This text presents a paradigm for modelling and solving production planning and scheduling problems in industry. Methodologically, this paradigm forms the basis for developing a sound scientific theory based on optimal control and the maximum principle. The book progresses from initial assumptions about a manufacturing environment, through mathematical models and construction of numerical methods, up to practical solutions. The case studies prove the relevance and efficiency of the theory to the real world. Software based on the developed methods is included. This is the only book which traces strong theoretical results of the scheduling theory into real case studies of large leading manufacturing systems.