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Production Planning by Mixed Integer Programming
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This book is about solving an important class of production planning problems (real life or industrial problems involving many items, many machines or resources, and complex product structures with multiple production stages) using a mixed integer programming (MIP) decomposition and reformulation approach.§The practical goal is to allow the non-expert reader to solve the problems by mixed integer programming, using standard modeling tools and MIP software. This requires the identification of the appropriate (and state-of-the-art) mathematical formulations for each specific planning problem. These formulations are based on polyhedral studies of "simple" sub-models arising in production planning problems, and the theory behind these has been developed over the last twenty years, and has never been collected together, or developed into an easy-to-use problem-solving tool.§On the other hand, for those wishing to go deeper and understand the formulations and mathematics underlying the approach, the book aims to provide a unique and complete presentation of the polyhedral combinatorics and MIP research results concerning production planning models.
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