Linear Programming, Sensitivity Analysis & Related Topics

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Linear Programming, Sensitivity Analysis and Related Topics
To my family, for their love and support
Contents
Preface
Acknowledgements
Introduction
	Modelling 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 Analysis
	The Geometric Approach
		The founding concepts of Linear Programming
		The Maximization Form
		The Minimization Form
		Chapter 2 Exercises and applications
	The Simplex Method
		The Maximization Form
		The Minimization Form
		The Revised Simplex Method
		Chapter 3 Exercises and applications
	Understanding Special Cases and Mixed Function Problems
		Identifying special cases: graphical and simplex approaches
		The mixed function problem
		Chapter 4 Exercises and applications
	Duality
		Theorems of duality and relationships
		The Dual Simplex Method
		Particular cases
		Chapter 5 Exercises and applications
	Sensitivity Analysis
		A visual approach to Sensitivity Analysis
			The Maximization Form
			The Minimization Form
		Sensitivity Analysis under the Simplex Method, using Matrix Algebra
			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 Applications
		Highlighting 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 Topics
	The Variants of Linear Programmes
		Integer Programming
		Game Theory
		The Transportation Problem
		The Assignment Model
		Chapter 8 Exercises and applications
	Related Topics: Graphs and Networks
		The 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 Programming
	Mathematical 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
		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