Applied Integer Programming: Modeling and Solution Review

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(More customer reviews)A timely, comprehensive, easy-to-read, and self-contained application textbook for integer programming - the first readable text this 30 year veteran has seen in a decade - a must-have for every practitioner. The book is formatted as a traditional textbook, with problems at the end of each chapter, and solutions in the back of the book for many of the more difficult problems. This text is a natural extension of the well-known introductory texts: e.g. Winston. An extensive reference list bridges the practical solutions to the underlying theory. The references are linked from the historical notes at the end of each chapter. The text covers integer programming in 3 major sections: modeling, linear programming theory, and classical and modern solutions.
The modeling section covers all the classical problems: knapsack, production planning, and scheduling - followed by the network models: assignment, transshipment, maxflow, and shortest path.
Since linear programming based branch and bound solutions are state-of-the-art, the second section reviews linear programming fundamentals as both a traditional linear algebra formulation and, in preparation for branch and bound cuts, a geometrical formulation where the columns are the basis vectors spanning the feasible solution space. Figures are extensively used to crystallize the geometric concepts.
In the final, integer programming methods are covered in general: branch and bound, cutting plane, and group theoretic - focusing on using the methods in combinations, especially, branch and bound with cutting plane. Detailed, but tractable, examples with figures are included every step of the way emphasizing how and why the algorithms work. Rarely introduced in a text are 3 modeling languages that can actually be used in commercial applications.
An excellent application text - enjoy.


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An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software
In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently.
The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems.
Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book.
Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

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