## INTEGER AND MIXED INTEGER MODEL

TABLE OF CONTENT
Title page
Approval page
Dedication
Acknowledgement
Abstract
Table of content

CHAPTER ONE: INTRODUCTION
1.0 Basic Concept
1. 1. 0Definitions of basic Terminologies and Application
1.1.1 Decision Variables (Activities)
1.1.2 Objective Function
1.1.3 Optimal Value
1.1.4 The Constraints
1.1.5 Solution
1.1.6 Feasible Solution to Integer Programming Model

CHAPTER TWO: LITERATURE REVIEW

CHAPTER THREE: ASSUMPTION, TYPES, APPLICATION AND METHODS OF INTEGER AND MIXED INTEGER MODEL
3.1 Assumption
3.2 Types of Integer Programming Model
3.2.1 Pure Integer Programming Model
3.2.2. Mixed Integer Programming Model
3.2.3 Zero-One (Binary)  Integer Programming Model
3.2.4 Application of Integer Linear Programming Model
3.2.5 Production Planning
3.2.6 Scheduling
3.2 .7 Telecommunication Networks
3.2.8 Cellular Networks
4.2.9 Graphical Method of Solution
4.2.10 Corner Point Method
3.2. 11The Simplex Method of solution
3.2.12 Dual Simplex Method of Solution
3.2.13 Branch and Bound Method
3.2.14 Cutting Plane Method
3.2. 15 Gomory Algorithm Method
3.2. 16 Steps  of Gomory’s all Integer Programming  Algorithm
3.2.17. Method For Constructing Additional Constraint  (CUT)

CHAPTER FOUR: MATHEMATICAL FORMULATION OF INTEGER AND MIXED INTEGER PROGRAMMING MODEL
4.1.0 Steps in Formulation of Integer and mixed integer Programming model
4.1.1 Step one: Identify the Decision Variables
4.1.2 Step2: Identify the Problem Data
4.1.3 Step 3: Formulate the constraints
4.1.4 Step 4: Formulate the Objective Function
4.2.0 Modeling of integer and mixed integer programming problem
4.3.0  Method of Solving Integer and Mixed Integer Programming Problem
4. 3. 1 Graphical Method of Solution
4.3. 2 Cutting Plane Method
4.3. 3 Dual Simplex Method
4.3.4 Branch  and Bound Method

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 Discussion of the solution
5.2 Summary/ Conclusion
5.3 Recommendation
REFERENCES

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....

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