The name integer programming refers to the class of constrained optimization problems in which some or all of the variables are required to be integers. In the most widely studied and used integer programs, the objective function is linear and the constraints are linear inequalities. The field of integer programming has achieved great success in the academic and business worlds. Hundreds of papers are published every year in a variety of journals, several international conferences are held annu- ally and software for solving integer programs, both commercial and open source, is widely available and used by thousands of organizations. The application areas include logistics and supply chains, telecommunications, finance, manufacturing and many others.

This book is dedicated to the theoretical, algorithmic and computational aspects of integer programming. While it is not a textbook, it can be read as an introduction to the field and provides a historical perspective. Graduate students, academics and practitioners, even those who have spent most of their careers in discrete optimization, will all find something useful to learn from the material in this book. Given the amount that has been accomplished, it is remarkable that the field of integer programming began only fifty years ago.