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2. Managing a Production Facility
The Linear Programming Problem

3. The Simplex Method
Initialization
Unboundedness
Geometry

4. Definition of Degeneracy
Two Examples of Degenerate Problems
The Perturbation/Lexicographic Method
Bland’s Rule
Fundamental Theorem of Linear
Programming
Geometry

5. Performance Measures
Measuring the Size of a Problem
Measuring the Effort to Solve a Problem
Worst-Case Analysis of the Simplex
Method

6. Motivation—Finding Upper Bounds
The Dual Problem
The Weak Duality Theorem
The Strong Duality Theorem
Complementary Slackness
The Dual Simplex Method
A Dual-Based Phase I Algorithm
The Dual of a Problem in General Form
Resource Allocation Problems
Lagrangian Duality

7. Sensitivity Analysis
Parametric Analysis and the Homotopy
Method
The Parametric Self-Dual Simplex Method

8. Solving Systems of Equations: LU-Factorization
Exploiting Sparsity
Reusing a Factorization
Performance Tradeoffs
Updating a Factorization
Shrinking the Bump
Partial Pricing
Steepest Edge

9. Convex Sets
Caratheodory’s Theorem
The Separation Theorem
Farkas’ Lemma
Strict Complementarity

10. Matrix Games
Optimal Strategies
The Minimax Theorem
Poker

11. Measures of Mediocrity
Multidimensional Measures: Regression
Analysis
Regression
Regression
Iteratively Reweighted Least Squares

12. Networks
Spanning Trees and Bases
The Primal Network Simplex Method
The Dual Network Simplex Method
Putting It All Together
The Integrality Theorem

13. The Transportation Problem
The Assignment Problem
The Shortest-Path Problem
Upper-Bounded Network Flow Problems
The Maximum-Flow Problem

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