The subject of this book is the nested partitions method(NP), arelatively new optimization method that has been found to be very effective solving discrete optimization problems. Such discrete problems are common in many practical applications and the NP method is thus useful in diverse application areas. It can be applied to both operational and planning problems and has been demonstrated to effectively solve complex problems in both manufacturing and service industries. To illustrate its broad applicability and effectiveness, in this book we will show how the NP method has been successful in solving complex problems in planning and scheduling, logistics and transportation, supply chain design, data mining, and health care. All of these diverse app- cations have one characteristic in common: they all lead complex large-scale discreteoptimization problems that are intractable using traditionaloptimi- tion methods.