The authoritative guide to modeling and solving complex problems
with linear programming--extensively revised, expanded, and
updated
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.
Autorentext
Mokhtar S. Bazaraa, PhD, is Emeritus Professor at the H.
Milton Stewart School of Industrial and Systems Engineering at
Georgia Institute of Technology. He is the coauthor of Nonlinear
Programming: Theory and Algorithms, Third Edition and Linear
Programming and Network Flows, Third Edition, both published by
Wiley.
John J. Jarvis, PhD, is Emeritus Professor at the H.
Milton Stewart School of Industrial and Systems Engineering at
Georgia Institute of Technology. A Fellow of the Institute of
Industrial Engineers (IIE) and the Institute for Operations
Research and the Management Sciences (INFORMS), Dr. Jarvis is the
coauthor of Linear Programming and Network Flows, Third
Edition (Wiley).
Hanif D. Sherali, PhD, is University Distinguished
Professor and the W. Thomas Rice Chaired Professor of Engineering
at the Virginia Polytechnic and State University. A Fellow of
INFORMS and IIE, he is the coauthor of Nonlinear Programming:
Theory and Algorithms, Third Edition and Linear Programming
and Network Flows, Third Edition, both published by Wiley.
Zusammenfassung
The authoritative guide to modeling and solving complex problems with linear programmingextensively revised, expanded, and updated
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.
Inhalt
Preface.
ONE: INTRODUCTION.
1.1 The Linear Programming Problem.
1.2 Linear Programming Modeling and Examples.
1.3 Geometric Solution.
1.4 The Requirement Space.
1.5 Notation.
Exercises.
Notes and References.
TWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND POLYHEDRAL SETS.
2.1 Vectors.
2.2 Matrices.
2.3 Simultaneous Linear Equations.
2.4 Convex Sets and Convex Functions.
2.5 Polyhedral Sets and Polyhedral Cones.
2.6 Extreme Points, Faces, Directions, and Extreme Directions of Polyhedral Sets: Geometric Insights.
2.7 Representation of Polyhedral Sets.
Exercises.
Notes and References.
THREE: THE SIMPLEX METHOD.
3.1 Extreme Points and Optimality.
3.2 Basic Feasible Solutions.
3.3 Key to the Simplex Method.
3.4 Geometric Motivation of the Simplex Method.
3.5 Algebra of the Simplex Method.
3.6 Termination: Optimality and Unboundedness.
3.7 The Simplex Method.
3.8 The Simplex Method in Tableau Format.
3.9 Block Pivoting.
Exercises.
Notes and References.
FOUR: STARTING SOLUTION AND CONVERGENCE.
4.1 The Initial Basic Feasible Solution.
4.2 The Two-Phase Method.
4.3 The Big-M Method.
4.4 How Big Should Big-M Be?
4.5 The Single Artificial Variable Technique.
4.6 Degeneracy, Cycling, and Stalling.
4.7 Validation of Cycling Prevention Rules.
Exercises.
Notes and References.
FIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND O…