The Linear Ordering Problem : Exact and Heuristic Methods in Combinatorial Optimization 1 Introduction 2 Heuristic Methods 3 Meta Heuristics 4 Branch and Bound 5 Branch and Cut 6 The Linear Ordering Polytope 7 Further Aspects References Index. Complex optimization problems abound in the real world. In the face of these challenges established methods often fall short of providing solutions. However ‘exact’ and ‘heuristic’ techniques are dramatically enhancing our ability to solve significant practical problems in the world of optimization. They are changing the landscape in the field broadening the frontiers of the possible and allowing us to engage effectively with a whole new range of challenges. This monograph sets out state of the art optimization methods for tackling the ‘linear ordering problem’ (LOP). Whereas important applications in business engineering and economics lie beyond the reach of methodologies that have been the focus of academic research for three decades the fresh approaches set out in this volume provide practical solutions to the LOP. The focus on the LOP does not limit the monograph’s scope and applicability however. The exact and heuristic techniques outlined in these pages can be put to use in any number of combinatorial optimization problems. While the authors employ the LOP to illustrate cutting edge optimization technologies the book is also a tutorial on how to design effective and successful implementations of exact and heuristic procedures alike. The information in these pages provides readers with a toolkit that can be employed in a variety of settings. As a result the book will be of great interest to researchers and practitioners in a number of fields including computer science mathematics operations research management science industrial engineering and economics. It is also suitable for use as a textbook on issues of practical optimization in a masters course or as a reference book for engineering optimization algorithms. The authors have sought to make the book accessible to as wide an audience as possible by providing the reader with basic definitions and concepts in optimization. In addition the numerous tutorials aid speedy assimilation while the coverage given to the next generation of Flash software prepares readers for future developments.