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E-raamat: Linear Programming and Network Flows 3rd Revised edition [Wiley Online]

  • Formaat: 744 pages, Illustrations
  • Ilmumisaeg: 01-Dec-2004
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 047170377X
  • ISBN-13: 9780471703778
Teised raamatud teemal:
  • Wiley Online
  • Hind: 157,27 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Linear Programming and Network Flows 3rd Revised editionSuurem pilt
  • Formaat: 744 pages, Illustrations
  • Ilmumisaeg: 01-Dec-2004
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 047170377X
  • ISBN-13: 9780471703778
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9780471703778
Bazaraa (global logistics, Georgia Institute of Technology) adds new content on topics including modeling languages, anti-cycling rules, and affine scaling methods to this third edition of a text for advanced undergraduates and first-year graduates in industrial engineering, management, operations research, computer science, and mathematics. Detailed geometrically motivated discussions dealing with the structure of polyhedral sets, optimality conditions, and the nature of solution algorithms have been included for this edition. Pertinent results from linear algebra and convex analysis are included as a review. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)

Linear Programming and Network Flows, now in its third edition, addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequility constraints. This book:
* Provides methods for modeling complex problems via effective algorithms on modern computers.
* Presents the general theory and characteristics of optimization problems, along with effective solution algorithms.
* Explores linear programming (LP) and network flows, employing polynomial-time algorithms and various specializations of the simplex method.
Introduction
1(42)
The Linear Programming Problem
1(6)
Linear Programming Modeling and Examples
7(10)
Geometric Solution
17(5)
The Requirement Space
22(5)
Notation
27(16)
Exercises
28(13)
Notes and References
41(2)
Linear Algebra, Convex Analysis, and Polyhedral Sets
43(46)
Vectors
43(6)
Matrices
49(10)
Simultaneous Linear Equations
59(3)
Convex Sets and Convex Functions
62(6)
Polyhedral Sets and Polyhedral Cones
68(1)
Extreme Points, Faces, Directions, and Extreme Directions of Polyhedral Sets: Geometric Insights
69(4)
Representation of Polyhedral Sets
73(16)
Exercises
80(8)
Notes and References
88(1)
The Simplex Method
89(60)
Extreme Points and Optimality
89(3)
Basic Feasible Solutions
92(9)
Key to the Simplex Method
101(1)
Geometric Motivation of the Simplex Method
102(4)
Algebra of the Simplex Method
106(6)
Termination: Optimality and Unboundedness
112(6)
The Simplex Method
118(5)
The Simplex Method in Tableau Format
123(9)
Block Pivoting
132(17)
Exercises
133(14)
Notes and References
147(2)
Starting Solution and Convergence
149(48)
The Initial Basic Feasible Solution
149(3)
The Two--Phase Method
152(11)
The Big--M Method
163(7)
How Big Should Big--M Be?
170(1)
The Single Artificial Variable Technique
171(2)
Degeneracy, Cycling, and Stalling
173(6)
Validation of the Two Cycling Prevention Rules
179(18)
Exercises
184(11)
Notes and References
195(2)
Special Simplex Implementations and Optimality Conditions
197(58)
The Revised Simplex Method
197(20)
The Simplex Method for Bounded Variables
217(13)
Farkas' Lemma via the Simplex Method
230(3)
The Karush--Kuhn--Tucker Optimality Conditions
233(22)
Exercises
239(13)
Notes and References
252(3)
Duality and Sensitivity Analysis
255(78)
Formulation of the Dual Problem
255(5)
Primal-Dual Relationships
260(5)
Economic Interpretation of the Dual
265(8)
The Dual Simplex Method
273(8)
The Prima-Dual Method
281(8)
