FUNDAMENTALS OF SENSITIVITY AND PARAMETRIC ANALYSIS OF A LINEAR PROGRAMMING PROBLEM

FUNDAMENTALS OF  SENSITIVITY AND PARAMETRIC ANALYSIS

OF A LINEAR PROGRAMMING PROBLEM

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TABLE OF CONTENT

Title Page-            -        -                  -        -        -        -        -        -i

Dedication             -        -                  -        -        -        -        -        -iii

Table of Content              -        -                  -        -        -        -        -v      

Abstract                -        -                  -        -        -        -        -        -vii

CHAPTER ONE

1.0 Introduction               -        -                  -        -        -        -        -1

1.1 Background of the Study               -        -                  -        -        -2

1.2 Parametric Analysis            -        -                  -        -        -        -5

1.3 Statement of Problem -        -                  -        -        -                  6

1.4 Significant of the Study-      -                  -        -        -                  -7

CHAPTER TWO

2.0 Literature Review -    -                  -        -        -        -        -        -8

2.1 Classification of Sensitivity and Parametric Analysis- -                  -14

CHAPTER THREE

3.0 Parametric Analysis- -                  -        -        -        -        -        -16

3.1 The LP Model and Continuous Changes in the R.H.S.-          -        -18

3.2 Background of the Procedure-       -                  -        -        -        -19

3.3 The Algorithm -         -                  -        -        -        -        -        -22

CHAPTER FOUR

4.0 Numerical Illustration and Discussion -    -                  -        -        -33

4.1 Numerical Illustration of Parametric-       -                  -        -        -33

4.2 Discussion and Analysis-    -                  -        -        -        -        -47

CHAPTER FIVE

  SUMMARY AND CONCLUSION

5.1 Summary-        -                  -        -        -        -        -        -        -49

5.2 Conclusion-     -                  -        -        -        -        -        -        -55

References -         -                  -        -        -        -        -        -        -57

CHAPTER ONE

1.0 Introduction

Sensitivity analysis is the study of what happens to the optimal solution when discrete changes occur in the original coefficients of an LP problem. The changes in this case may be in the form of additional constraints or variables.

A Mathematical Model Comprises of independent and dependents variables and a system of relationship in the form of equations or inequalities that exist between the variables. Mathematically, the numerical methods employed to solve the equations underlying the mathematical model are often the important aspect of the model development process. Furthermore, mathematical models also include variable parameters which constitute the relationship that unfold from experiments and as such, their actual values are not precisely known precisely but may vary within some ranges of uncertainty. The sensitivity analysis of a mathematical model becomes even more complicated if the numerical calculations cannot be handled with known methods.

The simplest and also the most common procedure for assessing the effects of parameter variations on a model’s result is to vary selected input parameters, Rerun code and record the corresponding changes in the result. The model parameters responsible for the largest relative changes are classified to be the most important. For complex models, though the large amount of computing time needed by such re-calculations severely restricts the scope of this sensitivity analysis. In practice, this means that the modeler can investigate only a few parameters that he judges a priori to be important. Cacuci(2002).

1.1 Background of the Study

There are certain questions that are often asked regarding optimal solution of a linear programming (LP) problem. For example, what happens to the optimum solution (both the values of the variable and the value of the objective function) when certain changes occur in some of the values of the original data? These are some of the questions that sensitivity analysis tries to answer. If the objective function or the variables change when an original coefficient is changed then we say that the optimal  solution of the programming is sensitive. A sort of examination of the impact of the input data on the output result is crucial. The procedures and algorithms of mathematical programming are important but the problems that one often encounter in practice are usually associated with data; getting it at all and getting accurate data. Some data, necessary for mathematical models are inherently uncertain

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