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 theapproach, the book aims to provide a unique and complete presentation of the polyhedral combinatorics and MIP research results concerning production planning models
This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and related supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. This book addresses the solution of real life or industrial production planning problems (involving complex production structures with multiple production stages) using a MIP modeling and reformulation approach. It is based on close to twenty years of research in which the authors have played a significant role. One of the goals of this book is to allow non-expert readers, students in business, engineering, applied mathematics and computer science to solve such problems using standard modeling tools and MIP software. To achieve this the book provides a unique collection of reformulation results, integrating them into a comprehensive modeling and reformulation approach, as well as an easy to use problem-solving library. Moreover this approach is demonstrated through a series of real life case studies, exercises and detailed illustrations.
Graduate students and researchers in operations research, management, science and applied mathematics wishing to gain a deeper understanding of the formulations and mathematics underlying this approach will find this book useful because of its detailed treatment of the polyhedral structure of the basic lot-sizing problems and simple mixed integer sets that arise in the decomposition of more complicated problems. This book will allow the reader to improve formulations of non-standard MIP models and produce state-of-the-art models and algorithms.
Graduate students and researchers in operations research, management, science and applied mathematics wishing to gain a deeper understanding of the formulations and mathematics underlying this approach will find this book useful because of its detailed treatment of the polyhedral structure of the basic lot-sizing problems and simple mixed integer sets that arise in the decomposition of more complicated problems. This book will allow the reader to improve formulations of non-standard MIP models and produce state-of-the-art models and algorithms.
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