**Best Reference Books on Integer Programming**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Integer Programming Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Integer Programming below.

## 1. Integer Programming: Theory and Computations

1."Integer and Combinatorial Optimization" by G L Nemhauser and L A Wolsey
Book Review: This book serves as an introductory guide to diverse domains of combinatorial optimization. It covers linear programming problems, where variables are constrained to integers, providing valuable insights into the structure and resolution of resulting integer programming problems. The book proves highly beneficial for comprehending and addressing complex problem-solving scenarios in discrete optimization. It is well-suited as a textbook for graduate courses focusing on discrete optimization and serves as a valuable reference for both researchers and practitioners. With its clear and up-to-date content, the book offers guidance on effectively solving challenging problems and maximizing the utilization of integer programming techniques.
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2."Integer Programming" by L A Wolsey
Book Review: This reference book is highly commendable for tackling optimization problems involving discrete or integer variables. It offers clear explanations on constructing customized algorithms to achieve optimal solutions for real-world challenges, such as production line schedules and electricity production. The book showcases recent advancements that effectively address complex optimization problems with remarkable accuracy. It includes chapters dedicated to improved modeling techniques, plane theory algorithms, and heuristic methods. With its wide applicability, the book is a suitable choice for courses on integer and mathematical problems in the fields of operations research, mathematics, engineering, and computer science.
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3."Theory of Linear and Integer Programming" by A Schrijver
Book Review: This book provides an exploration of linear and integer programming theory, accompanied by a detailed examination of the associated algorithms with a focus on complexity analysis. It incorporates the latest advancements in the field, offering an overview of the recent developments in linear and integer programming. With its content designed for graduate students and researchers in operations research, mathematics, and computer science, the book covers a wide range of topics, including linear algebra and its complexity, lattice theory, Diophantine equations and their algorithms, polyhedral structure, polarity, blocking, and more.
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4."Production Planning by Mixed Integer Programming" by Y Pochet and L A Wolsey
Book Review: This book serves as a guide, showcasing effective modeling, reformulation, and optimization strategies for addressing production planning and supply chain planning problems. It covers a wide range of topics, including an introduction to planning systems, mixed integer programming problems, and various polyhedral combinatorics algorithms utilized for problem-solving. The book goes beyond theory and demonstrates the practical application of MIP modeling and reformulation approaches to tackle real-life industrial production planning challenges. It offers numerous case studies, exercises, and detailed illustrations to enhance understanding and provide practical insights.
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5."Optimization Over Integers" by D Bertsimas and R Weismantel
Book Review: This book offers cohesive exploration of the theory of integer optimization. Divided into four distinct parts, the book discusses formulations and relaxations, the algebra and geometry of integer optimization, integer optimization algorithms, and extensions of integer optimization. It showcases the evolution of integer optimization theory through the utilization of integral generating sets. The book emphasizes strong formulations, duality, and relaxations, while also discussing the applications of lattices and algebraic geometry in the context of integer optimization. The book focuses on a wide array of enumerative and heuristic methods, supported by numerous examples and exercises for practical learning.
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6."Production Planning by Mixed Integer Programming" by Yves Pochet Laurence A Wolsey
“Production Planning by Mixed Integer Programming” Book Review: This book will be useful for industrial engineers and research professionals alike. It begins with an overview of the general categorization of integer applications, accompanied by an explanation of the three fundamental techniques of integer programming. The concept of implicit enumeration is subsequently discussed, followed by chapters dedicated to branch-and-bound methods, the cutting-plane method, and the formulation and execution of integer programming models. The book also highlights the diverse applications of integer programming in various fields, including binary programs. It focuses on numerous algorithms, techniques, problems, and advantages related to integer programming, making it a comprehensive resource on the subject matter.
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7."Integer Programming: Theory, Applications and Computations" by Hamdy Abdelaziz Taha
“Integer Programming: Theory, Applications and Computations” Book Review: The book begins by looking at the history of integer programming and providing a simple explanation of what it means. It then goes on to explain the different types and approaches used in integer programming. As you continue reading, the book delves into quadratic programming, which involves decision-making with specific limitations. It covers important concepts like solving methods and dealing with fractional programming problems. Throughout the book, there are plenty of exercises and problems to help you practice and better understand the material. The book emphasizes the real-world applications of both integer and quadratic programming in various industries and fields.
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8."Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming" by M Tawarmalani
“Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming” Book Review: The book provides an overview of techniques used to address convexification and global optimization challenges in continuous and mixed-integer nonlinear programs. The algorithms, mechanisms, and enhancements are systematically presented, offering practical insights and applicable solutions. The user-friendly nature of the book allows for easy implementation in various fields. The concepts presented in the book are complemented by geometric interpretations, aiding in better understanding and visualization. With advanced techniques featured throughout, the book serves as a valuable resource for developing new results and frameworks. It will benefit students and professionals engaged in non-linear optimization, integer programming, global optimization, applied mathematics, convex analysis, and engineering design.
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9."Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming" by Ivo Nowak
“Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming” Book Review: The book explores relaxation and decomposition methods employed in solving non-convex structured mixed integer nonlinear programs (MINLPs). It introduces a contemporary approach known as the generic branch-cut-and-price (BCP) framework, which proves effective in tackling MINLPs. The book offers detailed insights into solution techniques, along with the process of MINLP separation and pricing sub-problems to generate cuts and columns. Specialized MINLP solvers are utilized to facilitate this process, ensuring an understanding of the techniques and their practical application.
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10."Linear and Integer Optimization: Theory and Practice, Third Edition" by Gerard Sierksma
“Linear and Integer Optimization: Theory and Practice, Third Edition” Book Review: The book offers an exploration of both theoretical and practical aspects of “Linear and Integer Optimization.” It begins by covering the fundamentals of linear and integer optimization, including topics such as Dantzig’s simplex algorithm, duality, sensitivity analysis, integer optimization models, network models, interior point algorithms, the branch-and-bound algorithm, cutting planes, complexity, standard combinatorial optimization models, the assignment problem, minimum/maximum cost flow, and the minimum cut theorem. As the book progresses, it transitions into practical concepts and real-world case studies, delving into techniques such as column generation, multi-objective optimization, dynamic optimization, machine learning (support vector machines), combinatorial optimization, approximation algorithms, and game theory. Each chapter is enriched with numerous examples and exercises to reinforce learning and facilitate practical application. The book serves as an invaluable resource for advanced undergraduate and graduate courses across various disciplines, including mathematics, computer science, industrial engineering, operations research, and management science. It provides a foundation and practical insights for students seeking to expand their knowledge in the field of linear and integer optimization. | |