Finding an Initial Dual Feasible Solution: The Artificial Constraint Technique
289(1)
Sensitivity Analysis
290(17)
Parametric Analysis
307(26)
Exercises
315(16)
Notes and References
331(2)
The Decomposition Principle
333(50)
The Decomposition Principle
334(5)
Numerical Example
339(8)
Getting Started
347(1)
The Case of Unbounded Region X
348(7)
Block Diagonal or Angular Structure
355(9)
Duality and Relationships with other Decomposition Procedures
364(19)
Exercises
369(13)
Notes and References
382(1)
Complexity of the Simplex Algorithm and Polynomial Algorithms
383(62)
Polynomial Complexity Issues
383(4)
Computational Complexity of the Simplex Algorithm
387(4)
Khachian's Ellipsoid Algorithm
391(1)
Karmarkar's Projective Algorithm
392(17)
Analysis of Karmarkar's Algorithm: Convergence, Complexity, Sliding Objective Method, and Basic Optimal Solutions
409(11)
Affine Scaling, Primal-Dual Path-Following, and Predictor--Corrector Variants of Interior Point Methods
420(25)
Exercises
427(14)
Notes and References
441(4)
Minimal-Cost Network Flows
445(60)
The Minimal-Cost Network Flow Problem
445(2)
Some Basic Definitions and Terminology from Graph Theory
447(4)
Properties of the A Matrix
451(6)
Representation of a Nonbasic Vector in Terms of the Basic Vectors
457(1)
The Simplex Method for Network Flow Problems
458(9)
An Example of the Network Simplex Method
467(1)
Finding an Initial Basic Feasible Solution
467(3)
Network Flows with Lower and Upper Bounds
470(3)
The Simplex Tableau Associated with a Network Flow Problem
473(1)
List Structures for Implementing the Network Simplex Algorithm
474(6)
Degeneracy, Cycling, and Stalling
480(6)
Generalized Network Problems
486(19)
Exercises
489(13)
Notes and References
502(3)
The Transportation and Assignment Problems
505(50)
Definition of the Transportation Problem
505(3)
Properties of the A Matrix
508(4)
Representation of a Nonbasic Vector in Terms of the Basic Vectors
512(2)
The Simplex Method for Transportation Problems
514(6)
Illustrative Examples and a Note on Degeneracy
520(7)
The Simplex Tableau Associated with a Transportation Tableau
527(1)
The Assignment Problem: (Kuhn's) Hungarian Algorithm
527(9)
Alternating Basis Algorithm for Assignment Problems
536(2)
A Polynomial Successive Shortest Path Approach for Assignment Problems
538(4)
The Transshipment Problem
542(13)
Exercises
542(11)
Notes and References
553(2)
The Out-of-Kilter Algorithm
555(40)
The Out-of-Kilter Formulation of a Minimal Cost Network Flow Problem
555(7)
Strategy of the Out-of-Kilter Algorithm
562(12)
Summary of the Out-of-Kilter Algorithm
574(2)
An Example of the Out-of-Kilter Algorithm
576(1)
A Labeling Procedure for the Out-of-Kilter Algorithm
576(3)
Insight into Changes in Primal and Dual Function Values
579(3)
Relaxation Algorithms
582(13)
Exercises
584(10)
Notes and References
594(1)
Maximal Flow, Shortest Path, Multicommodity Flow, and Network Synthesis Problems
595(70)
The Maximal Flow Problem
595(12)
The Shortest Path Problem
607(12)
Polynomial Shortest Path Algorithms for Networks Having Arbitrary Costs
619(4)
Multicommodity Flows
623(10)
Characterization of a Basis for the Multicommodity Minimal-Cost Flow Problem
633(5)
Synthesis of Multiterminal Flow Networks
638(27)
Exercises
647(15)
Notes and References
662(3)
Bibliography 665(50)
Index 715


MOKHTAR S. BAZARAA, PhD, is Managing Director for Global Logistics, The Logistics Institute, at Georgia Institute of Technology. He, along with Dr. Sherali, are coauthors of Nonlinear Programming: Theory and Algorithms (Wiley). JOHN J. JARVIS, PhD, is Professor Emeritus at Georgia Institute of Technology. HANIF D. SHERALI, PhD, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at Virginia Polytechnic and State University.
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