Linear Programming,Sensitivity Analysisand Related TopicsMarie-France Derhy
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Linear Programming, SensitivityAnalysis & Related Topics
Table of Contents
Cover
Linear Programming, Sensitivity Analysis and Related Topics
To my family, for their love and support
Contents
Preface
Acknowledgements
IntroductionModelling using Linear Programming
Solving linear programmes
Linear Programming: the approach par excellence for understanding modelling
The approach of the book
Part I Linear Programming and Sensitivity AnalysisThe Geometric Approach
The founding concepts of Linear Programming
The Maximization Form
The Minimization Form
Chapter 2 Exercises and applications
The Simplex MethodThe Maximization Form
The Minimization Form
The Revised Simplex Method
Chapter 3 Exercises and applications
Understanding Special Cases and Mixed Function ProblemsIdentifying special cases: graphical and simplex approaches
The mixed function problem
Chapter 4 Exercises and applications
DualityTheorems of duality and relationships
The Dual Simplex Method
Particular cases
Chapter 5 Exercises and applications
Sensitivity AnalysisA visual approach to Sensitivity Analysis
The Maximization Form
The Minimization Form
Sensitivity Analysis under the Simplex Method, using Matrix Algebra
Table of Contents
The Maximization Form
Introduction of a new variable or of a new constraint
Note on the Minimization Form [The Portfolio 3D modified]
Embedded modifications
Revisiting mixed function problem
Discussion on optimality ranges: simplex and graphical approaches
Chapter 6 Exercises and applications
Understanding Computer Outputs and LP ApplicationsHighlighting outputs
Using software packages to solve LP problems
Study of outputs with respect to Chapters 3 and 6: the Simplex Method and
Sensitivity Analysis
Commented outputs with respect to Chapters 4 and 5: special cases and duality
The Various Fields of Application
Production and make-or-buy
Purchase plans
Finance
Advertising
Staff scheduling
Blending and nutrition
Efficiency problems
Chapter 7 Applications
Part II Variants and Related TopicsThe Variants of Linear Programmes
Integer Programming
Game Theory
The Transportation Problem
The Assignment Model
Chapter 8 Exercises and applications
Related Topics: Graphs and NetworksThe main building concepts of Graph Theory
Flow networks
The shortest path
The Minimal Spanning Tree
Chapter 9 Exercises and applications
Part III Mathematical Corner and Note on Nonlinear ProgrammingMathematical Corner
Coping with infeasibility
Flow networks
The Shortest Route Algorithm: discussion on Sensitivity Analysis
The Minimal Spanning Tree
Chapter 10 Exercises and applications
Note on Nonlinear Programming
Table of Contents
Quadratic Programming: definition
Illustrations and graphical displays: solution method using Lagrange multipliers
Formulating the quadratic programme
Comment on shadow prices and RHS ranges
Chapter 11 Exercises
Basic Review Chapter
Basic Matrix Algebra
Derivatives and local extrema
Answers to Selected Problems and Applications
Study Applications
Index