The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics.
The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the Fourth Edition include:
The cycling phenomenon in linear programming and the geometry of cycling
Duality relationships with cycling
Elaboration on stable factorizations and implementation strategies
Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods
Line search and dual ascent ideas for the out-of-kilter algorithm
Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems
The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by Notes and References sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study.
Linear Programming and Network Flows, Fourth Edition is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques.
1 de 1 votos han sido útiles para otras personas:
The techniques described are very theoretical but are friendly to be used in Computer programs. Has a great deal of depth.
2 de 3 votos han sido útiles para otras personas:
I am using this book for a linear programming course. The most flagrant problem with this book is that it is filled with typos, making reading through proofs and examples very frustrating because you're never sure what is supposed to be written. The book is also not very good at explaining concepts and leaves many steps out in the development of new ideas. If you can avoid it, do not use this book to learn linear programming.
2 de 3 votos han sido útiles para otras personas:
I used this text while taking a graduate linear programming (LP)course on LP and network flows. I really liked the treatment. The typesetting was clear ,consistent and easily followed (not as good as Nash and Sofer's). The book also includes lots of nice side discussion on how or why the theory is the way it is. Plenty of references are offered for further study. Proofs were not rigorous. The highly mathematical reader may be disappointed by the "show proof" style used instead of a rigorous theorem-proof style. In fact, I seem to recall a time or two where the theorem came after the usage. For me, I didn't mind that, but a pure math guy would likely grind his teeth.
The network material was acceptable. I personally thought the text problems were not of the best quality. I would suggest a teacher supplement their own favorites outside of the book.
One caution is that the book is somewhat aged. I noticed a text like Nash and Sofer seems to have newer updates on the theory.
Overall, a great read for getting into the nitty gritty details of LP.
3 de 4 votos han sido útiles para otras personas:
I am currently working toward a Ph.D. in Management Science and used this book for a LP course. If you can get past the matrix algebra (which isn't too terribly difficult) you will find that this book contains more practical LP information than any other resource available. However, those looking for a "how to" book on linear programming might want to try a more elementary text first. This book is geared toward those interested in the more advanced computational aspects of LP (e.g., revised simplex method, LU decomposition, product form of the inverse, bounded variables, etc.). The chapter on sensitivity analysis is particularly well written and thorough. But beware, this book packs more info per page than I have ever seen!!!
3 de 3 votos han sido útiles para otras personas:
I used this book as part of my grad level LP course that covered the first half of the book. Let me start out by saying that this is by no means a beginner's book. This book assumes a strong Linear Algebra and basic OR (assumes you know the Simplex method solution procedure, etc.) knowledge.If you are looking to get these OR prerequisites, then refer to the basic OR books by Hillier & Lieberman, Wayne Winston, Ignizio & Cavalier or A. Ravindran; this book is not for you.
This book is outstanding for understanding the theory and mathematical mechanics of LP and the first half of the book covers this comprehensively. The excercises in this book are outstanding (and can be hard). For those who need this book but are weak or rusty on the basics (like I was :) ) refer to one of the books above (I liked the Ignizio & Cavalier book a lot). I can't comment on the Network flows part of the book but it will almost surely be excellent if it is anything like the first half.
An excellent book for the intended audience.