Book excerpt: This book is the continuation of the textbook Lean Compendium – Introduction to Modern Manufacturing Theory. It extends the theory of mathematical modeling to batch & queue-based cyber-physical production systems. To facilitate learning, the book continues to develop a Cartesian-derived understanding of the system’s behavior by applying manufacturing-specific theorems, corollaries and lemmas. A law-based description enables to model production mathematically and understand upfront their dynamics in terms of WIP generation, lead-times, exit-rates, and on-time delivery performance. While simulation alone only allows to explore the optimum solution, the development of a theory allows to gain knowledge. This improves the learning of the “physics” of manufacturing systems and contributes to a solid production’s understanding and a clear and cognitive problem determination that leads to a thorough mental capture for mastering a systematic design of such highly complex systems.