Linear programming and network flows:
Gespeichert in:
Hauptverfasser: | , , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York
Wiley-Interscience
2005
|
Ausgabe: | 3. ed. |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XIII, 727 S. |
ISBN: | 0471636819 |
Internformat
MARC
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245 | 1 | 0 | |a Linear programming and network flows |c Mokhtar S. Bazaraa ; John J. Jarvis ; Hanif D. Sherali |
250 | |a 3. ed. | ||
264 | 1 | |a New York |b Wiley-Interscience |c 2005 | |
300 | |a XIII, 727 S. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
650 | 4 | |a Analyse de réseau (Planification) | |
650 | 7 | |a Lineaire programmering |2 gtt | |
650 | 7 | |a Netwerkplanning |2 gtt | |
650 | 7 | |a Programação inteira e fluxos em rede |2 larpcal | |
650 | 7 | |a Programação linear (teoria;métodos) |2 larpcal | |
650 | 4 | |a Programmation linéaire | |
650 | 4 | |a Linear programming | |
650 | 4 | |a Network analysis (Planning) | |
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Datensatz im Suchindex
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---|---|
adam_text | Titel: Linear programming and network flows
Autor: Bazaraa, Mokhtar S
Jahr: 2005
CONTENTS
ONE: INTRODUCTION......................................................................................1
1.1 The Linear Programming Problem.............................................I
1.2 Linear Programming Modeling and Examples...........................7
1.3 Geometric Solution...................................................................17
1.4 The Requirement Space............................................................22
1.5 Notation....................................................................................27
Exercises...................................................................................28
Notes and References...............................................................41
TWO: LINEAR ALGEBRA, CONVEX ANALYSIS, AND
POLYHEDRAL SETS.............................................................................43
2.1 Vectors......................................................................................43
2.2 Matrices....................................................................................49
2.3 Simultaneous Linear Equations................................................59
2.4 Convex Sets and Convex Functions..........................................62
2.5 Polyhedral Sets and Polyhedral Cones......................................68
2.6 Extreme Points, Faces, Directions, and Extreme
Directions of Polyhedral Sets: Geometric Insights...................69
2.7 Representation of Polyhedral Sets............................................73
Exercises...................................................................................80
Notes and References...............................................................88
THREE: THE SIMPLEX METHOD.....................................................................89
3.1 Extreme Points and Optimality.................................................89
3.2 Basic Feasible Solutions...........................................................92
3.3 Key to the Simplex Method....................................................101
3.4 Geometric Motivation of the Simplex Method.......................102
3.5 Algebra of the Simplex Method..............................................106
3.6 Termination: Optimality and Unboundedness........................112
3.7 The Simplex Method..............................................................118
3.8 The Simplex Method in Tableau Format................................123
3.9 Block Pivoting........................................................................132
Exercises.................................................................................133
Notes and References.............................................................147
FOUR: STARTING SOLUTION AND CONVERGENCE.............................149
4.1 The Initial Basic Feasible Solution.........................................149
4.2 The Two-Phase Method.........................................................152
4.3 The Big-A/Method.................................................................163
4.4 How Big Should Big-A/Be?..................................................170
4.5 The Single Artificial Variable Technique...............................171
4.6 Degeneracy, Cycling, and Stalling..........................................173
4.7 Validation of the Two Cycling Prevention Rules...................179
Exercises.................................................................................184
Notes and References.............................................................195
FIVE: SPECIAL SIMPLEX IMPLEMENTATIONS AND
OPTIMALITY CONDITIONS.............................................................197
5.1 The Revised Simplex Method.................................................197
5.2 The Simplex Method for Bounded Variables.........................217
5.3 Farkas Lemma via the Simplex Method................................230
5.4 The Karush-Kuhn-Tucker Optimality Conditions.................233
XI
Exercises.................................................................................239
Notes and References.............................................................252
SIX: DUALITY AND SENSITIVITY ANALYSIS.......................................255
6.1 Formulation of the Dual Problem...........................................255
6.2 Primal-Dual Relationships.....................................................260
6.3 Economic Interpretation of the Dual.......................................265
