efficient calculations. The method uses standard task-sequencing and resource-requirements matrices. Matrix-based techniques are compared with Petri net and max-plus algebra ideas. The software discussed in 'Manufacturing Systems Control Design' supplies a graphical user interface that can do many things to make the design and control of FMS easier. The examples presented herein tackle the real problems faced by engineers trying to put into practice methods developed in academia. Common concerns confronted include: predictability; producibility and productivity. Covering all the steps from identification of operations and resources to the transformation of virtual models into real-world algorithms, this monograph is a sound practical basis for the design of controllers for manufacturing systems.