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Linear Programming and its Applications
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Linear Programming and its Applications
von: H.A. Eiselt, C.-L. Sandblom
Springer-Verlag, 2007
ISBN: 9783540736714
380 Seiten, Download: 6146 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  PREFACE 6  
  CONTENTS 8  
  SYMBOLS 11  
     Notation 11  
  A LINEAR ALGEBRA 13  
     A.1 Matrix Algebra 13  
     A.2 Systems of Simultaneous Linear Equations 17  
     A.3 Convexity 35  
  B COMPUTATIONAL COMPLEXITY 43  
     B.1 Algorithms and Time Complexity Functions 43  
     B.2 Examples of Time Complexity Functions 49  
     B.3 Classes of Problems and Their Relations 53  
  1 INTRODUCTION 57  
     1.1 A Short History of Linear Programming 57  
     1.2 Assumptions and the Main Components of Linear Programming Problems 60  
     1.3 The Modeling Process 65  
     1.4 The Three Phases in Optimization 69  
     1.5 Solving the Model and Interpreting the Printout 72  
  2 APPLICATIONS 79  
     2.1 The Diet Problem 79  
     2.2 Allocation Problems 83  
     2.4 Employee Scheduling 92  
     2.5 Data Envelopment Analysis 94  
     2.6 Inventory Planning 97  
     2.7 Blending Problems 101  
     2.8 Transportation Problems 103  
     2.9 Assignment Problems 114  
     2.10 A Production – Inventory Model: A Case Study 119  
  3 THE SIMPLEX METHOD 141  
     3.1 Graphical Concepts 141  
     3.2 Algebraic Concepts 155  
  4 DUALITY 178  
     4.1 The Fundamental Theory of Duality 178  
     4.2 Primal-Dual Relations 194  
     4.3 Interpretations of the Dual Problem 209  
  5 EXTENSIONS OF THE SIMPLEX METHOD 214  
     5.1 The Dual Simplex Method 214  
     5.2 The Upper Bounding Technique 223  
     5.3 Column Generation 230  
  6 POSTOPTIMALITY ANALYSES 236  
     6.1 Graphical Sensitivity Analysis 238  
     6.2 Changes of the Right-Hand Side Values 243  
     6.3 Changes of the Objective Function Coefficients 251  
     6.4 Sensitivity Analyses in the Presence of Degeneracy 256  
     6.5 Addition of a Constraint 259  
     6.6 Economic Analysis of an Optimal Solution 263  
  7 NON-SIMPLEX BASED SOLUTION METHODS 272  
     7.1 Alternatives to the Simplex Method 273  
     7.2 Interior Point Methods 284  
  8 PROBLEM REFORMULATIONS 306  
     8.1 Reformulations of Variables 306  
     8.2 Reformulations of Constraints 309  
     8.3 Reformulations of the Objective Function 312  
  9 MULTIOBJECTIVE PROGRAMMING 335  
     9.1 Vector Optimization 337  
     9.2 Models with Exogenous Tradeoffs Between Objectives 347  
     9.3 Models with Exogenous Achievement Levels 351  
     9.4 Bilevel Programming 369  
  REFERENCES 373  
  SUBJECT INDEX 387  


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