LINEAR PROGRAMMING

Managing a Production Facility The Linear Programming Problem

INTRODUCTION

The Simplex Method Initialization Unboundedness Geometry

THE SIMPLEX METHOD

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

Programming Geometry

DEGENERACY

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

Method

EFFICIENCY OF THE SIMPLEX METHOD

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

DUALITY THEORY

Sensitivity Analysis Parametric Analysis and the Homotopy

Method The Parametric Self-Dual Simplex Method

SENSITIVITY AND PARAMETRIC ANALYSES

Solving Systems of Equations: LU-Factorization

Exploiting Sparsity Reusing a Factorization Performance Tradeoffs Updating a Factorization Shrinking the Bump Partial Pricing Steepest Edge

IMPLEMENTATION ISSUES

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

CONVEX ANALYSIS

Matrix Games Optimal Strategies The Minimax Theorem Poker

GAME THEORY

Measures of Mediocrity Multidimensional Measures: Regression

Analysis Regression Regression Iteratively Reweighted Least Squares

REGRESSION

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

NETWORK FLOW PROBLEMS

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

APPLICATIONS

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