E-Book, Englisch, 416 Seiten, Web PDF
Kolman / Beck / Rheinboldt Elementary Linear Programming with Applications
1. Auflage 2014
ISBN: 978-1-4832-6968-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 416 Seiten, Web PDF
ISBN: 978-1-4832-6968-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Elementary Linear Programming with Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;Acknowledgments;14
8;PROLOGUE: INTRODUCTION TO OPERATIONS RESEARCH;16
8.1;Further Readings;20
9;CHAPTER 0. REVIEW OF LINEAR ALGEBRA (OPTIONAL);22
9.1;0.1 Matrices;22
9.2;0.2 Gauss-Jordan Reduction;30
9.3;0.3 The Inverse of a Matrix;39
9.4;0.4 Subspaces;44
9.5;0.5 Linear Independence and Basis;49
10;CHAPTER 1. GEOMETRY IN Rn;60
10.1;1.1 Hyperplanes;60
10.2;1.2 Convex Sets;65
11;CHAPTER 2. INTRODUCTION TO LINEAR PROGRAMMING;74
11.1;2.1 The Linear Programming Problem;74
11.2;2.2 Matrix Notation; Geometric Solutions;93
11.3;2.3 The Simplex Method;114
11.4;2.4 Degeneracy and Cycling (Optional);130
11.5;2.5 Artificial Variables;136
12;CHAPTER 3. FURTHER TOPICS IN LINEAR PROGRAMMING;158
12.1;3.1 Duality;158
12.2;3.2 Computational Relations between the Primal and Dual Problems;179
12.3;3.3 The Dual Simplex Method;205
12.4;3.4 The Revised Simplex Method;211
12.5;3.5 Sensitivity Analysis;221
12.6;3.6 Computer Aspects (Optional);231
13;CHAPTER 4. INTEGER PROGRAMMING;242
13.1;4.1 Examples;242
13.2;4.2 Cutting Plane Methods;255
13.3;4.3 Branch and Bound Methods;269
13.4;4.4 Computer Aspects (Optional);282
14;CHAPTER 5. SPECIAL TYPES OF LINEAR PROGRAMMING PROBLEMS;286
14.1;5.1 The Transportation Problem;286
14.2;5.2 The Assignment Problem;315
14.3;5.3 Graphs and Networks. Basic Definitions;329
14.4;5.4 The Maximal Flow Problem;334
14.5;5.5 The Shortest Route Problem;353
14.6;5.6 The Critical Path Method;364
14.7;5.7 Computer Aspects (Optional);374
15;Solutions to Odd-Numbered Exercises;382
16;Index;410