## 2. Applied Integer Programming

1."Integer Programming" by H M Salkin | |

2."Integer Programming" by R S Garfinkel and G L Nemhauser
Book Review: This book is a comprehensive guide that introduces the concept of integer programming and explores its various aspects. The book begins with a historical overview and provides a clear definition of integer programming. It covers topics such as mathematical formulation, cutting plane algorithms, branch and bound methods, computational experience, and applications in diverse fields. The chapters are structured to offer a gradual understanding of the subject, with examples and exercises to reinforce learning. This book serves as a valuable resource for those interested in learning and applying integer programming techniques.
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3."Integer Programming and Network Flows" by T C Hu | |

4."Integer Programming" by H Greenberg | |

5."Applied Integer Programming : Modeling and Solution" by Yu Dang
“Applied Integer Programming: Modeling and Solution” Book Review: This well-structured and updated book provides an exploration of the applications of integer programming. It covers a range of topics, including systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing. The chapters delve into key concepts of linear programming theory and network flows, offering insights based on algebra and geometry. The book includes numerous examples, figures, and numerical illustrations, enhancing the reader’s understanding and application of the content. It serves as an excellent resource for courses on integer programming, as well as application-oriented courses at the upper-undergraduate and graduate levels. Students with backgrounds in engineering, business, or applied mathematics will find this book particularly beneficial in their studies and practical endeavors.
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6."Logic and Integer Programming" by H Paul Williams
“Logic and Integer Programming” Book Review: This book primarily targets graduate and postgraduate students, professionals, and practitioners engaged in the field of integer programming. It begins with introductory chapters that provide a foundation, including an overview of logic, explanations of propositional and predicate calculus, linear programming, integer programming, and fundamental mathematical and structural properties of models. The main methods for solving integer programming models are also covered in this section. Subsequent chapters discusses the application of logic in formulating integer programming models, addressing the fundamental computational logic problem and the satisfiability problem. Each chapter concludes with relevant examples, exercises, and practical applications of the discussed topics across various fields.
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7."Integer Programming and Related Areas" by Rabe V Randow | |

8."Location, Scheduling, Design and Integer Programming" by Minendra P
“Location, Scheduling, Design and Integer Programming” Book Review: This book focuses on location, scheduling, and design problems, providing an exploration of these topics. It goes beyond theory by discussing their applications in a wide range of disciplines, including anthropology, archaeology, architecture, chemistry, computer science, economics, electronics, ergonomics, marketing, operations management, political science, statistical physics, and zoology. The book focuses on the mathematical properties of various problem types, such as quadratic assignment problems, traveling salesman problems, triangulation problems, linear assignment problems, VLSI circuit layout design problems, multi-processor problems, scheduling problems with interaction costs, operation-scheduling problems, graph and clique partitioning problems, and Boolean quadratic problems. By examining these mathematical properties, the book provides insights into the underlying structures and complexities of these problems.
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9."Linear and Integer Programming Made Easy" by T C Hu
“Linear and Integer Programming Made Easy” Book Review: This book discusses the fundamentals of linear and integer programming, which have emerged as essential tools in the fields of data science and technology. With numerous exercises and numerical examples, it equips readers with the skills to solve combinatorial problems using mathematical programming optimizations and formulate linear objectives and constraints. The book not only guides readers in selecting the appropriate solution methods but also helps them interpret the results effectively. It is a valuable resource for students across various disciplines, including engineering, operations research, statistics, machine learning, control system design, scheduling, formal verification, and computer vision.
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10."Linear and Integer Programming: Theory and Practice" by Gerard Sierksma
“Linear and Integer Programming: Theory and Practice” Book Review: This book provides a coverage of both theoretical and practical aspects of linear and integer programming. It delves into important topics such as duality, optimality criteria, and sensitivity analysis, providing a solid foundation in the subject. The book offers numerous problems along with their solution techniques, enabling readers to apply the concepts learned. It introduces a user-friendly IBM-compatible software package specifically designed for solving linear-programming problems, enhancing the practical learning experience. To further enhance the readers’ understanding and provide real-world context, the book includes various case studies that offer practical knowledge and relatable content.
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