Linear Programming and its Applications

✍ Scribed by H.A. Eiselt, C.-L. Sandblom

• Year: 2007
• Tongue: English
• Leaves: 390
• Edition: 1
• Category: Library

✦ Synopsis

In the pages of this text readers will find nothing less than a unified treatment of linear programming. Without sacrificing mathematical rigor, the main emphasis of the book is on models and applications. The most important classes of problems are surveyed and presented by means of mathematical formulations, followed by solution methods and a discussion of a variety of "what-if" scenarios. Non-simplex based solution methods and newer developments such as interior point methods are covered.

✦ Table of Contents

3540736700......Page 1
Contents......Page 8
Symbols......Page 11
A.1 Matrix Algebra......Page 13
A.2 Systems of Simultaneous Linear Equations......Page 17
A.3 Convexity......Page 35
B.1 Algorithms and Time Complexity Functions......Page 43
B.2 Examples of Time Complexity Functions......Page 49
B.3 Classes of Problems and Their Relations......Page 53
1.1. A Short History of Linear Programming......Page 57
1.2 Assumptions and the Main Components of Linear Programming Problems......Page 60
1.3 The Modeling Process......Page 65
1.4 The Three Phases in Optimization......Page 69
1.5 Solving the Model and Interpreting the Printout......Page 72
2.1 The Diet Problem......Page 79
2.2 Allocation Problems......Page 83
2.3 Cutting Stock Problems......Page 87
2.4 Employee Scheduling......Page 92
2.5 Data Envelopment Analysis......Page 94
2.6 Inventory Planning......Page 97
2.7 Blending Problems......Page 101
2.8 Transportation Problems......Page 103
2.9 Assignment Problems......Page 114
2.10 A Production – Inventory Model: A Case Study......Page 119
3.1.1 The Graphical Solution Technique......Page 141
3.1.2 Four Special Cases......Page 150
3.2.1 The Algebraic Solution Technique......Page 155
3.2.2 Four Special Cases Revisited......Page 170
4.1 The Fundamental Theory of Duality......Page 178
4.2 Primal-Dual Relations......Page 194
4.3 Interpretations of the Dual Problem......Page 209
5.1 The Dual Simplex Method......Page 214
5.2 The Upper Bounding Technique......Page 223
5.3 Column Generation......Page 230
6. Postoptimality Analyses......Page 236
6.1 Graphical Sensitivity Analysis......Page 238
6.2 Changes of the Right-Hand Side Values......Page 243
6.3 Changes of the Objective Function Coefficients......Page 251
6.4 Sensitivity Analyses in the Presence of Degeneracy......Page 256
6.5 Addition of a Constraint......Page 259
6.6 Economic Analysis of an Optimal Solution......Page 263
7. Non-Simplex Based Solution Methods......Page 272
7.1 Alternatives to the Simplex Method......Page 273
7.2 Interior Point Methods......Page 284
8.1.1 Lower Bounding Constraints......Page 306
8.1.2 Variables Unrestricted in Sign......Page 307
8.2 Reformulations of Constraints......Page 309
8.3.1 Minimize the Weighted Sum of Absolute Values......Page 312
8.3.2 Bottleneck Problems......Page 317
8.3.3 Minimax and Maximin Problems......Page 324
8.3.4 Fractional (Hyperbolic) Programming......Page 331
9. Multiobjective Programming......Page 335
9.1 Vector Optimization......Page 337
9.2.1 The Weighting Method......Page 347
9.2.2 The Constraint Method......Page 349
9.3 Models with Exogenous Achievement Levels......Page 351
9.3.1 Reference Point Programming......Page 352
9.3.2 Fuzzy Programming......Page 356
9.3.3 Goal Programming......Page 361
9.4 Bilevel Programming......Page 369
References......Page 373
D......Page 387
L......Page 388
R......Page 389
W......Page 390