Linear Programming and Network Flows by Mokhtar S. Bazaraa (English) Hardcover B

Description: Linear Programming and Network Flows by Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. Flap 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. Author Biography 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. Table of Contents 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 Khachians Ellipsoid Algorithm. 8.4 Karmarkars Projective Algorithm. 8.5 Analysis of Karmarkars 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: (Kuhns) 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. Review "The book can be used both as reference and as textbook for advanced undergraduate students and first-year graduate students in the fields of industrial engineering, management, operation research, computer science, mathematics and other engineering disciplines that deal with the subjects of linear programming and network flows." (Zentralblatt MATH, 2011) Long Description 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. Review Text "The book can be used both as reference and as textbook for advanced undergraduate students and first-year graduate students in the fields of industrial engineering, management, operation research, computer science, mathematics and other engineering disciplines that deal with the subjects of linear programming and network flows." (Zentralblatt MATH, 2011) Â Review Quote "The book can be used both as reference and as textbook for advanced undergraduate students and first-year graduate students in the fields of industrial engineering, management, operation research, computer science, mathematics and other engineering disciplines that deal with the subjects of linear programming and network flows." (Zentralblatt MATH, 2011) Details ISBN0470462728 Author Hanif D. Sherali Language English Edition 4th ISBN-10 0470462728 ISBN-13 9780470462720 Media Book Format Hardcover DEWEY 519.72 Short Title LINEAR PROGRAMMING & NETWOR-4E Affiliation Georgia Institute of Technology, Atlanta Georgia Institute of Technolo Country of Publication United States UK Release Date 2010-01-15 AU Release Date 2009-12-01 NZ Release Date 2009-12-01 Pages 768 Publisher John Wiley & Sons Inc Edition Description 4th edition Year 2010 Publication Date 2010-01-15 Imprint John Wiley & Sons Inc Place of Publication New York Replaces 9780471485995 Illustrations Charts: 125 B&W, 0 Color; Drawings: 10 B&W, 0 Color; Graphs: 100 B&W, 0 Color Audience Undergraduate US Release Date 2010-01-15 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:23167916;

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