Linear Programming,Sensitivity Analysisand Related TopicsMarie-France Derhy

• Acircularapproachallowsthesameapplicationstobelookedatthrough

• Thebooktakesahighlygraphicalapproachtoaidunderstandingand

• Eachchapterincludesasetofobjectivesandproposesproblemsand

www.pearson-books.com

We work with leading authors to develop the

strongest educational materials in mathematics,

bringing cutting-edge thinking and best learning

practice to a global market.

Under a range of well-known imprints, including

Prentice Hall, we craft high quality print and

electronic publications which help readers to understand

and apply their content, whether studying or at work.

To find out more about the complete range of our

publishing, please visit us on the World Wide Web at:

www.pearsoned.co.uk

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