This book presents a unified optimal control approach to a large
class of problems arising in the field of production planning and
scheduling. It introduces a leading optimal flow control paradigm
which results in efficient solutions for planning and scheduling
problems. This book also introduces the reader to analytical and
numerical methods of the maximum principle, used here as a
mathematical instrument in modeling and solving production planning
and scheduling problems. The book examines control of production
flows rather than sequencing of distinct jobs. Methodologically,
this paradigm allows us to progress from initial assumptions about
a manufacturing environment, through mathematical models and
construction of numerical methods, up to practical applications
which prove the relevance of the theory developed here to the real
world. Given a manufacturing system, the goal is to control the
production, subject to given constraints, in such a way that the
demands are tracked as closely as possible. The book considers a
wide variety of problems encountered in actual production planning
and scheduling. Among the problems are production flow sequencing
and timing, capacity expansion and deterioration, subcontracting
and overtime. The last chapter is entirely devoted to applications
of the theory to scheduling production flows in real-life
manufacturing systems. The enclosed disk provides software
implementations of the developed methods with easy, convenient user
interface. We aimed this book at a student audience - final year
undergraduates as weIl as master and Ph. D.
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