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出版社 Springer Berlin Heidelberg
DOI 10.1007/978-3-540-73671-4
版权 2008
ISBN 978-3-540-73670-7 (Print) 978-3-540-73671-4 (Online)
Subject Collection 商业和经济
学科 经济学与管理科学, 经营研究与决策理论, Operations Research, Mathematical Programming, Engineering Economics, Organization, Logistics, Marketing
SpringerLink Date 2007年8月15日
CONTENTS
Symbols XIII
A. Linear Algebra 1
A.1 Matrix Algebra 1
A.2 Systems of Simultaneous Linear Equations 5
A.3 Convexity 23
B. Computational Complexity 31
B.1 Algorithms and Time Complexity Functions 31
B.2 Examples of Time Complexity Functions 37
B.3 Classes of Problems and Their Relations 41
1. Introduction 45
1.1. A Short History of Linear Programming 45
1.2 Assumptions and the Main Components
of Linear Programming Problems 48
1.3 The Modeling Process 53
1.4 The Three Phases in Optimization 57
1.5 Solving the Model and Interpreting the Printout 60
2. Applications 67
2.1 The Diet Problem 67
2.2 Allocation Problems 71
2.3 Cutting Stock Problems 75
2.4 Employee Scheduling 80
2.5 Data Envelopment Analysis 82
2.6 Inventory Planning 85
2.7 Blending Problems 89
2.8 Transportation Problems 91
2.9 Assignment Problems 102
2.10 A Production – Inventory Model: A Case Study 107
3. The Simplex Method 129
3.1 Graphical Concepts 129
3.1.1 The Graphical Solution Technique 129
3.1.2 Four Special Cases 138
3.2 Algebraic Concepts 143
3.2.1 The Algebraic Solution Technique 143
3.2.2 Four Special Cases Revisited 158
4. Duality 167
4.1 The Fundamental Theory of Duality 167
4.2 Primal-Dual Relations 183
4.3 Interpretations of the Dual Problem 198
5. Extensions of the Simplex Method 203
5.1 The Dual Simplex Method 203
5.2 The Upper Bounding Technique 212
5.3 Column Generation 219
6. Postoptimality Analyses 225
6.1 Graphical Sensitivity Analysis 227
6.2 Changes of the Right-Hand Side Values 232
6.3 Changes of the Objective Function Coefficients 240
6.4 Sensitivity Analyses in the Presence of Degeneracy 245
6.5 Addition of a Constraint 248
6.6 Economic Analysis of an Optimal Solution 252
7. Non-Simplex Based Solution Methods 261
7.1 Alternatives to the Simplex Method 262
7.2 Interior Point Methods 273
8. Problem Reformulations 295
8.1 Reformulations of Variables 295
8.1.1 Lower Bounding Constraints 295
8.1.2 Variables Unrestricted in Sign 296
8.2 Reformulations of Constraints 298
8.3. Reformulations of the Objective Function 301
8.3.1. Minimize the Weighted Sum of Absolute Values 301
8.3.2 Bottleneck Problems 306
8.3.3 Minimax and Maximin Problems 313
8.3.4 Fractional (Hyperbolic) Programming 320
9. Multiobjective Programming 325
9.1 Vector Optimization 327
9.2 Models with Exogenous Tradeoffs Between Objectives 337
9.2.1 The Weighting Method 337
9.2.2 The Constraint Method 339
9.3 Models with Exogenous Achievement Levels 341
9.3.1 Reference Point Programming 342
9.3.2 Fuzzy Programming 346
9.3.3 Goal Programming 351
9.4 Bilevel Programming 359
References 363
Subject Index 377
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