Derhy M.-F. Linear Programming, Sensitivity Analysis & Related Topics

New York: Prentice Hall, 2010. — 465 p.This book covers all aspects of linear programming from the two-dimensional LPs and their extension to higher dimensional LPs, through duality and sensitivity analysis and finally to the examination of commented software outputs.
The book is organised into three distinct parts: the first part studies the concepts of linear programming and presents its founding theorems complete with proofs and applications; the second part presents linear programming in the diversity of its variants (Integer Programming, Game Theory, Transportation Problem, Assignment Model), and highlights the modelling problems that are involved in network optimisation; the final part furthers the discussion on selected topics and presents an opening to nonlinear programming through quadratic programming.Linear Programming, Sensitivity Analysis and Related Topics
To my family, for their love and supportAcknowledgementsModelling using Linear Programming
Solving linear programmes
Linear Programming: the approach par excellence for understanding modelling
The approach of the bookLinear Programming and Sensitivity AnalysisThe Geometric Approach
The founding concepts of Linear Programming
The Maximization Form
The Minimization Form
Exercises and applications
The Simplex Method
The Maximization Form
The Minimization Form
The Revised Simplex Method
Exercises and applications
Understanding Special Cases and Mixed Function Problems
Identifying special cases: graphical and simplex approaches
The mixed function problem
Exercises and applications
Duality
Theorems of duality and relationships
The Dual Simplex Method
Particular cases
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
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
ApplicationsVariants 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 Networks
The main building concepts of Graph Theory
Flow networks
The shortest path
The Minimal Spanning Tree
Exercises and applicationsMathematical Corner and Note on Nonlinear ProgrammingMathematical Corner
Coping with infeasibility
Flow networks
The Shortest Route Algorithm: discussion on Sensitivity Analysis
The Minimal Spanning Tree
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’
Exercises
Basic Review Chapter
Basic Matrix Algebra
Derivatives and local extrema
Answers to Selected Problems and Applications
Study Applications