A Survey of Linear Programming Concepts

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