This work addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints. It provides methods for modeling complex problems via effective algorithms on modern computers. The general theory and characteristics of optimization problems are presented, along with effective solution algorithms. The text also explores linear programming and network flows, employing polynomial-time algorithms and various specializations of the simplex method. Includes many numerical examples to illustrate theory and techniques.
Linear Programming and Network Flows
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Book Description
Editorial Reviews
Review
“I am finding this book useful both for students and other readers interested in this field, welcomed in the operation research literature.” (Zentralbaltt MATH, June 2005)
--This text refers to an out of print or unavailable edition of this title.
From the Publisher
Addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints. Provided are methods for modeling complex problems via effective algorithms on modern computers. The general theory and characteristics of optimization problems are presented, along with effective solution algorithms. Explores linear programming and network flows, employing polynomial-time algorithms and various specializations of the simplex method. Includes many numerical examples to illustrate theory and techniques.
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Most Helpful Customer Reviews
4 of 4 people found the following review helpful:
5.0 out of 5 stars
Best Math oriented LP book,
By AR PSU "aratpennstate" (State College, PA United States) - See all my reviews
This review is from: Linear Programming and Network Flows (Hardcover)
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.
3 of 3 people found the following review helpful:
4.0 out of 5 stars
Great book for graduate OR/MS students,
This review is from: Linear Programming and Network Flows (Hardcover)
I used this book in my graduate linear programming class. The text is very descriptive in its theory and has a wealth of exercises from simple to doctorate level.
5 of 6 people found the following review helpful:
5.0 out of 5 stars
THE Linear Programming Book.,
By
This review is from: Linear Programming and Network Flows (Hardcover)
I came across this book as a graduate student and hated it! But as I went deeper into Linear Programming (and stochastic programming) I realized the true worth of this book. It is definitely an intermediate-advanced level book rather than a beginner's book. Each concept is developed in painstaking detail with a strong base in Linear Algebra.While the linear programming part is quite strong on the traditional algorithms, it is a little weak on interior point algorithms. For network flows, I would suggest the book by Ahuja et al... not because this book is bad but simply because Ahuja's done an unbeatable job. Bottomline: This book is the best there is for a strong background in linear programming. If you are interested in theory look up Schrijver's "Theory of Linear and Integer Programming".
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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polyhedral sets, cycling prevention rule, restricted primal problem, unbounded optimal objective value, independent defining hyperplanes, usual minimum ratio test, foregoing tableau, negative cost circuits, following network flow problem, multiply the new second row, starting basic feasible solution, nonbasic variable space, artificial variable technique, kilter number, revised simplex tableau, strongly feasible tree, objective row coefficients, transportation tableau, single artificial variable, affine scaling variant, nonbasic cell, nonbasic arc, improved basic feasible solution, basis subgraph, minimal disconnecting set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Minimal Cost Network Flows, The Decomposition Principle, Convex Analysis, Linear Algebra, Bland's Rule, Noting Equation, Solve Exercise, Los Angeles, Cramer's Rule, Consider Example, Using Figure, Yrk Yrk Yrk, Examining Figure, Dantzig's Rule, Kansas City, Consider Exercise, Examining Equation Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
polyhedral sets, cycling prevention rule, restricted primal problem, unbounded optimal objective value, independent defining hyperplanes, usual minimum ratio test, foregoing tableau, negative cost circuits, following network flow problem, multiply the new second row, starting basic feasible solution, nonbasic variable space, artificial variable technique, kilter number, revised simplex tableau, strongly feasible tree, objective row coefficients, transportation tableau, single artificial variable, affine scaling variant, nonbasic cell, nonbasic arc, improved basic feasible solution, basis subgraph, minimal disconnecting set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Minimal Cost Network Flows, The Decomposition Principle, Convex Analysis, Linear Algebra, Bland's Rule, Noting Equation, Solve Exercise, Los Angeles, Cramer's Rule, Consider Example, Using Figure, Yrk Yrk Yrk, Examining Figure, Dantzig's Rule, Kansas City, Consider Exercise, Examining Equation Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
85
books
cite this book:
See all 85 books citing this book
- Large Scale Linear and Integer Optimization: A Unified Approach by Richard Kipp Martin on 4 pages
- Mathematical Programming (Chapman & Hall/CRC Pure and Applied Mathematics) by Melvyn W. Jeter on page 117, page 174, and page 213
- Theory of Linear and Integer Programming by Alexander Schrijver in Front Matter, and Back Matter
- Optimization Algorithms for Networks and Graphs, Second Edition, by James Evans on page 25, and page 177
- Integer and Combinatorial Optimization by Laurence A. Wolsey in Back Matter (1), and Back Matter (2)
See all 85 books citing this book
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