6.4 The Dual Simplex Method......................................................273
6.5 The Prima-Dual Method........................................................281
6.6 Finding an Initial Dual Feasible Solution: The
Artificial Constraint Technique..............................................289
6.7 Sensitivity Analysis................................................................290
6.8 Parametric Analysis................................................................307
Exercises.................................................................................315
Notes and References............................................................331
SEVEN: THE DECOMPOSITION PRINCIPLE...............................................333
7.1 The Decomposition Principle.................................................334
7.2 Numerical Example................................................................339
7.3 Getting Started........................................................................347
7.4 The Case of Unbounded Region X..........................................348
7.5 Block Diagonal or Angular Structure.....................................355
7.6 Duality and Relationships with other
Decomposition Procedures.....................................................364
Exercises.................................................................................369
Notes and References.............................................................382
EIGHT: COMPLEXITY OF THE SIMPLEX ALGORITHM
AND POLYNOMIAL ALGORITHMS................................................383
8.1 Polynomial Complexity Issues...............................................383
8.2 Computational Complexity of the Simplex Algorithm...........387
8.3 Khachian s Ellipsoid Algorithm.............................................391
8.4 Karmarkar s Projective Algorithm..........................................392
8.5 Analysis of Karmarkar s Algorithm: Convergence,
Complexity, Sliding Objective Method, and Basic
Optimal Solutions...................................................................409
8.6 Affine Scaling, Primal-Dual Path-Following, and
Predictor-Corrector Variants of Interior Point Methods.........420
Exercises.................................................................................427
Notes and References.............................................................441
NINE: MINIMAL-COST NETWORK FLOWS.............................................445
9.1 The Minimal-Cost Network Flow Problem............................445
9.2 Some Basic Definitions and Terminology
from Graph Theory.................................................................447
9.3 Properties of the A Matrix......................................................451
9.4 Representation of a Nonbasic Vector in
Terms of the Basic Vectors.....................................................457
9.5 The Simplex Method for Network Flow Problems.................458
9.6 An Example of the Network Simplex Method........................467
9.7 Finding an Initial Basic Feasible Solution..............................467
9.8 Network Flows with Lower and Upper Bounds......................470
9.9 The Simplex Tableau Associated with a Network
Flow Problem.........................................................................473
XII
9.10 List Structures for Implementing the Network
Simplex Algorithm.................................................................474
9.11 Degeneracy, Cycling, and Stalling..........................................480
9.12 Generalized Network Problems..............................................486
Exercises.................................................................................489
Notes and References.............................................................502
TEN: THE TRANSPORTATION AND ASSIGNMENT PROBLEMS.......505
10.1 Definition of the Transportation Problem...............................505
10.2 Properties of the A Matrix......................................................508
10.3 Representation of a Nonbasic Vector in Terms
of the Basic Vectors................................................................512
10.4 The Simplex Method for Transportation Problems.................514
10.5 Illustrative Examples and a Note on Degeneracy...................520
10.6 The Simplex Tableau Associated with a Transportation
Tableau...................................................................................527
10.7 The Assignment Problem: (Kuhn s) Hungarian
Algorithm...............................................................................527
10.8 Alternating Basis Algorithm for Assignment Problems..........536
10.9 A Polynomial Successive Shortest Path
Approach for Assignment Problems.......................................538
10.10 The Transshipment Problem...................................................542
Exercises.................................................................................542
Notes and References.............................................................553
ELEVEN: THE OUT-OF-KILTER ALGORITHM.............................................555
11.1 The Out-of-Kilter Formulation of a Minimal
Cost Network Flow Problem..................................................555
11.2 Strategy of the Out-of-Kilter Algorithm................................562
11.3 Summary of the Out-of-Kilter Algorithm..............................574
11.4 An Example of the Out-of-Kilter Algorithm.........................576
11.5 A Labeling Procedure for the Out-of-Kilter Algorithm.........576
11.6 Insight into Changes in Primal and Dual Function Values.....579
