Linear programming is a mathematical tool that is used to maximize or minimize a function when constraints are linear. In this project, we considered some examples and applications of linear programming problems.
TABLE OF CONTENTS
Title page
Certification
Dedication
Acknowledgements
Abstract
Table of Contents
List of Tables
List of Figures
CHAPTER ONE
1.0. Introduction
1.1. Definition of basic terms
1.2. Aim and objectives of the study
1.2.1. Aim
1.2.2. Objectives
1.3. Model Formulation
1.4. Types of Optimization problems
CHAPTER TWO
2.0. Literature review
CHAPTER THREE
3.0. Linear programming problems
3.1. Definition
3.2. Linear programming problem formulation
3.3. Features of Linear programming problem
3.4. Mathematical structure of a linear programming problem
3.5. Duality of a linear programming problem
3.5.1. Determination of a dual
3.5.2. Primal-Dual Relationship
3.6. Methods of solution to linear programming problems
3.6.1. Graphical method
3.6.1.1. Working Rule for graphical method
3.6.1.2. Limitations of graphical method
3.6.2. Algebraic method
3.6.2.1. Working Rule for algebraic method
3.6.2.2. Limitations of algebraic method
3.6.3. Simplex method
3.6.3.1. Working rule for simplex method
3.6.4. Solving a LPP using a spread sheet application
3.7. Degeneracy of a linear programming problem
3.8. Applications of linear programming
3.9. Sensitivity analysis
CHAPTER FOUR
4.0. Transportation models
4.1. Model Formulation
4.2. Types of transportation problem
4.2.1. Balanced transportation problem
4.2.2. Unbalanced transportation problem
4.3. Features of transportation models
4.4. Solution procedure to transportation models
4.4.1. Initial basic feasible solution
4.4.1.1. Properties of initial basic feasible solution
4.4.1.2. Degenerate basic feasible solution
4.4.1.3. North-West corner method
4.4.1.3.1. Working rule for North-West corner method
4.4.1.4. Minimum cost method
4.4.1.5. Vogel’s approximation method
4.4.1.5.1. Working rule for Vogel’s approximation method
4.4.2. Optimal solution
4.4.2.1. Looping of cells
4.4.2.2. Stepping stone method
4.4.2.3. Modified distribution method
4.4.2.3.1. Working rule for Modified distribution method
CHAPTER FIVE
5.0. Conclusion and Recommendation
5.1. Conclusion
5.2. Recommendation
References
LIST OF FIGURES
Fig. 3.1: Graphical solution of linear programming problem
Fig. 3.2: Microsoft Excel Solver
Fig. 4.1: Representation of transportation model with nodes and arcs
