Table of Contents
1. How This Book Was Born..........................................5
2. The Graphical Method.............................................9
3. The Algebraic Method............................................37
4. The Simplex Method
4.1 Review of Simultaneous Linear
Equations................61
4.2 The Corner Rule .............................................67
4.3 Justification for the Corner Rule
..........................92
4.4 Degeneracy in Linear
Programming........................94
4.5 Alternative Formulation for the Objective Function:
"Z-subtracted" Form
.......................................106
4.6 Evaluators
...................................................113
Appendix..........................................................121
5. Some Microcomputer Methods
5.1
Introduction.................................................125
5.2 The Program RODLIN.......................................127
5.3 The Huth Program
LP262...................................136
5.4 LINDO and Other Programs
................................141
6. Matrix Review
6.1 Basic
Operations............................................151
6.2 Matrix
Inversion.............................................163
6.3 Special Cases of Matrix Inversion
........................177
6.4 Partitioning
Matrices.......................................184
6.5 the Sweepout Method Applied to Linear
Programming.....189
7. Vectors
7.1
Introduction..................................................199
7.2 Vector Spaces................................................202
7.3 Spanning Sets and
Bases....................................206
7.4 Dimensionality...............................................224
7.5 Changing Bases...............................................229
8. Matrix Iteration Method
8.1
Introduction..................................................249
8.2 Revised Simplex
Method...................................259
8.3 Formal Notation for Matrix.
...............................266
9 Minimization
9.1
Introduction................................................285
9.2
The Big-M
Method.........................................286
9.3
The Two-Phase
Method...................................299
9.4
The "Reverse" (Dual Simplex)
Method...................305
10 Special Situations
10.1
Introduction..................................................325
10.2 Unbounded
Solutions........................................326
10.3 Inconsistent
Constraints.....................................336
10.4Multiple
solutions.............................................340
10.5 Convex
Combinations.......................................344
10.6 Equality
Constraints.........................................346
10.7 Variables
Not Bounded Below by Zero....................360
10.8 Other
Special
Cases.........................................366
10.9 A
More Realistic Formulation...............................371
11.
The Dual
11.1 The
Concept of Duality in Linear Programming..........381
11.2
The Dual Simplex ("Reverse")
Method....................407
11.3 An
Ambiguous Situation......................................414
11.4 Primal-Dual
Geometry.......................................421
11.5 Why
Canonical Form is Necessary..........................430
12.
Sensitivity (Post-optimality) Analysis
12.1
Introduction...................................................431
12.2 Computer
Method of RHS Sensitivity Analysis............460
12.3 Objective
Function Changes................................472
12.4 Objective
Function Sensitivity : Computer Method.....484
12.5 Added
Sensitivity Topics....................................488
13
More About
Evaluators
13.1 Selecting
The Incoming Variable............................499
13.2 Shadow
Prices.................................................502
14
The Transportation Method
14.1 Problem
Formulation..........................................505
14.2 Searching for
Optimality.....................................520
14.3 The U,V
Method...............................................528
14.4 The Transportation Problem in LP
Format.................555
14.5 Inspection
(Trial & Error) Method..........................565
Index......................................................................573