# Integer Programming

## 1st Edition

### Theory, Applications, and Computations

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eBook ISBN: 9781483260372
Published Date: 28th July 1975
Page Count: 394
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## Description

Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming.

Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models.

This book is a valuable resource for industrial engineers and research workers.

Preface

Chapter 1 Integer Optimization and Its Applications

1.1 What Is Integer Optimization?

1.2 "Solving" the Integer Problem by Rounding the Continuous Optimum

1.3 Examples of the Applications of Integer Programming

1.4 Methods of Integer Programming

1.5 Organization of the Book

Problems

Chapter 2 Linear Programming

2.1 Introduction

2.2 Definition of Linear Programming

2.3 The Simplex Method

2.4 The Revised Simplex Method

2.5 The Dual Problem

2.6 Bounded Variables

Problems

Chapter 3 Zero-One Implicit Enumeration

3.1 Introduction

3.2 Zero-One Equivalence of the Integer Problem

3.3 Concept of Implicit Enumeration

3.4 Enumeration Scheme

3.5 Fathoming Tests

3.6 Nonlinear Zero-One Problem

3.7 Mixed Zero-One Problem

3.8 Concluding Remarks

Problems

Chapter 4 Branch-and-Bound Methods

4.1 The Concept of Branch-and-Bound

4.2 Branch-and-Bound Principle

4.3 General (Mixed) Integer Linear Problem

4.4 Solution of Nonlinear Integer Programs by Branch-and-Bound

4.5 Concluding Remarks

Problems

Chapter 5 Cutting Methods

5.1 Introduction

5.2 Dual Cutting Methods

5.3 Primal Cutting Methods

5.5 Concluding Remarks

Problems

Chapter 6 The Asymptotic Integer Algorithm

6.1 Introduction

6.2 The Idea of the Asymptotic Algorithm

6.3 Development of the Asymptotic Algorithm

6.4 Solution of the Group (Relaxed) Problem

6.5 Solution of Integer Programs by the Group Problem

6.6 Reducing the Number of Congruences

6.7 Faces of the Corner Polyhedron

6.8 Concluding Remarks

Problems

Chapter 7 Algorithms for Specialized Integer Models

7.1 Introduction

7.2 Knapsack Problem

7.3 Fixed-Charge and Plant Location Problems

7.4 Traveling Salesman Problem

7.5 Set Covering Problem

7.6 Concluding Remarks

Problems

Chapter 8 Computational Considerations in Integer Programming

8.1 Introduction

8.2 Model Formulation in Integer Programming

8.3 A Composite Algorithm

8.4 "General" Approximate Methods for Integer Programming

8.5 Concluding Remarks

References

Index

No. of pages:
394
Language:
English
Published:
28th July 1975
Imprint: