Deterministic operations research: models and methods in linear optimization
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, New Jersey
Wiley
[2010]
|
| Schlagworte: | |
| Online-Zugang: | Titelbild Inhaltsverzeichnis Klappentext |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XV, 613 Seiten Diagramme 25 cm |
| ISBN: | 9780470484517 0470484519 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804176690024284160 |
|---|---|
| adam_text | CONTENTS
PREFACE xi
1 INTRODUCTION TO OPERATIONS RESEARCH 1
1.1 What is Deterministic Operations Research? 1
1.2 Introduction to Optimization Modeling 5
1.3 Common Classes of Mathematical Programs 13
1.4 About this Book 18
Exercises 19
2 LINEAR PROGRAMMING MODELING 21
2.1 Resource Allocation Models 21
2.2 Work Scheduling Models 25
2.3 Models and Data 28
2.4 Blending Models 30
2.5 Production Process Models 36
2.6 Multiperiod Models: Work Scheduling and Inventory 42
2.7 Linearization of Special Nonlinear Models 46
2.8 Various Forms of Linear Programs 51
2.9 Network Models 56
Exercises 68
viii CONTENTS
3 INTEGER AND COMBINATORIAL MODELS 85
3.1 Fixed-Charge Models 85
3.2 Set Covering Models 92
3.3 Models Using Logical Constraints 94
3.4 Combinatorial Models» 99
3.5 Sports Scheduling and an Introduction to IP Solution Techniques 109
Exercises 112
4 REAL-WORLD OPERATIONS RESEARCH APPLICATIONS:
AN INTRODUCTION 126
4.1 Vehicle Routing Problems 126
4.2 Facility Location and Network Design Models 130
4.3 Applications in the Airline Industry 139
Exercises 152
5 INTRODUCTION TO ALGORITHM DESIGN 159
5.1 Exact and Heuristic Algorithms 159
5.2 What to Ask When Designing Algorithms? 161
5.3 Constructive versus Local Search Algorithms 162
5.4 How Good is our Heuristic Solution? 168
5.5 Examples of Constructive Methods 169
5.6 Example of a Local Search Method 181
5.7 Other Heuristic Methods 182
5.8 Designing Exact Methods: Optimality Conditions 183
Exercises 189
6 IMPROVING SEARCH ALGORITHMS AND CONVEXITY 197
6.1 Improving Search and Optimal Solutions 198
6.2 Finding Better Solutions 201
6.3 Convexity: When Does Improving Search Imply
Global Optimality? 214
6.4 Farkas’ Lemma: When Can No Improving Feasible Direction
be Found? 227
Exercises 232
7 GEOMETRY AND ALGEBRA OF LINEAR PROGRAMS 238
7.1 Geometry and Algebra of “Corner Points” 239
7.2 Fundamental Theorem of Linear Programming 248
7.3 Linear Programs in Canonical Form 250
Exercises 262
CONTENTS
ix
8 SOLVING LINEAR PROGRAMS: SIMPLEX METHOD 271
8.1 Simplex Method 271
8.2 Making the Simplex Method More Efficient 285
8.3 Convergence, Degeneracy, and the Simplex Method 289
8.4 Finding an Initial Solution: Two-Phase Method 294
8.5 Bounded Simplex Method 300
8.6 Computational Issues 305
Exercises 308
9 LINEAR PROGRAMMING DUALITY 317
9.1 Motivation: Generating Bounds 317
9.2 Dual Linear Program 321
9.3 Duality Theorems 327
9.4 Another Interpretation of the Simplex Method 333
9.5 Farkas’ Lemma Revisited 334
9.6 Economic Interpretation of the Dual 336
9.7 Another Duality Approach: Lagrangian Duality 338
Exercises 344
10 SENSITIVITY ANALYSIS OF LINEAR PROGRAMS 351
10.1 Graphical Sensitivity Analysis 351
10.2 Sensitivity Analysis Calculations 359
10.3 Use of Sensitivity Analysis 368
10.4 Parametric Programming 375
Exercises 380
11 ALGORITHMIC APPLICATIONS OF DUALITY 389
11.1 Dual Simplex Method 389
11.2 Transportation Problem 401
11.3 Column Generation 414
11.4 Dantzig-Wolfe Decomposition 420
11.5 Primal-Dual Interior Point Method 432
Exercises 441
12 NETWORK OPTIMIZATION ALGORITHMS 449
12.1 Introduction to Network Optimization 449
12.2 Shortest Path Problems 449
12.3 Maximum Flow Problems 458
12.4 Minimum Cost Network Flow Problems 470
Exercises 484
X CONTENTS
13 INTRODUCTION TO INTEGER PROGRAMMING 489
13.1 Basic Definitions and Formulations 490
13.2 Relaxations and Bounds 496
13.3 Preprocessing and Probing 500
13.4 When are Integer Programs “Easy?” 506
Exercises 511
14 SOLVING INTEGER PROGRAMS: EXACT METHODS 514
14.1 Complete Enumeration 514
14.2 Branch-and-Bound Methods 516
14.3 Valid Inequalities and Cutting Planes 524
14.4 Gomory’s Cutting Plane Algorithm 531
14.5 Valid Inequalities for 0-1 Knapsack Constraints 536
14.6 Branch-and-Cut Algorithms 540
14.7 Computational Issues 547
Exercises 551
15 SOLVING INTEGER PROGRAMS: MODERN
HEURISTIC TECHNIQUES 556
15.1 Review of Local Search Methods: Pros and Cons 556
15.2 Simulated Annealing 558
15.3 Tabu Search 562
15.4 Genetic Algorithms 565
15.5 GRASP Algorithms 570
Exercises 574
APPENDIX A BACKGROUND REVIEW 579
A.l Basic Notation 579
A.2 Graph Theory 581
A.3 Linear Algebra 583
REFERENCE 597
INDEX
603
Optimization modeling and algorithms are key components to problem-solving across various
