Branch-and-Price

This open access book is a unique resource in computational mathematical optimization. It conveys the entire spectrum from the basic theory to the most advanced tricks in reformulations and decomposition approaches to solving mixed-integer linear programs. The book has useful and partly previously unpublished facts for students, teachers, and practitioners alike. The content covers algorithmic ideas like column generation, cutting planes, and branch-and-price, reformulation techniques like Dantzig-Wolfe decomposition, Lagrangian relaxation, and Benders decomposition, the very important application domains of vehicle routing and crew scheduling, and has some practical advise when it comes to an implementation. Many notes and even more didactic illustrations and examples bring the theory to life, complemented by almost 140 exercises, including solutions. As a side effect, readers learn ways how to formulate integer programming models for a great variety of combinatorial optimization problems. The material draws from more than 400 references and the four authors' own decades of experience in the field. Several photos taken by the authors bring a personal touch to the writing, among other tiny anecdotal elements that the connoisseur will appreciate. The book is not, and cannot be encyclopedic, but it has the ambition to be the standard text and main reference in the field for the years to come. Students, researchers, and practitioners aiming to solve large, complex discrete and combinatorial optimization problems-whether in industry, science, or technology-will find this book essential for exploring optimal and near-optimal solutions through decomposition methods and column generation.