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• Integer Programming: Theory, Applications, and Computations
• Copyright Page
• Table of Contents
• Dedication
• 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
• 5.4 Comments on Computational Experience
• 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