Linear programming and network flows

by Mokhtar S. Bazaraa

Other authorsJohn J. Jarvis (Author), Hanif D. Sherali (Author)

Paper Book, 1990

Status

Available

Call number

519.7

Library's review

Indeholder "Preface", "1. Introduction", " 1.1 The Linear Programming Problem", " 1.2 Linear Programming Modelling and Examples", " 1.3 Geometric Solution", " 1.4 The Requirement Space", " 1.5 Notation", " Exercises", " Notes and References", "2. 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", "3. 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", "4. 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 Comparison of the Two-Phase and the Big-M Methods: How Big Should Big-M Be?", " 4.5 The Single Artificial Variable Technique", " 4.6 Degeneracy, Cycling, and Stalling", " 4.7 Validation of the Two Cycling Prevention Rules", " Exercises", " Notes and References", "5. Special Simplex Implementations and Optimal Conditions", " 5.1 The Revised Simplex Method", " 5.2 The Simplex Method for Bounded Variables", " 5.3 Farkos' Lemma via the Simplex Method", " 5.4 The Karush - Kuhn - Tucker Optimality Conditions", " Exercises", " Notes and References", "6. 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-Simplex 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", "7. The Decomposition Principle", " 7.1 The Decomposition Principle", " 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 Dualy and Relationships with Other Decomposition Procedures", " Exercises", " Notes and References", "8. Complexity of the Simplex Algorithm and Polynomial Algorithms", " 8.1 Polyomial Complexity Issues", " 8.2 Computational Complexity of the Simplex Algorithm", " 8.3 Khachians'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", " Exercises", " Notes and References", "9. 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 Besic 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", "10. 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 Basis Algorithm for Assignment Problems", " 10.9 A Polynomial Successive Shortest Path Approach for Assignment Problems", " 10.10 The Transshipment Problem", " Exercises", " Notes and References", "11. 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", " Exercises", " Notes and References", "12. 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 Shortest Path Algorithms for Networks with 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".

Lineær programmering og Simplex metoden i ret stor detalje.

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Genres

Publication

New York, N.Y. ; Chichester : Wiley, 1990.

Description

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.