INTEGER AND MIXED INTEGER MODEL (STATISTICS PROJECT TOPICS AND MATERIALS)
ABSTRACT
In this work, we study integer and mixed integer linear programming problems. The methods such as simplex, Dual simplex, Branch and Bound and cutting plane method where discussed. We also worked an example where we used cutting plane method to remove the fraction part of the solution, leaving the integer solution.
CHAPTER ONE
INTRODUCTION
1.0 Basic Concept
Linear programming is a mathematical technique useful for allocation of scarce or limited resource to several competing activities on the basis of a given criterion of optimality.
The adjective “linear” refers to linear relationship among variables in a model. Thus, a given change in one variable will always cause a resulting proportional change in another variable. For example doubling the investment on a certain project also doubles the rate of return .
The word “programming” here does not mean computer programming; rather it is essentially a synonym for planning. Furthermore, the word “programming” refers to mathematical modeling and solving of a problem that involves economic allocation of limited resources by choosing a particular course of action or strategy among various alternative strategies in order to achieve the desired objective. Also the word “integer” refers to whole number, both positive and negative.
Thus, integer linear programming is a mathematical technique useful for allocation of scarce or limited resource to several competing activities on the basis of a given criterion of optimality in which all the variables are restricted to be integer (or discrete) values, while mixed integer linear programming is also a….