fields of research, from operations research and mathematics to computer science and engineering.
Addressing the importance of the algorithm design process. Deterministic Operations Research focuses
on the design of solution methods for both continuous and discrete linear optimization problems. The
result is a clear-cut resource for understanding three cornerstones of deterministic operations research:
modeling real-world problems as linear optimization problems; designing the necessary algorithms to
solve these problems; and using mathematical theory to justify algorithmic development.
Treating real-world examples as mathematical problems, the author begins with an introduction to
operations research and optimization modeling that includes applications from sports scheduling
and the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimi-
zation problems, covering topics such as convexity, Farkas Lemma, and the study of polyhedra before
culminating in a discussion of the Simplex Method. The book also addresses linear programming
duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe
decomposition, and a primal-dual interior point algorithm. The final chapters present network
optimization and integer programming problems, highlighting various specialized topics including
label-correcting algorithms for the shortest path problem, preprocessing and probing in integer
programming, lifting of valid inequalities, and branch and cut algorithms.
Concepts and approaches are introduced by outlining examples that demonstrate and motivate
theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to
understand and encourages readers to understand how to think about the problem, not just what
to think. Relevant historical summaries can be found throughout the book, and each chapter is de-
signed as the continuation of the story” of how to both model and solve optimization problems by
using the specific problems—linear and integer programs-as guides, The book’s various examples
are accompanied by the appropriate models and calculations, and a related Web site features these
models along with Maple ” and MATLAB® content for the discussed calculations.
Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations
Research is an excellent book for operations research or linear optimization courses at the upper-
undergraduate and graduate levels. It also serves as an insightful reference for individuals working
in the fields of mathematics, engineering, computer science, and operations research who use and
design algorithms to solve problems in their everyday work.
|
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| spelling | Rader, David J. 1970- Verfasser (DE-588)142435856 aut Deterministic operations research models and methods in linear optimization David J. Rader Hoboken, New Jersey Wiley [2010] XV, 613 Seiten Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematik Operations Research (DE-588)4043586-6 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Operations research / Mathematics Mathematical optimization Linear programming Operations Research (DE-588)4043586-6 s Optimierung (DE-588)4043664-0 s DE-604 V:DE-576;X:wiley application/pdf http://swbplus.bsz-bw.de/bsz330080261cov.htm Titelbild Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029239968&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029239968&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Rader, David J. 1970- Deterministic operations research models and methods in linear optimization Mathematik Operations Research (DE-588)4043586-6 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043586-6 (DE-588)4043664-0 |
| title | Deterministic operations research models and methods in linear optimization |
| title_auth | Deterministic operations research models and methods in linear optimization |
| title_exact_search | Deterministic operations research models and methods in linear optimization |
| title_full | Deterministic operations research models and methods in linear optimization David J. Rader |
| title_fullStr | Deterministic operations research models and methods in linear optimization David J. Rader |
| title_full_unstemmed | Deterministic operations research models and methods in linear optimization David J. Rader |
| title_short | Deterministic operations research |
| title_sort | deterministic operations research models and methods in linear optimization |
| title_sub | models and methods in linear optimization |
| topic | Mathematik Operations Research (DE-588)4043586-6 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathematik Operations Research Optimierung |
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