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.
Autorentext
Der-San Chen, PhD, is Professor Emeritus in the Department of Industrial Engineering at The University of Alabama. He has over thirty years of academic and consulting experience on the applications of linear programming, integer programming, optimization, and decision support systems. Dr. Chen currently focuses his research on modeling optimization problems arising in production, transportation, distribution, supply chain management, and the application of optimization and statistical software for problem solving.
Robert G. Batson, PhD, PE, is Professor of Construction Engineering at The University of Alabama, where he is also Director of Industrial Engineering Programs. A Fellow of the American Society for Quality Control, Dr. Batson has written numerous journal articles in his areas of research interest, which include operations research, applied statistics, and supply chain management.
Yu Dang, PhD, is Qualitative Manufacturing Analyst at Quickparts.com, a manufacturing services company that provides customers with an online e-commerce system to procure custom manufactured parts. She received her PhD in operations management from The University of Alabama in 2004.
Klappentext
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.
Inhalt
PREFACE.
PART I MODELING.
1 Introduction.
1.1 Integer Programming.
1.2 Standard Versus Nonstandard Forms.
1.3 Combinatorial Optimization Problems.
1.4 Successful Integer Programming Applications.
1.5 Text Organization and Chapter Preview.
1.6 Notes.
1.7 Exercises.
2 Modeling and Models.
2.1 Assumptions on Mixed Integer Programs.
2.2 Modeling Process.
2.3 Project Selection Problems.
2.4 Production Planning Problems.
2.5 Workforce/Staff Scheduling Problems.
2.6 Fixed-Charge Transportation and Distribution Problems.
2.7 Multicommodity Network Flow Problem.
2.8 Network Optimization Problems with Side Constraints.
2.9 Supply Chain Planning Problems.
2.10 Notes.
2.11 Exercises.
3 Transformation Using 01 Variables.
3.1 Transform Logical (Boolean) Expressions.
3.2 Transform Nonbinary to 01 Variable.
3.3 Transform Piecewise Linear Functions.
3.4 Transform 01 Polynomial Functions.
3.5 Transform Functions with Products of Binary and Continuous Variables: Bundle Pricing Problem.
3.6 Transform Nonsimultaneous Constraints.
3.7 Notes.
3.8 Exercises.
4 Better Formulation by Preprocessing.
4.1 Better Formulation.
4.2 Automatic Problem Preprocessing.
4.3 Tightening Bounds on Variables.
4.4 Preprocessing Pure 01 Integer Programs.
4.5 Decomposing a Problem into Independent Subproblems.
4.6 Scaling the Coefficient Matrix.
4.7 Notes.
4.8 Exercises.
5 Modeling Combinatorial Optimization Problems I.
5.1 Introduction.
5.2 Set Covering and Set Partitioning.
5.3 Matching Problem.
5.4 Cutting Stock Problem.
5.5 Comparisons for Above Problems.
5.6 Computational Complexity of COP.
5.7 Notes.
5.8 Exercises.
6 Modeling Combinatorial Optimization Problems II.<…