Integer Programming and Network Models

The purpose of this book is to provide readers with an introduction to the very active field of integer programming and network models. The idea is to cover the main parts of the field without being too detailed or too technical. As a matter of fact, we found it somewhat surprising that most--especially newer---books are strongly algorithmically oriented. In contrast, the main emphasis of this book is on models rather than methods. This focus expresses our view that methods are tools to solve actual problems and not ends in themselves. As such, graduate (and with some omissions, undergraduate) students may find this book helpful in their studies as will practitioners who would like to get acquainted with a field or use this text as a refresher. This premise has resulted in a coverage that omits material that is standard fare in other books, whereas it covers topics that are only infrequently found elsewhere. There are some, yet relatively few, prerequisites for the reader. Most material that is required for the understanding of more than one chapter is presented in one of the four chapters of the introductory part, which reviews the main results in linear programming, the analysis of algorithms, graphs and networks, and dynamic programming, respectively. Readers who are familiar with the issues involved can safely skip that part. The three main parts of the book rely on intuitive reasoning and examples, whenever practical, instead of theorems and proofs. Front Matter....Pages I-XII Front Matter....Pages 1-1 Linear Programming....Pages 3-12 Analysis of Algorithms....Pages 13-33 Graph Theory....Pages 35-64 Dynamic Programming....Pages 65-85 Front Matter....Pages 87-87 The Integer Programming Problem and its Properties....Pages 89-109 Formulations in Logical Variables....Pages 111-128 Applications and Special Structures....Pages 129-160 Reformulation of Problems....Pages 161-185 Cutting Plane Methods....Pages 187-204 Branch and Bound Methods....Pages 205-228 Heuristic Algorithms....Pages 229-258 Front Matter....Pages 259-259 Tree Networks....Pages 261-281 Shortest Path Problems....Pages 283-313 Traveling Salesman Problems and Extensions....Pages 315-341 ARC Routing....Pages 343-357 Front Matter....Pages 359-359 Basic Principles of Network Models....Pages 361-375 Applications of Network Flow Models....Pages 377-397 Network Flow Algorithms....Pages 399-434 Multicommodity Network Flows....Pages 435-455 Networks with Congestion....Pages 457-477 Back Matter....Pages 479-504 The book presents a unified treatment of integer programming and network models with topics ranging from exact and heuristic algorithms to network flows, traveling salesman tours, and traffic assignment problems. While the emphasis of the book is on models and applications, the most important methods and algorithms are described in detail and illustrated by numerical examples. The formulations and the discussion of a large variety of models provides insight into their structures that allows the user to better evaluate the solutions to the problems. This book, designed for students who have already developed a basic competence in German, aims to broaden and improve their vocabulary and is invaluable as a guide to finding the right word for the context. It provides detailed information on groups of German words with related meanings, including examples of usage, English glosses, and regional variations. There are two indexes allowing users quickly to locate words in German or English. The book is an essential reference for undergraduates, teachers of German, and other professional linguists. Basic Definitions and Results Integer Programming Network Path Models Network Flow and Network Design Models.