11.7 Relaxation Algorithms............................................................582
Exercises.................................................................................584
Notes and References.............................................................594
TWELVE: MAXIMAL FLOW, SHORTEST PATH, MULTICOMMODITY
FLOW, AND NETWORK SYNTHESIS PROBLEMS.......................595
12.1 The Maximal Flow Problem..................................................595
12.2 The Shortest Path Problem.....................................................607
12.3 Polynomial Shortest Path Algorithms for Networks
Having Arbitrary Costs...........................................................619
12.4 Multicommodity Flows..........................................................623
12.5 Characterization of a Basis for the Multicommodity
Minimal-Cost Flow Problem..................................................633
12.6 Synthesis of Multiterminal Flow Networks............................638
Exercises.................................................................................647
Notes and References.............................................................662
BIBLIOGRAPHY ................................................................................................665
INDEX ................................................................................................715
|
any_adam_object | 1 |
author | Bazaraa, Mokhtar S. 1943- Jarvis, John J. 1941- Sherali, Hanif D. 1952- |
author_GND | (DE-588)13576856X (DE-588)138447896 (DE-588)135768586 |
author_facet | Bazaraa, Mokhtar S. 1943- Jarvis, John J. 1941- Sherali, Hanif D. 1952- |
author_role | aut aut aut |
author_sort | Bazaraa, Mokhtar S. 1943- |
author_variant | m s b ms msb j j j jj jjj h d s hd hds |
building | Verbundindex |
bvnumber | BV035874986 |
callnumber-first | T - Technology |
callnumber-label | T57 |
callnumber-raw | T57.74 |
callnumber-search | T57.74 |
callnumber-sort | T 257.74 |
callnumber-subject | T - General Technology |
classification_rvk | SK 870 |
classification_tum | MAT 912f |
ctrlnum | (OCoLC)55633958 (DE-599)BVBBV035874986 |
dewey-full | 519.7/2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.7/2 |
dewey-search | 519.7/2 |
dewey-sort | 3519.7 12 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
edition | 3. ed. |
format | Book |
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language | English |
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spelling | Bazaraa, Mokhtar S. 1943- Verfasser (DE-588)13576856X aut Linear programming and network flows Mokhtar S. Bazaraa ; John J. Jarvis ; Hanif D. Sherali 3. ed. New York Wiley-Interscience 2005 XIII, 727 S. txt rdacontent n rdamedia nc rdacarrier Analyse de réseau (Planification) Lineaire programmering gtt Netwerkplanning gtt Programação inteira e fluxos em rede larpcal Programação linear (teoria;métodos) larpcal Programmation linéaire Linear programming Network analysis (Planning) Optimierung (DE-588)4043664-0 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Transportproblem (DE-588)4060694-6 gnd rswk-swf Netzwerkfluss (DE-588)4126130-6 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Netzwerktheorie (DE-588)4171531-7 s Transportproblem (DE-588)4060694-6 s DE-604 Optimierung (DE-588)4043664-0 s 1\p DE-604 Netzwerkfluss (DE-588)4126130-6 s 2\p DE-604 Jarvis, John J. 1941- Verfasser (DE-588)138447896 aut Sherali, Hanif D. 1952- Verfasser (DE-588)135768586 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Bazaraa, Mokhtar S. 1943- Jarvis, John J. 1941- Sherali, Hanif D. 1952- Linear programming and network flows Analyse de réseau (Planification) Lineaire programmering gtt Netwerkplanning gtt Programação inteira e fluxos em rede larpcal Programação linear (teoria;métodos) larpcal Programmation linéaire Linear programming Network analysis (Planning) Optimierung (DE-588)4043664-0 gnd Netzwerktheorie (DE-588)4171531-7 gnd Transportproblem (DE-588)4060694-6 gnd Netzwerkfluss (DE-588)4126130-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
subject_GND | (DE-588)4043664-0 (DE-588)4171531-7 (DE-588)4060694-6 (DE-588)4126130-6 (DE-588)4035816-1 |
title | Linear programming and network flows |
title_auth | Linear programming and network flows |
title_exact_search | Linear programming and network flows |
title_full | Linear programming and network flows Mokhtar S. Bazaraa ; John J. Jarvis ; Hanif D. Sherali |
title_fullStr | Linear programming and network flows Mokhtar S. Bazaraa ; John J. Jarvis ; Hanif D. Sherali |
title_full_unstemmed | Linear programming and network flows Mokhtar S. Bazaraa ; John J. Jarvis ; Hanif D. Sherali |
title_short | Linear programming and network flows |
title_sort | linear programming and network flows |
topic | Analyse de réseau (Planification) Lineaire programmering gtt Netwerkplanning gtt Programação inteira e fluxos em rede larpcal Programação linear (teoria;métodos) larpcal Programmation linéaire Linear programming Network analysis (Planning) Optimierung (DE-588)4043664-0 gnd Netzwerktheorie (DE-588)4171531-7 gnd Transportproblem (DE-588)4060694-6 gnd Netzwerkfluss (DE-588)4126130-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
topic_facet | Analyse de réseau (Planification) Lineaire programmering Netwerkplanning Programação inteira e fluxos em rede Programação linear (teoria;métodos) Programmation linéaire Linear programming Network analysis (Planning) Optimierung Netzwerktheorie Transportproblem Netzwerkfluss Lineare Optimierung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT bazaraamokhtars linearprogrammingandnetworkflows AT jarvisjohnj linearprogrammingandnetworkflows AT sheralihanifd linearprogrammingandnetworkflows |