Linear programming and network flows Fourth Edition by Bazaraa, John Jarvis, Hanif Sherali Bazaraa, John Jarvis, Hanif Sherali ISBN 978-0470462720 0470462728
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Linear programming and network flows Fourth Edition by M. S. Bazaraa, John J. Jarvis, Hanif D. Sherali M. S. Bazaraa, John J. Jarvis, Hanif D. Sherali – Ebook PDF Instant Download/Delivery: 978-0470462720, 0470462728
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Product details:
ISBN 10: 0470462728
ISBN 13: 978-0470462720
Author: M. S. Bazaraa, John J. Jarvis, Hanif D. Sherali M. S. Bazaraa, John J. Jarvis, Hanif D. Sherali
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.
Table of contents:
ONE: INTRODUCTION
The Linear Programming Problem
Linear Programming Modeling and Examples
Geometric Solution
The Requirement Space
Notation
Exercises
Notes and References
TWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND POLYHEDRAL SETS
Vectors
Matrices
Simultaneous Linear Equations
Convex Sets and Convex Functions
Polyhedral Sets and Polyhedral Cones
Extreme Points, Faces, Directions, and Extreme Directions of Polyhedral Sets: Geometric Insights
Representation of Polyhedral Sets
Exercises
Notes and References
THE SIMPLEX METHOD
Extreme Points and Optimality
Basic Feasible Solutions
Key to the Simplex Method
Geometric Motivation of the Simplex Method
Algebra of the Simplex Method
Termination: Optimality and Unboundedness
The Simplex Method
The Simplex Method in Tableau Format
Block Pivoting
Exercises
Notes and References
STARTING SOLUTION AND CONVERGENCE
The Initial Basic Feasible Solution
The Two-Phase Method
The Big-M Method
How Big Should Big-M Be?
The Single Artificial Variable Technique
Degeneracy, Cycling, and Stalling
Validation of Cycling Prevention Rules
Exercises
Notes and References
FIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND OPTIMALITY CONDITIONS
The Revised Simplex Method
The Simplex Method for Bounded Variables
SIX: DUALITY AND SENSITIVITY ANALYSIS
Formulation of the Dual Problem
Primal-Dual Relationships
Economic Interpretation of the Dual
The Dual Simplex Method
The Primal-Dual Method
Finding an Initial Dual Feasible Solution: The Artificial Constraint Technique
Sensitivity Analysis
Parametric Analysis
Exercises
Notes and References
SEVEN: THE DECOMPOSITION PRINCIPLE
The Decomposition Algorithm
Numerical Example
Getting Started
The Case of an Unbounded Region X
Block Diagonal or Angular Structure
Duality and Relationships with other Decomposition Procedures
Exercises
Notes and References
EIGHT: COMPLEXITY OF THE SIMPLEX ALGORITHM AND POLYNOMIAL-TIME ALGORITHMS
Polynomial Complexity Issues
Computational Complexity of the Simplex Algorithm
Khachian’s Ellipsoid Algorithm
Karmarkar’s Projective Algorithm
Analysis of Karmarkar’s Algorithm: Convergence, Complexity, Sliding Objective Method, and Basic Optimal Solutions
Affine Scaling, Primal-Dual Path Following, and Predictor-Corrector Variants of Interior Point Methods
Exercises
Notes and References
NINE: MINIMAL-COST NETWORK FLOWS
The Minimal Cost Network Flow Problem
Some Basic Definitions and Terminology from Graph Theory
Properties of the A Matrix
Representation of a Nonbasic Vector in Terms of the Basic Vectors
The Simplex Method for Network Flow Problems
An Example of the Network Simplex Method
Finding an Initial Basic Feasible Solution
Network Flows with Lower and Upper Bounds
TEN: THE TRANSPORTATION AND ASSIGNMENT PROBLEMS
Definition of the Transportation Problem
Properties of the A Matrix
Representation of a Nonbasic Vector in Terms of the Basic Vectors
Illustrative Examples and a Note on Degeneracy
The Simplex Method for Transportation Problems
The Simplex Tableau Associated with a Transportation Tableau
The Assignment Problem: Kuhn’s Hungarian Algorithm
Alternating Path Basis Algorithm for Assignment Problems
A Polynomial-Time Successive Shortest Path Approach for Assignment Problems
The Transshipment Problem
Exercises
Notes and References
ELEVEN: THE OUT-OF-KILTER ALGORITHM
The Out-of-Kilter Formulation of a Minimal Cost Network Flow Problem
Strategy of the Out-of-Kilter Algorithm
Summary of the Out-of-Kilter Algorithm
An Example of the Out-of-Kilter Algorithm
A Labeling Procedure for the Out-of-Kilter Algorithm
Insight into Changes in Primal and Dual Function Values
Relaxation Algorithms
Exercises
Notes and References
TWELVE: MAXIMAL FLOW, SHORTEST PATH, MULTICOMMODITY FLOW, AND NETWORK SYNTHESIS PROBLEMS
The Maximal Flow Problem
The Shortest Path Problem
Polynomial-Time Shortest Path Algorithms for Networks Having Arbitrary Costs
Multicommodity Flows
Characterization of a Basis for the Multicommodity Minimal-Cost Flow Problem
Synthesis of Multiterminal Flow Networks
Exercises
Notes and References
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