Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali

Linear Programming and Network Flows

• Gebundenes Buch

Produktbeschreibung

Linear Programming and Network Flows presents the problem of minimizing and maximizing a linear function in the presence of linear equality or inequality constraints. This text provides methods for modeling complex problems via effective algorithms on modern computers, optimization problems, and effective solution algorithms. The book also explores linear programming and network flows, polynomial-time algorithms, and geometric concepts. This modified edition includes new exercises, comments, and references on recent developments, like the geometry of cycling. This is the only text that covers both linear programming techniques and network flows for students.

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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.

Produktdetails

• Verlag: Wiley & Sons
• 4. Aufl.
• Seitenzahl: 768
• Erscheinungstermin: 1. Dezember 2009
• Englisch
• Abmessung: 240mm x 161mm x 45mm
• Gewicht: 1299g
• ISBN-13: 9780470462720
• ISBN-10: 0470462728
• Artikelnr.: 27135949

Autorenporträt

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.

Inhaltsangabe

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 OPTIMALITY CONDITIONS. 5.1 The Revised Simplex Method.
5.2 The Simplex Method for Bounded Variables. 5.3 Farkas' Lemma via the
Simplex Method. 5.4 The Karush-Kuhn-Tucker Optimality Conditions.
Exercises. Notes and References. SIX: DUALITY AND SENSITIVITY ANALYSIS. 6.1
Formulation of the Dual Problem. 6.2 Primal-Dual Relationships. 6.3
Economic Interpretation of the Dual. 6.4 The Dual Simplex Method. 6.5 The
Primal-Dual Method. 6.6 Finding an Initial Dual Feasible Solution: The
Artificial Constraint Technique. 6.7 Sensitivity Analysis. 6.8 Parametric
Analysis. Exercises. Notes and References. SEVEN: THE DECOMPOSITION
PRINCIPLE. 7.1 The Decomposition Algorithm. 7.2 Numerical Example. 7.3
Getting Started. 7.4 The Case of Unbounded Region X. 7.5 Block Diagonal or
Angular Structure. 7.6 Duality and Relationships with other Decomposition
Procedures. Exercises. Notes and References. EIGHT: COMPLEXITY OF THE
SIMPLEX ALGORITHM AND POLYNOMIAL-TIME ALGORITHMS. 8.1 Polynomial Complexity
Issues. 8.2 Computational Complexity of the Simplex Algorithm. 8.3
Khachian's Ellipsoid Algorithm. 8.4 Karmarkar's Projective Algorithm. 8.5
Analysis of Karmarkar's Algorithm: Convergence, Complexity, Sliding
Objective Method, and Basic Optimal Solutions. 8.6 Affine Scaling,
Primal-Dual Path-Following, and Predictor-Corrector Variants of Interior
Point Methods. Exercises. Notes and References. NINE: MINIMAL-COST NETWORK
FLOWS. 9.1 The Minimal-Cost Network Flow Problem. 9.2 Some Basic
Definitions and Terminology from Graph Theory. 9.3 Properties of the A
Matrix. 9.4 Representation of a Nonbasic Vector in Terms of the Basic
Vectors. 9.5 The Simplex Method for Network Flow Problems. 9.6 An Example
of the Network Simplex Method. 9.7 Finding an Initial Basic Feasible
Solution. 9.8 Network Flows with Lower and Upper Bounds. 9.9 The Simplex
Tableau Associated with a Network Flow Problem. 9.10 List Structures for
Implementing the Network Simplex Algorithm. 9.11 Degeneracy, Cycling, and
Stalling. 9.12 Generalized Network Problems. Exercises. Notes and
References. TEN: THE TRANSPORTATION AND ASSIGNMENT PROBLEMS. 10.1
Definition of the Transportation Problem. 10.2 Properties of the A Matrix.
10.3 Representation of a Nonbasic Vector in Terms of the Basic Vectors.
10.4 The Simplex Method for Transportation Problems. 10.5 Illustrative
Examples and a Note on Degeneracy. 10.6 The Simplex Tableau Associated with
a Transportation Tableau. 10.7 The Assignment Problem: (Kuhn's) Hungarian
Algorithm. 10.8 Alternating Path Basis Algorithm for Assignment Problems.
10.9 A Polynomial-Time Successive Shortest Path Approach for Assignment
Problems. 10.10 The Transshipment Problem. Exercises. Notes and References.
ELEVEN: THE OUT-OF-KILTER ALGORITHM. 11.1 The Out-of-Kilter Formulation of
a Minimal Cost Network Flow Problem. 11.2 Strategy of the Out-of-Kilter
Algorithm. 11.3 Summary of the Out-of-Kilter Algorithm. 11.4 An Example of
the Out-of-Kilter Algorithm. 11.5 A Labeling Procedure for the
Out-of-Kilter Algorithm. 11.6 Insight into Changes in Primal and Dual
Function Values. 11.7 Relaxation Algorithms. Exercises. Notes and
References. TWELVE: MAXIMAL FLOW, SHORTEST PATH, MULTICOMMODITY FLOW, AND
NETWORK SYNTHESIS PROBLEMS. 12.1 The Maximal Flow Problem. 12.2 The
Shortest Path Problem. 12.3 Polynomial-Time Shortest Path Algorithms for
Networks Having Arbitrary Costs. 12.4 Multicommodity Flows. 12.5
Characterization of a Basis for the Multicommodity Minimal-Cost Flow
Problem. 12.6 Synthesis of Multiterminal Flow Networks. Exercises. Notes
and References. BIBLIOGRAPHY. INDEX.