1
How This Book Was Born
1
End of Chapter
6
2
The Graphical Method
1
End of Chapter
30
3
The Algebraic Method
1
End of Chapter
25
4
The Simplex Method
4.1 Review of Simultaneous Linear Equations
1
4.2 The Corner Rule
7
4.3 Justification for the Corner Rule
32
4.4 Degeneracy in Linear Programming
33
4.5 Alternative Formulation for the Objective Function:
z-subtracted form
46
4.6 Evaluators
51
Appendix
58
End of Chapter
61
5
Some Microcomputer Methods
5.1 Introduction
1
5.2 The Program RodlinDG
4
5.3 The Program LP100
14
5.4 LINDO and Other Programs
20
End of Chapter
28
6
Matrix Review
6.1 Basic Operations
1
6.2 Matrix Inversion
12
6.3 Special Cases of Matrix Inversion
25
6.4 Partitioning Matrices
31
6.5 The Sweepout Method Applied to Linear Programming
36
End of Chapter
45
7
Vectors
7.1 Introduction
1
7.2 Vector Spaces
4
7.3 Spanning Sets and Bases
9
7.4 Dimensionality
26
7.5 Changing Bases
31
End of Chapter
48
8
Matrix Iteration Method
8.1 Introduction
1
8.2 Revised Simplex Method
10
8.3 Formal Notation for Matrix Method
17
End of Chapter
30
9
Minimization
9.1 Introduction
1
9.2 The Big-M Method
2
9.3 The Two-Phase Method
15
9.4 The "Reverse" (Dual Simplex) Method
21
End of Chapter
40
10
Special Situations
10.1 Introduction
1
10.2 Unbounded Solutions
2
10.3 Inconsistent Constraints
10
10.4 Multiple Solutions
12
10.5 Convex Combinations
17
10.6 Equality Constraints
19
10.7 Variables Not Bounded Below by Zero
32
10.8 Other Special Cases
38
10.9 A More Realistic Formulation (for Real-world problems)
50
End of Chapter
58
11
The Dual
11.1 The Concept of Duality in Linear Programming
1
11.2 The Dual Simplex (Reverse) Method
29
11.3 An Ambiguous Situation
38
11.4 Primal-Dual Geometry
45
11.5 Why Canonical Form is Necessary
56
End of Chapter
60
12
Sensitivity (Post-optimality) Analysis
12.1 Introduction
1
12.2 Computer Method of RHS Sensitivity Analysis
33
12.3 Objective Functions Changes
44
12.4 Objective Function Sensitivity: Computer Method
56
12.5 Added Sensitivity Topics
61
End of Chapter
13
More About Evaluators
13.1 Selecting the Incoming Variable
1
13.2 Shadow Prices
4
End of Chapter
6
14
The Transportation Method
14.1 Problem Formulation
1
14.2 Searching for Optimality
17
14.3 The U,V Method
26
14.4 The Transportation Problem in LP Format
51
14.5 Inspection (Trial & Error) Method
60
End of Chapter
67
Appendix A: List of Tables
Appendix B: List of Figures
Students whose problems were used
Ordering Information
Index